Chapter 15 – Processing Sequences Using RNNs and CNNs
This notebook contains all the sample code and solutions to the exercises in chapter 15.
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Setup¶
This project requires Python 3.7 or above:
In [1]:
import sys
assert sys.version_info >= (3, 7)
And TensorFlow ≥ 2.8:
In [2]:
from packaging import version
import tensorflow as tf
assert version.parse(tf.__version__) >= version.parse("2.8.0")
As we did in earlier chapters, let's define the default font sizes to make the figures prettier:
In [3]:
import matplotlib.pyplot as plt
plt.rc('font', size=14)
plt.rc('axes', labelsize=14, titlesize=14)
plt.rc('legend', fontsize=14)
plt.rc('xtick', labelsize=10)
plt.rc('ytick', labelsize=10)
And let's create the images/rnn folder (if it doesn't already exist), and define the save_fig() function which is used through this notebook to save the figures in high-res for the book:
In [4]:
from pathlib import Path
IMAGES_PATH = Path() / "images" / "rnn"
IMAGES_PATH.mkdir(parents=True, exist_ok=True)
def save_fig(fig_id, tight_layout=True, fig_extension="png", resolution=300):
path = IMAGES_PATH / f"{fig_id}.{fig_extension}"
if tight_layout:
plt.tight_layout()
plt.savefig(path, format=fig_extension, dpi=resolution)
This chapter can be very slow without a GPU, so let's make sure there's one, or else issue a warning:
In [5]:
if not tf.config.list_physical_devices('GPU'):
print("No GPU was detected. Neural nets can be very slow without a GPU.")
if "google.colab" in sys.modules:
print("Go to Runtime > Change runtime and select a GPU hardware "
"accelerator.")
if "kaggle_secrets" in sys.modules:
print("Go to Settings > Accelerator and select GPU.")
Basic RNNs¶
Let's download the ridership data from the ageron/data project. It originally comes from Chicago's Transit Authority, and was downloaded from the Chicago's Data Portal.
In [6]:
tf.keras.utils.get_file(
"ridership.tgz",
"https://github.com/ageron/data/raw/main/ridership.tgz",
cache_dir=".",
extract=True
)
Downloading data from https://github.com/ageron/data/raw/main/ridership.tgz 114688/108512 [===============================] - 0s 0us/step 122880/108512 [=================================] - 0s 0us/step
Out[6]:
'./datasets/ridership.tgz'
In [7]:
import pandas as pd
from pathlib import Path
path = Path("datasets/ridership/CTA_-_Ridership_-_Daily_Boarding_Totals.csv")
df = pd.read_csv(path, parse_dates=["service_date"])
df.columns = ["date", "day_type", "bus", "rail", "total"] # shorter names
df = df.sort_values("date").set_index("date")
df = df.drop("total", axis=1) # no need for total, it's just bus + rail
df = df.drop_duplicates() # remove duplicated months (2011-10 and 2014-07)
In [8]:
df.head()
Out[8]:
| day_type | bus | rail | |
|---|---|---|---|
| date | |||
| 2001-01-01 | U | 297192 | 126455 |
| 2001-01-02 | W | 780827 | 501952 |
| 2001-01-03 | W | 824923 | 536432 |
| 2001-01-04 | W | 870021 | 550011 |
| 2001-01-05 | W | 890426 | 557917 |
Let's look at the first few months of 2019 (note that Pandas treats the range boundaries as inclusive):
In [9]:
import matplotlib.pyplot as plt
df["2019-03":"2019-05"].plot(grid=True, marker=".", figsize=(8, 3.5))
save_fig("daily_ridership_plot") # extra code – saves the figure for the book
plt.show()
In [10]:
diff_7 = df[["bus", "rail"]].diff(7)["2019-03":"2019-05"]
fig, axs = plt.subplots(2, 1, sharex=True, figsize=(8, 5))
df.plot(ax=axs[0], legend=False, marker=".") # original time series
df.shift(7).plot(ax=axs[0], grid=True, legend=False, linestyle=":") # lagged
diff_7.plot(ax=axs[1], grid=True, marker=".") # 7-day difference time series
axs[0].set_ylim([170_000, 900_000]) # extra code – beautifies the plot
save_fig("differencing_plot") # extra code – saves the figure for the book
plt.show()
In [11]:
list(df.loc["2019-05-25":"2019-05-27"]["day_type"])
Out[11]:
['A', 'U', 'U']
Mean absolute error (MAE), also called mean absolute deviation (MAD):
In [12]:
diff_7.abs().mean()
Out[12]:
bus 43915.608696 rail 42143.271739 dtype: float64
Mean absolute percentage error (MAPE):
In [13]:
targets = df[["bus", "rail"]]["2019-03":"2019-05"]
(diff_7 / targets).abs().mean()
Out[13]:
bus 0.082938 rail 0.089948 dtype: float64
Now let's look at the yearly seasonality and the long-term trends:
In [14]:
period = slice("2001", "2019")
df_monthly = df.resample('M').mean() # compute the mean for each month
rolling_average_12_months = df_monthly[period].rolling(window=12).mean()
fig, ax = plt.subplots(figsize=(8, 4))
df_monthly[period].plot(ax=ax, marker=".")
rolling_average_12_months.plot(ax=ax, grid=True, legend=False)
save_fig("long_term_ridership_plot") # extra code – saves the figure for the book
plt.show()
In [15]:
df_monthly.diff(12)[period].plot(grid=True, marker=".", figsize=(8, 3))
save_fig("yearly_diff_plot") # extra code – saves the figure for the book
plt.show()
If running on Colab or Kaggle, install the statsmodels library:
In [16]:
if "google.colab" in sys.modules:
%pip install -q -U statsmodels
In [17]:
from statsmodels.tsa.arima.model import ARIMA
origin, today = "2019-01-01", "2019-05-31"
rail_series = df.loc[origin:today]["rail"].asfreq("D")
model = ARIMA(rail_series,
order=(1, 0, 0),
seasonal_order=(0, 1, 1, 7))
model = model.fit()
y_pred = model.forecast() # returns 427,758.6
In [18]:
y_pred[0] # ARIMA forecast
Out[18]:
427758.62631318445
In [19]:
df["rail"].loc["2019-06-01"] # target value
Out[19]:
379044
In [20]:
df["rail"].loc["2019-05-25"] # naive forecast (value from one week earlier)
Out[20]:
426932
In [21]:
origin, start_date, end_date = "2019-01-01", "2019-03-01", "2019-05-31"
time_period = pd.date_range(start_date, end_date)
rail_series = df.loc[origin:end_date]["rail"].asfreq("D")
y_preds = []
for today in time_period.shift(-1):
model = ARIMA(rail_series[origin:today], # train on data up to "today"
order=(1, 0, 0),
seasonal_order=(0, 1, 1, 7))
model = model.fit() # note that we retrain the model every day!
y_pred = model.forecast()[0]
y_preds.append(y_pred)
y_preds = pd.Series(y_preds, index=time_period)
mae = (y_preds - rail_series[time_period]).abs().mean() # returns 32,040.7
In [22]:
mae
Out[22]:
32040.72008847262
In [23]:
# extra code – displays the SARIMA forecasts
fig, ax = plt.subplots(figsize=(8, 3))
rail_series.loc[time_period].plot(label="True", ax=ax, marker=".", grid=True)
ax.plot(y_preds, color="r", marker=".", label="SARIMA Forecasts")
plt.legend()
plt.show()
In [24]:
# extra code – shows how to plot the Autocorrelation Function (ACF) and the
# Partial Autocorrelation Function (PACF)
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(15, 5))
plot_acf(df[period]["rail"], ax=axs[0], lags=35)
axs[0].grid()
plot_pacf(df[period]["rail"], ax=axs[1], lags=35, method="ywm")
axs[1].grid()
plt.show()
In [25]:
import tensorflow as tf
my_series = [0, 1, 2, 3, 4, 5]
my_dataset = tf.keras.utils.timeseries_dataset_from_array(
my_series,
targets=my_series[3:], # the targets are 3 steps into the future
sequence_length=3,
batch_size=2
)
list(my_dataset)
2022-02-17 19:19:46.679147: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 FMA To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
Out[25]:
[(<tf.Tensor: shape=(2, 3), dtype=int32, numpy=
array([[0, 1, 2],
[1, 2, 3]], dtype=int32)>,
<tf.Tensor: shape=(2,), dtype=int32, numpy=array([3, 4], dtype=int32)>),
(<tf.Tensor: shape=(1, 3), dtype=int32, numpy=array([[2, 3, 4]], dtype=int32)>,
<tf.Tensor: shape=(1,), dtype=int32, numpy=array([5], dtype=int32)>)]
In [26]:
for window_dataset in tf.data.Dataset.range(6).window(4, shift=1):
for element in window_dataset:
print(f"{element}", end=" ")
print()
0 1 2 3 1 2 3 4 2 3 4 5 3 4 5 4 5 5
2022-02-17 19:19:46.784180: W tensorflow/core/framework/dataset.cc:744] Input of Window will not be optimized because the dataset does not implement the AsGraphDefInternal() method needed to apply optimizations.
In [27]:
dataset = tf.data.Dataset.range(6).window(4, shift=1, drop_remainder=True)
dataset = dataset.flat_map(lambda window_dataset: window_dataset.batch(4))
for window_tensor in dataset:
print(f"{window_tensor}")
[0 1 2 3] [1 2 3 4] [2 3 4 5]
In [28]:
def to_windows(dataset, length):
dataset = dataset.window(length, shift=1, drop_remainder=True)
return dataset.flat_map(lambda window_ds: window_ds.batch(length))
In [29]:
dataset = to_windows(tf.data.Dataset.range(6), 4)
dataset = dataset.map(lambda window: (window[:-1], window[-1]))
list(dataset.batch(2))
Out[29]:
[(<tf.Tensor: shape=(2, 3), dtype=int64, numpy=
array([[0, 1, 2],
[1, 2, 3]])>,
<tf.Tensor: shape=(2,), dtype=int64, numpy=array([3, 4])>),
(<tf.Tensor: shape=(1, 3), dtype=int64, numpy=array([[2, 3, 4]])>,
<tf.Tensor: shape=(1,), dtype=int64, numpy=array([5])>)]
Before we continue looking at the data, let's split the time series into three periods, for training, validation and testing. We won't look at the test data for now:
In [30]:
rail_train = df["rail"]["2016-01":"2018-12"] / 1e6
rail_valid = df["rail"]["2019-01":"2019-05"] / 1e6
rail_test = df["rail"]["2019-06":] / 1e6
In [31]:
seq_length = 56
tf.random.set_seed(42) # extra code – ensures reproducibility
train_ds = tf.keras.utils.timeseries_dataset_from_array(
rail_train.to_numpy(),
targets=rail_train[seq_length:],
sequence_length=seq_length,
batch_size=32,
shuffle=True,
seed=42
)
valid_ds = tf.keras.utils.timeseries_dataset_from_array(
rail_valid.to_numpy(),
targets=rail_valid[seq_length:],
sequence_length=seq_length,
batch_size=32
)
In [32]:
tf.random.set_seed(42)
model = tf.keras.Sequential([
tf.keras.layers.Dense(1, input_shape=[seq_length])
])
early_stopping_cb = tf.keras.callbacks.EarlyStopping(
monitor="val_mae", patience=50, restore_best_weights=True)
opt = tf.keras.optimizers.SGD(learning_rate=0.02, momentum=0.9)
model.compile(loss=tf.keras.losses.Huber(), optimizer=opt, metrics=["mae"])
history = model.fit(train_ds, validation_data=valid_ds, epochs=500,
callbacks=[early_stopping_cb])
Epoch 1/500 33/33 [==============================] - 0s 5ms/step - loss: 0.0098 - mae: 0.1118 - val_loss: 0.0071 - val_mae: 0.0966 Epoch 2/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0070 - mae: 0.0883 - val_loss: 0.0052 - val_mae: 0.0768 Epoch 3/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0059 - mae: 0.0796 - val_loss: 0.0050 - val_mae: 0.0741 Epoch 4/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0055 - mae: 0.0761 - val_loss: 0.0049 - val_mae: 0.0732 Epoch 5/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0054 - mae: 0.0749 - val_loss: 0.0043 - val_mae: 0.0666 Epoch 6/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0051 - mae: 0.0724 - val_loss: 0.0041 - val_mae: 0.0638 Epoch 7/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0047 - mae: 0.0696 - val_loss: 0.0040 - val_mae: 0.0615 Epoch 8/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0051 - mae: 0.0735 - val_loss: 0.0038 - val_mae: 0.0599 Epoch 9/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0045 - mae: 0.0670 - val_loss: 0.0037 - val_mae: 0.0599 Epoch 10/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0046 - mae: 0.0677 - val_loss: 0.0041 - val_mae: 0.0658 Epoch 11/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0044 - mae: 0.0664 - val_loss: 0.0038 - val_mae: 0.0611 Epoch 12/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0042 - mae: 0.0634 - val_loss: 0.0034 - val_mae: 0.0551 Epoch 13/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0046 - mae: 0.0680 - val_loss: 0.0056 - val_mae: 0.0829 Epoch 14/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0044 - mae: 0.0671 - val_loss: 0.0039 - val_mae: 0.0637 Epoch 15/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0044 - mae: 0.0673 - val_loss: 0.0037 - val_mae: 0.0610 Epoch 16/500 33/33 [==============================] - 0s 4ms/step - loss: 0.0045 - mae: 0.0676 - val_loss: 0.0035 - val_mae: 0.0584 Epoch 17/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0044 - mae: 0.0662 - val_loss: 0.0033 - val_mae: 0.0544 Epoch 18/500 <<396 more lines>> 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0440 - val_loss: 0.0023 - val_mae: 0.0404 Epoch 217/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0029 - mae: 0.0500 - val_loss: 0.0028 - val_mae: 0.0526 Epoch 218/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0458 - val_loss: 0.0023 - val_mae: 0.0387 Epoch 219/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0027 - mae: 0.0454 - val_loss: 0.0023 - val_mae: 0.0396 Epoch 220/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0444 - val_loss: 0.0026 - val_mae: 0.0425 Epoch 221/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0452 - val_loss: 0.0023 - val_mae: 0.0387 Epoch 222/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0025 - mae: 0.0433 - val_loss: 0.0024 - val_mae: 0.0432 Epoch 223/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0441 - val_loss: 0.0029 - val_mae: 0.0489 Epoch 224/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0031 - mae: 0.0524 - val_loss: 0.0023 - val_mae: 0.0394 Epoch 225/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0025 - mae: 0.0424 - val_loss: 0.0023 - val_mae: 0.0386 Epoch 226/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0438 - val_loss: 0.0023 - val_mae: 0.0383 Epoch 227/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0027 - mae: 0.0463 - val_loss: 0.0023 - val_mae: 0.0405 Epoch 228/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0445 - val_loss: 0.0023 - val_mae: 0.0384 Epoch 229/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0025 - mae: 0.0430 - val_loss: 0.0023 - val_mae: 0.0382 Epoch 230/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0026 - mae: 0.0451 - val_loss: 0.0023 - val_mae: 0.0397 Epoch 231/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0025 - mae: 0.0434 - val_loss: 0.0023 - val_mae: 0.0401 Epoch 232/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0027 - mae: 0.0459 - val_loss: 0.0022 - val_mae: 0.0389 Epoch 233/500 33/33 [==============================] - 0s 3ms/step - loss: 0.0027 - mae: 0.0464 - val_loss: 0.0025 - val_mae: 0.0469
In [33]:
# extra code – evaluates the model
valid_loss, valid_mae = model.evaluate(valid_ds)
valid_mae * 1e6
3/3 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0379
Out[33]:
37866.38006567955
Using a Simple RNN¶
In [34]:
tf.random.set_seed(42) # extra code – ensures reproducibility
model = tf.keras.Sequential([
tf.keras.layers.SimpleRNN(1, input_shape=[None, 1])
])
In [35]:
# extra code – defines a utility function we'll reuse several time
def fit_and_evaluate(model, train_set, valid_set, learning_rate, epochs=500):
early_stopping_cb = tf.keras.callbacks.EarlyStopping(
monitor="val_mae", patience=50, restore_best_weights=True)
opt = tf.keras.optimizers.SGD(learning_rate=learning_rate, momentum=0.9)
model.compile(loss=tf.keras.losses.Huber(), optimizer=opt, metrics=["mae"])
history = model.fit(train_set, validation_data=valid_set, epochs=epochs,
callbacks=[early_stopping_cb])
valid_loss, valid_mae = model.evaluate(valid_set)
return valid_mae * 1e6
In [36]:
fit_and_evaluate(model, train_ds, valid_ds, learning_rate=0.02)
Epoch 1/500 33/33 [==============================] - 1s 11ms/step - loss: 0.0219 - mae: 0.1637 - val_loss: 0.0195 - val_mae: 0.1394 Epoch 2/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0170 - mae: 0.1553 - val_loss: 0.0179 - val_mae: 0.1482 Epoch 3/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0166 - mae: 0.1555 - val_loss: 0.0176 - val_mae: 0.1501 Epoch 4/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0164 - mae: 0.1558 - val_loss: 0.0173 - val_mae: 0.1534 Epoch 5/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0163 - mae: 0.1572 - val_loss: 0.0172 - val_mae: 0.1479 Epoch 6/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0162 - mae: 0.1555 - val_loss: 0.0170 - val_mae: 0.1496 Epoch 7/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0162 - mae: 0.1556 - val_loss: 0.0168 - val_mae: 0.1552 Epoch 8/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0161 - mae: 0.1580 - val_loss: 0.0169 - val_mae: 0.1448 Epoch 9/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0160 - mae: 0.1563 - val_loss: 0.0168 - val_mae: 0.1451 Epoch 10/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0159 - mae: 0.1562 - val_loss: 0.0167 - val_mae: 0.1454 Epoch 11/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0159 - mae: 0.1564 - val_loss: 0.0164 - val_mae: 0.1491 Epoch 12/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0158 - mae: 0.1559 - val_loss: 0.0165 - val_mae: 0.1445 Epoch 13/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0158 - mae: 0.1556 - val_loss: 0.0162 - val_mae: 0.1514 Epoch 14/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0157 - mae: 0.1564 - val_loss: 0.0162 - val_mae: 0.1533 Epoch 15/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0157 - mae: 0.1553 - val_loss: 0.0165 - val_mae: 0.1420 Epoch 16/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0158 - mae: 0.1562 - val_loss: 0.0164 - val_mae: 0.1425 Epoch 17/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0156 - mae: 0.1570 - val_loss: 0.0164 - val_mae: 0.1407 Epoch 18/500 <<687 more lines>> Epoch 362/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0103 - mae: 0.1130 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 363/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0103 - mae: 0.1128 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 364/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0104 - mae: 0.1131 - val_loss: 0.0102 - val_mae: 0.1029 Epoch 365/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1133 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 366/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1128 - val_loss: 0.0103 - val_mae: 0.1028 Epoch 367/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0103 - mae: 0.1129 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 368/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1135 - val_loss: 0.0102 - val_mae: 0.1030 Epoch 369/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0103 - mae: 0.1129 - val_loss: 0.0103 - val_mae: 0.1028 Epoch 370/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1129 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 371/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0103 - mae: 0.1130 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 372/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0103 - mae: 0.1131 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 373/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0104 - mae: 0.1132 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 374/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1130 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 375/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1132 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 376/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1134 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 377/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0104 - mae: 0.1131 - val_loss: 0.0103 - val_mae: 0.1029 Epoch 378/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0103 - mae: 0.1128 - val_loss: 0.0103 - val_mae: 0.1029 3/3 [==============================] - 0s 3ms/step - loss: 0.0103 - mae: 0.1028
Out[36]:
102786.95076704025
In [37]:
tf.random.set_seed(42) # extra code – ensures reproducibility
univar_model = tf.keras.Sequential([
tf.keras.layers.SimpleRNN(32, input_shape=[None, 1]),
tf.keras.layers.Dense(1) # no activation function by default
])
In [38]:
# extra code – compiles, fits, and evaluates the model, like earlier
fit_and_evaluate(univar_model, train_ds, valid_ds, learning_rate=0.05)
Epoch 1/500 33/33 [==============================] - 1s 13ms/step - loss: 0.0489 - mae: 0.2061 - val_loss: 0.0060 - val_mae: 0.0854 Epoch 2/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0060 - mae: 0.0813 - val_loss: 0.0052 - val_mae: 0.0825 Epoch 3/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0042 - mae: 0.0647 - val_loss: 0.0041 - val_mae: 0.0656 Epoch 4/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0041 - mae: 0.0636 - val_loss: 0.0042 - val_mae: 0.0714 Epoch 5/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0039 - mae: 0.0595 - val_loss: 0.0023 - val_mae: 0.0387 Epoch 6/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0033 - mae: 0.0542 - val_loss: 0.0026 - val_mae: 0.0423 Epoch 7/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0502 - val_loss: 0.0021 - val_mae: 0.0354 Epoch 8/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0030 - mae: 0.0500 - val_loss: 0.0020 - val_mae: 0.0345 Epoch 9/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0033 - mae: 0.0539 - val_loss: 0.0050 - val_mae: 0.0825 Epoch 10/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0034 - mae: 0.0573 - val_loss: 0.0023 - val_mae: 0.0399 Epoch 11/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0030 - mae: 0.0493 - val_loss: 0.0022 - val_mae: 0.0377 Epoch 12/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0029 - mae: 0.0478 - val_loss: 0.0019 - val_mae: 0.0328 Epoch 13/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0028 - mae: 0.0460 - val_loss: 0.0024 - val_mae: 0.0404 Epoch 14/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0029 - mae: 0.0487 - val_loss: 0.0022 - val_mae: 0.0371 Epoch 15/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0029 - mae: 0.0469 - val_loss: 0.0019 - val_mae: 0.0306 Epoch 16/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0027 - mae: 0.0465 - val_loss: 0.0019 - val_mae: 0.0348 Epoch 17/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0029 - mae: 0.0485 - val_loss: 0.0024 - val_mae: 0.0426 Epoch 18/500 <<201 more lines>> Epoch 119/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0024 - mae: 0.0428 - val_loss: 0.0020 - val_mae: 0.0334 Epoch 120/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0024 - mae: 0.0423 - val_loss: 0.0019 - val_mae: 0.0362 Epoch 121/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0023 - mae: 0.0408 - val_loss: 0.0019 - val_mae: 0.0356 Epoch 122/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0023 - mae: 0.0397 - val_loss: 0.0020 - val_mae: 0.0395 Epoch 123/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0024 - mae: 0.0429 - val_loss: 0.0017 - val_mae: 0.0297 Epoch 124/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0025 - mae: 0.0437 - val_loss: 0.0019 - val_mae: 0.0359 Epoch 125/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0024 - mae: 0.0430 - val_loss: 0.0017 - val_mae: 0.0305 Epoch 126/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0023 - mae: 0.0399 - val_loss: 0.0021 - val_mae: 0.0409 Epoch 127/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0023 - mae: 0.0411 - val_loss: 0.0018 - val_mae: 0.0314 Epoch 128/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0023 - mae: 0.0394 - val_loss: 0.0021 - val_mae: 0.0392 Epoch 129/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0023 - mae: 0.0416 - val_loss: 0.0017 - val_mae: 0.0329 Epoch 130/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0023 - mae: 0.0418 - val_loss: 0.0020 - val_mae: 0.0389 Epoch 131/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0023 - mae: 0.0398 - val_loss: 0.0017 - val_mae: 0.0297 Epoch 132/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0023 - mae: 0.0415 - val_loss: 0.0018 - val_mae: 0.0333 Epoch 133/500 33/33 [==============================] - 0s 12ms/step - loss: 0.0023 - mae: 0.0398 - val_loss: 0.0019 - val_mae: 0.0319 Epoch 134/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0023 - mae: 0.0401 - val_loss: 0.0019 - val_mae: 0.0333 Epoch 135/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0022 - mae: 0.0384 - val_loss: 0.0020 - val_mae: 0.0398 3/3 [==============================] - 0s 6ms/step - loss: 0.0018 - mae: 0.0290
Out[38]:
29014.97296988964
Deep RNNs¶
In [39]:
tf.random.set_seed(42) # extra code – ensures reproducibility
deep_model = tf.keras.Sequential([
tf.keras.layers.SimpleRNN(32, return_sequences=True, input_shape=[None, 1]),
tf.keras.layers.SimpleRNN(32, return_sequences=True),
tf.keras.layers.SimpleRNN(32),
tf.keras.layers.Dense(1)
])
In [40]:
# extra code – compiles, fits, and evaluates the model, like earlier
fit_and_evaluate(deep_model, train_ds, valid_ds, learning_rate=0.01)
Epoch 1/500 33/33 [==============================] - 2s 32ms/step - loss: 0.0393 - mae: 0.2109 - val_loss: 0.0085 - val_mae: 0.1110 Epoch 2/500 33/33 [==============================] - 1s 25ms/step - loss: 0.0068 - mae: 0.0858 - val_loss: 0.0032 - val_mae: 0.0629 Epoch 3/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0055 - mae: 0.0750 - val_loss: 0.0035 - val_mae: 0.0638 Epoch 4/500 33/33 [==============================] - 1s 27ms/step - loss: 0.0048 - mae: 0.0678 - val_loss: 0.0021 - val_mae: 0.0429 Epoch 5/500 33/33 [==============================] - 1s 27ms/step - loss: 0.0043 - mae: 0.0606 - val_loss: 0.0020 - val_mae: 0.0408 Epoch 6/500 33/33 [==============================] - 1s 27ms/step - loss: 0.0042 - mae: 0.0591 - val_loss: 0.0027 - val_mae: 0.0502 Epoch 7/500 33/33 [==============================] - 1s 25ms/step - loss: 0.0045 - mae: 0.0635 - val_loss: 0.0025 - val_mae: 0.0469 Epoch 8/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0042 - mae: 0.0592 - val_loss: 0.0027 - val_mae: 0.0498 Epoch 9/500 33/33 [==============================] - 1s 26ms/step - loss: 0.0039 - mae: 0.0555 - val_loss: 0.0034 - val_mae: 0.0619 Epoch 10/500 33/33 [==============================] - 1s 25ms/step - loss: 0.0041 - mae: 0.0590 - val_loss: 0.0022 - val_mae: 0.0400 Epoch 11/500 33/33 [==============================] - 1s 25ms/step - loss: 0.0037 - mae: 0.0526 - val_loss: 0.0022 - val_mae: 0.0408 Epoch 12/500 33/33 [==============================] - 1s 26ms/step - loss: 0.0037 - mae: 0.0543 - val_loss: 0.0019 - val_mae: 0.0349 Epoch 13/500 33/33 [==============================] - 1s 23ms/step - loss: 0.0034 - mae: 0.0493 - val_loss: 0.0019 - val_mae: 0.0334 Epoch 14/500 33/33 [==============================] - 1s 23ms/step - loss: 0.0035 - mae: 0.0505 - val_loss: 0.0020 - val_mae: 0.0341 Epoch 15/500 33/33 [==============================] - 1s 23ms/step - loss: 0.0034 - mae: 0.0494 - val_loss: 0.0020 - val_mae: 0.0360 Epoch 16/500 33/33 [==============================] - 1s 23ms/step - loss: 0.0033 - mae: 0.0496 - val_loss: 0.0027 - val_mae: 0.0474 Epoch 17/500 33/33 [==============================] - 1s 23ms/step - loss: 0.0037 - mae: 0.0559 - val_loss: 0.0020 - val_mae: 0.0332 Epoch 18/500 <<103 more lines>> Epoch 70/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0026 - mae: 0.0422 - val_loss: 0.0022 - val_mae: 0.0363 Epoch 71/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0027 - mae: 0.0458 - val_loss: 0.0019 - val_mae: 0.0321 Epoch 72/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0025 - mae: 0.0413 - val_loss: 0.0020 - val_mae: 0.0335 Epoch 73/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0026 - mae: 0.0435 - val_loss: 0.0021 - val_mae: 0.0354 Epoch 74/500 33/33 [==============================] - 1s 25ms/step - loss: 0.0026 - mae: 0.0436 - val_loss: 0.0021 - val_mae: 0.0357 Epoch 75/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0026 - mae: 0.0432 - val_loss: 0.0021 - val_mae: 0.0347 Epoch 76/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0025 - mae: 0.0421 - val_loss: 0.0027 - val_mae: 0.0477 Epoch 77/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0027 - mae: 0.0444 - val_loss: 0.0019 - val_mae: 0.0320 Epoch 78/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0028 - mae: 0.0468 - val_loss: 0.0019 - val_mae: 0.0318 Epoch 79/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0027 - mae: 0.0466 - val_loss: 0.0021 - val_mae: 0.0366 Epoch 80/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0026 - mae: 0.0442 - val_loss: 0.0025 - val_mae: 0.0454 Epoch 81/500 33/33 [==============================] - 1s 25ms/step - loss: 0.0026 - mae: 0.0438 - val_loss: 0.0019 - val_mae: 0.0313 Epoch 82/500 33/33 [==============================] - 1s 26ms/step - loss: 0.0025 - mae: 0.0419 - val_loss: 0.0020 - val_mae: 0.0350 Epoch 83/500 33/33 [==============================] - 1s 27ms/step - loss: 0.0026 - mae: 0.0438 - val_loss: 0.0021 - val_mae: 0.0391 Epoch 84/500 33/33 [==============================] - 1s 27ms/step - loss: 0.0027 - mae: 0.0446 - val_loss: 0.0019 - val_mae: 0.0325 Epoch 85/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0027 - mae: 0.0456 - val_loss: 0.0019 - val_mae: 0.0318 Epoch 86/500 33/33 [==============================] - 1s 24ms/step - loss: 0.0025 - mae: 0.0419 - val_loss: 0.0021 - val_mae: 0.0372 3/3 [==============================] - 0s 9ms/step - loss: 0.0019 - mae: 0.0312
Out[40]:
31211.024150252342
Multivariate time series¶
In [41]:
df_mulvar = df[["bus", "rail"]] / 1e6 # use both bus & rail series as input
df_mulvar["next_day_type"] = df["day_type"].shift(-1) # we know tomorrow's type
df_mulvar = pd.get_dummies(df_mulvar) # one-hot encode the day type
In [42]:
mulvar_train = df_mulvar["2016-01":"2018-12"]
mulvar_valid = df_mulvar["2019-01":"2019-05"]
mulvar_test = df_mulvar["2019-06":]
In [43]:
tf.random.set_seed(42) # extra code – ensures reproducibility
train_mulvar_ds = tf.keras.utils.timeseries_dataset_from_array(
mulvar_train.to_numpy(), # use all 5 columns as input
targets=mulvar_train["rail"][seq_length:], # forecast only the rail series
sequence_length=seq_length,
batch_size=32,
shuffle=True,
seed=42
)
valid_mulvar_ds = tf.keras.utils.timeseries_dataset_from_array(
mulvar_valid.to_numpy(),
targets=mulvar_valid["rail"][seq_length:],
sequence_length=seq_length,
batch_size=32
)
In [44]:
tf.random.set_seed(42) # extra code – ensures reproducibility
mulvar_model = tf.keras.Sequential([
tf.keras.layers.SimpleRNN(32, input_shape=[None, 5]),
tf.keras.layers.Dense(1)
])
In [45]:
# extra code – compiles, fits, and evaluates the model, like earlier
fit_and_evaluate(mulvar_model, train_mulvar_ds, valid_mulvar_ds,
learning_rate=0.05)
Epoch 1/500 33/33 [==============================] - 1s 17ms/step - loss: 0.0386 - mae: 0.1872 - val_loss: 0.0011 - val_mae: 0.0346 Epoch 2/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0029 - mae: 0.0585 - val_loss: 0.0040 - val_mae: 0.0790 Epoch 3/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0018 - mae: 0.0435 - val_loss: 7.7056e-04 - val_mae: 0.0273 Epoch 4/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0017 - mae: 0.0407 - val_loss: 0.0010 - val_mae: 0.0362 Epoch 5/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0015 - mae: 0.0386 - val_loss: 8.1681e-04 - val_mae: 0.0306 Epoch 6/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0014 - mae: 0.0372 - val_loss: 0.0011 - val_mae: 0.0380 Epoch 7/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0014 - mae: 0.0366 - val_loss: 7.9942e-04 - val_mae: 0.0289 Epoch 8/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0013 - mae: 0.0344 - val_loss: 6.9211e-04 - val_mae: 0.0271 Epoch 9/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0015 - mae: 0.0374 - val_loss: 8.2185e-04 - val_mae: 0.0299 Epoch 10/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0014 - mae: 0.0363 - val_loss: 0.0017 - val_mae: 0.0494 Epoch 11/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0013 - mae: 0.0357 - val_loss: 0.0016 - val_mae: 0.0473 Epoch 12/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0013 - mae: 0.0337 - val_loss: 8.0260e-04 - val_mae: 0.0287 Epoch 13/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0013 - mae: 0.0349 - val_loss: 0.0011 - val_mae: 0.0389 Epoch 14/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0014 - mae: 0.0363 - val_loss: 6.3723e-04 - val_mae: 0.0245 Epoch 15/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0012 - mae: 0.0340 - val_loss: 6.2749e-04 - val_mae: 0.0255 Epoch 16/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0013 - mae: 0.0342 - val_loss: 0.0020 - val_mae: 0.0549 Epoch 17/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0012 - mae: 0.0332 - val_loss: 7.3463e-04 - val_mae: 0.0275 Epoch 18/500 <<181 more lines>> Epoch 109/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0319 - val_loss: 6.3961e-04 - val_mae: 0.0244 Epoch 110/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0012 - mae: 0.0354 - val_loss: 0.0013 - val_mae: 0.0433 Epoch 111/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0010 - mae: 0.0307 - val_loss: 7.3263e-04 - val_mae: 0.0281 Epoch 112/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0014 - mae: 0.0377 - val_loss: 7.8642e-04 - val_mae: 0.0293 Epoch 113/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0012 - mae: 0.0340 - val_loss: 0.0013 - val_mae: 0.0415 Epoch 114/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0012 - mae: 0.0344 - val_loss: 0.0011 - val_mae: 0.0376 Epoch 115/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0314 - val_loss: 0.0010 - val_mae: 0.0344 Epoch 116/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0013 - mae: 0.0374 - val_loss: 7.2942e-04 - val_mae: 0.0264 Epoch 117/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0336 - val_loss: 0.0011 - val_mae: 0.0393 Epoch 118/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0014 - mae: 0.0392 - val_loss: 0.0015 - val_mae: 0.0455 Epoch 119/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0012 - mae: 0.0369 - val_loss: 0.0011 - val_mae: 0.0363 Epoch 120/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0012 - mae: 0.0348 - val_loss: 0.0011 - val_mae: 0.0372 Epoch 121/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0316 - val_loss: 0.0012 - val_mae: 0.0408 Epoch 122/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0330 - val_loss: 0.0022 - val_mae: 0.0583 Epoch 123/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0014 - mae: 0.0402 - val_loss: 0.0014 - val_mae: 0.0438 Epoch 124/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0014 - mae: 0.0392 - val_loss: 8.6813e-04 - val_mae: 0.0323 Epoch 125/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0319 - val_loss: 6.3585e-04 - val_mae: 0.0243 3/3 [==============================] - 0s 4ms/step - loss: 5.6491e-04 - mae: 0.0221
Out[45]:
22062.301635742188
In [46]:
# extra code – build and train a multitask RNN that forecasts both bus and rail
tf.random.set_seed(42)
seq_length = 56
train_multask_ds = tf.keras.utils.timeseries_dataset_from_array(
mulvar_train.to_numpy(),
targets=mulvar_train[["bus", "rail"]][seq_length:], # 2 targets per day
sequence_length=seq_length,
batch_size=32,
shuffle=True,
seed=42
)
valid_multask_ds = tf.keras.utils.timeseries_dataset_from_array(
mulvar_valid.to_numpy(),
targets=mulvar_valid[["bus", "rail"]][seq_length:],
sequence_length=seq_length,
batch_size=32
)
tf.random.set_seed(42)
multask_model = tf.keras.Sequential([
tf.keras.layers.SimpleRNN(32, input_shape=[None, 5]),
tf.keras.layers.Dense(2)
])
fit_and_evaluate(multask_model, train_multask_ds, valid_multask_ds,
learning_rate=0.02)
Epoch 1/500 33/33 [==============================] - 1s 13ms/step - loss: 0.0398 - mae: 0.1953 - val_loss: 0.0073 - val_mae: 0.0998 Epoch 2/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0039 - mae: 0.0632 - val_loss: 0.0012 - val_mae: 0.0384 Epoch 3/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0027 - mae: 0.0509 - val_loss: 0.0010 - val_mae: 0.0362 Epoch 4/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0024 - mae: 0.0488 - val_loss: 0.0018 - val_mae: 0.0491 Epoch 5/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0023 - mae: 0.0473 - val_loss: 0.0012 - val_mae: 0.0372 Epoch 6/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0022 - mae: 0.0463 - val_loss: 0.0011 - val_mae: 0.0361 Epoch 7/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0019 - mae: 0.0442 - val_loss: 8.8553e-04 - val_mae: 0.0322 Epoch 8/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0018 - mae: 0.0427 - val_loss: 9.3772e-04 - val_mae: 0.0339 Epoch 9/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0017 - mae: 0.0411 - val_loss: 9.0027e-04 - val_mae: 0.0324 Epoch 10/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0019 - mae: 0.0440 - val_loss: 0.0014 - val_mae: 0.0427 Epoch 11/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0017 - mae: 0.0415 - val_loss: 0.0021 - val_mae: 0.0546 Epoch 12/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0017 - mae: 0.0412 - val_loss: 8.3458e-04 - val_mae: 0.0311 Epoch 13/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0016 - mae: 0.0399 - val_loss: 8.2083e-04 - val_mae: 0.0311 Epoch 14/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0015 - mae: 0.0391 - val_loss: 0.0010 - val_mae: 0.0358 Epoch 15/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0016 - mae: 0.0407 - val_loss: 0.0011 - val_mae: 0.0361 Epoch 16/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0014 - mae: 0.0378 - val_loss: 0.0012 - val_mae: 0.0380 Epoch 17/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0015 - mae: 0.0394 - val_loss: 9.6802e-04 - val_mae: 0.0346 Epoch 18/500 <<215 more lines>> Epoch 126/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0317 - val_loss: 6.8940e-04 - val_mae: 0.0271 Epoch 127/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0328 - val_loss: 0.0013 - val_mae: 0.0412 Epoch 128/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0012 - mae: 0.0344 - val_loss: 7.6342e-04 - val_mae: 0.0292 Epoch 129/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0328 - val_loss: 8.3261e-04 - val_mae: 0.0311 Epoch 130/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0011 - mae: 0.0316 - val_loss: 6.7921e-04 - val_mae: 0.0263 Epoch 131/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0320 - val_loss: 7.7970e-04 - val_mae: 0.0297 Epoch 132/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0334 - val_loss: 7.4201e-04 - val_mae: 0.0286 Epoch 133/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0330 - val_loss: 9.3328e-04 - val_mae: 0.0339 Epoch 134/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0011 - mae: 0.0322 - val_loss: 6.9349e-04 - val_mae: 0.0267 Epoch 135/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0011 - mae: 0.0317 - val_loss: 6.6078e-04 - val_mae: 0.0261 Epoch 136/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0011 - mae: 0.0322 - val_loss: 9.1503e-04 - val_mae: 0.0322 Epoch 137/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0011 - mae: 0.0327 - val_loss: 6.7553e-04 - val_mae: 0.0261 Epoch 138/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0010 - mae: 0.0311 - val_loss: 7.1123e-04 - val_mae: 0.0276 Epoch 139/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0011 - mae: 0.0317 - val_loss: 6.7194e-04 - val_mae: 0.0260 Epoch 140/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0012 - mae: 0.0342 - val_loss: 0.0010 - val_mae: 0.0361 Epoch 141/500 33/33 [==============================] - 0s 13ms/step - loss: 0.0011 - mae: 0.0325 - val_loss: 7.6832e-04 - val_mae: 0.0293 Epoch 142/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0011 - mae: 0.0324 - val_loss: 6.7870e-04 - val_mae: 0.0264 3/3 [==============================] - 0s 5ms/step - loss: 6.5248e-04 - mae: 0.0259
Out[46]:
25850.363075733185
In [47]:
# extra code – evaluates the naive forecasts for bus
bus_naive = mulvar_valid["bus"].shift(7)[seq_length:]
bus_target = mulvar_valid["bus"][seq_length:]
(bus_target - bus_naive).abs().mean() * 1e6
Out[47]:
43441.63157894738
In [48]:
# extra code – evaluates the multitask RNN's forecasts both bus and rail
Y_preds_valid = multask_model.predict(valid_multask_ds)
for idx, name in enumerate(["bus", "rail"]):
mae = 1e6 * tf.keras.metrics.mean_absolute_error(
mulvar_valid[name][seq_length:], Y_preds_valid[:, idx])
print(name, int(mae))
bus 26369 rail 25330
Forecasting Several Steps Ahead¶
In [49]:
import numpy as np
X = rail_valid.to_numpy()[np.newaxis, :seq_length, np.newaxis]
for step_ahead in range(14):
y_pred_one = univar_model.predict(X)
X = np.concatenate([X, y_pred_one.reshape(1, 1, 1)], axis=1)
In [50]:
# extra code – generates and saves Figure 15–11
# The forecasts start on 2019-02-26, as it is the 57th day of 2019, and they end
# on 2019-03-11. That's 14 days in total.
Y_pred = pd.Series(X[0, -14:, 0],
index=pd.date_range("2019-02-26", "2019-03-11"))
fig, ax = plt.subplots(figsize=(8, 3.5))
(rail_valid * 1e6)["2019-02-01":"2019-03-11"].plot(
label="True", marker=".", ax=ax)
(Y_pred * 1e6).plot(
label="Predictions", grid=True, marker="x", color="r", ax=ax)
ax.vlines("2019-02-25", 0, 1e6, color="k", linestyle="--", label="Today")
ax.set_ylim([200_000, 800_000])
plt.legend(loc="center left")
save_fig("forecast_ahead_plot")
plt.show()
Now let's create an RNN that predicts all 14 next values at once:
In [51]:
tf.random.set_seed(42) # extra code – ensures reproducibility
def split_inputs_and_targets(mulvar_series, ahead=14, target_col=1):
return mulvar_series[:, :-ahead], mulvar_series[:, -ahead:, target_col]
ahead_train_ds = tf.keras.utils.timeseries_dataset_from_array(
mulvar_train.to_numpy(),
targets=None,
sequence_length=seq_length + 14,
batch_size=32,
shuffle=True,
seed=42
).map(split_inputs_and_targets)
ahead_valid_ds = tf.keras.utils.timeseries_dataset_from_array(
mulvar_valid.to_numpy(),
targets=None,
sequence_length=seq_length + 14,
batch_size=32
).map(split_inputs_and_targets)
In [52]:
tf.random.set_seed(42)
ahead_model = tf.keras.Sequential([
tf.keras.layers.SimpleRNN(32, input_shape=[None, 5]),
tf.keras.layers.Dense(14)
])
In [53]:
# extra code – compiles, fits, and evaluates the model, like earlier
fit_and_evaluate(ahead_model, ahead_train_ds, ahead_valid_ds,
learning_rate=0.02)
Epoch 1/500 33/33 [==============================] - 1s 12ms/step - loss: 0.1250 - mae: 0.3791 - val_loss: 0.0287 - val_mae: 0.1935 Epoch 2/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0191 - mae: 0.1613 - val_loss: 0.0136 - val_mae: 0.1289 Epoch 3/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0131 - mae: 0.1303 - val_loss: 0.0102 - val_mae: 0.1113 Epoch 4/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0108 - mae: 0.1164 - val_loss: 0.0083 - val_mae: 0.1009 Epoch 5/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0093 - mae: 0.1068 - val_loss: 0.0071 - val_mae: 0.0931 Epoch 6/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0083 - mae: 0.0996 - val_loss: 0.0061 - val_mae: 0.0862 Epoch 7/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0076 - mae: 0.0941 - val_loss: 0.0055 - val_mae: 0.0811 Epoch 8/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0072 - mae: 0.0900 - val_loss: 0.0050 - val_mae: 0.0779 Epoch 9/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0068 - mae: 0.0869 - val_loss: 0.0046 - val_mae: 0.0751 Epoch 10/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0066 - mae: 0.0844 - val_loss: 0.0045 - val_mae: 0.0737 Epoch 11/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0063 - mae: 0.0822 - val_loss: 0.0041 - val_mae: 0.0709 Epoch 12/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0061 - mae: 0.0804 - val_loss: 0.0039 - val_mae: 0.0688 Epoch 13/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0060 - mae: 0.0796 - val_loss: 0.0039 - val_mae: 0.0690 Epoch 14/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0059 - mae: 0.0777 - val_loss: 0.0036 - val_mae: 0.0656 Epoch 15/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0058 - mae: 0.0766 - val_loss: 0.0035 - val_mae: 0.0649 Epoch 16/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0056 - mae: 0.0755 - val_loss: 0.0034 - val_mae: 0.0638 Epoch 17/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0055 - mae: 0.0744 - val_loss: 0.0033 - val_mae: 0.0633 Epoch 18/500 <<303 more lines>> Epoch 170/500 33/33 [==============================] - 0s 7ms/step - loss: 0.0032 - mae: 0.0474 - val_loss: 0.0014 - val_mae: 0.0359 Epoch 171/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0477 - val_loss: 0.0014 - val_mae: 0.0359 Epoch 172/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0479 - val_loss: 0.0014 - val_mae: 0.0353 Epoch 173/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0480 - val_loss: 0.0014 - val_mae: 0.0359 Epoch 174/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0481 - val_loss: 0.0015 - val_mae: 0.0365 Epoch 175/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0476 - val_loss: 0.0014 - val_mae: 0.0358 Epoch 176/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0474 - val_loss: 0.0014 - val_mae: 0.0355 Epoch 177/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0480 - val_loss: 0.0014 - val_mae: 0.0362 Epoch 178/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0476 - val_loss: 0.0014 - val_mae: 0.0353 Epoch 179/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0481 - val_loss: 0.0014 - val_mae: 0.0357 Epoch 180/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0476 - val_loss: 0.0014 - val_mae: 0.0352 Epoch 181/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0475 - val_loss: 0.0014 - val_mae: 0.0358 Epoch 182/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0474 - val_loss: 0.0014 - val_mae: 0.0357 Epoch 183/500 33/33 [==============================] - 0s 8ms/step - loss: 0.0032 - mae: 0.0477 - val_loss: 0.0014 - val_mae: 0.0358 Epoch 184/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0479 - val_loss: 0.0014 - val_mae: 0.0353 Epoch 185/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0473 - val_loss: 0.0015 - val_mae: 0.0368 Epoch 186/500 33/33 [==============================] - 0s 9ms/step - loss: 0.0032 - mae: 0.0475 - val_loss: 0.0014 - val_mae: 0.0356 3/3 [==============================] - 0s 3ms/step - loss: 0.0014 - mae: 0.0350
Out[53]:
35017.29667186737
In [54]:
X = mulvar_valid.to_numpy()[np.newaxis, :seq_length] # shape [1, 56, 5]
Y_pred = ahead_model.predict(X) # shape [1, 14]
Now let's create an RNN that predicts the next 14 steps at each time step. That is, instead of just forecasting time steps 56 to 69 based on time steps 0 to 55, it will forecast time steps 1 to 14 at time step 0, then time steps 2 to 15 at time step 1, and so on, and finally it will forecast time steps 56 to 69 at the last time step. Notice that the model is causal: when it makes predictions at any time step, it can only see past time steps.
To prepare the datasets, we can use to_windows() twice, to get sequences of consecutive windows, like this:
In [55]:
my_series = tf.data.Dataset.range(7)
dataset = to_windows(to_windows(my_series, 3), 4)
list(dataset)
Out[55]:
[<tf.Tensor: shape=(4, 3), dtype=int64, numpy=
array([[0, 1, 2],
[1, 2, 3],
[2, 3, 4],
[3, 4, 5]])>,
<tf.Tensor: shape=(4, 3), dtype=int64, numpy=
array([[1, 2, 3],
[2, 3, 4],
[3, 4, 5],
[4, 5, 6]])>]
Then we can split these elements into the desired inputs and targets:
In [56]:
dataset = dataset.map(lambda S: (S[:, 0], S[:, 1:]))
list(dataset)
Out[56]:
[(<tf.Tensor: shape=(4,), dtype=int64, numpy=array([0, 1, 2, 3])>,
<tf.Tensor: shape=(4, 2), dtype=int64, numpy=
array([[1, 2],
[2, 3],
[3, 4],
[4, 5]])>),
(<tf.Tensor: shape=(4,), dtype=int64, numpy=array([1, 2, 3, 4])>,
<tf.Tensor: shape=(4, 2), dtype=int64, numpy=
array([[2, 3],
[3, 4],
[4, 5],
[5, 6]])>)]
Let's wrap this idea into a utility function. It will also take care of shuffling (optional) and batching:
In [57]:
def to_seq2seq_dataset(series, seq_length=56, ahead=14, target_col=1,
batch_size=32, shuffle=False, seed=None):
ds = to_windows(tf.data.Dataset.from_tensor_slices(series), ahead + 1)
ds = to_windows(ds, seq_length).map(lambda S: (S[:, 0], S[:, 1:, 1]))
if shuffle:
ds = ds.shuffle(8 * batch_size, seed=seed)
return ds.batch(batch_size)
In [58]:
seq2seq_train = to_seq2seq_dataset(mulvar_train, shuffle=True, seed=42)
seq2seq_valid = to_seq2seq_dataset(mulvar_valid)
In [59]:
tf.random.set_seed(42) # extra code – ensures reproducibility
seq2seq_model = tf.keras.Sequential([
tf.keras.layers.SimpleRNN(32, return_sequences=True, input_shape=[None, 5]),
tf.keras.layers.Dense(14)
# equivalent: tf.keras.layers.TimeDistributed(tf.keras.layers.Dense(14))
# also equivalent: tf.keras.layers.Conv1D(14, kernel_size=1)
])
In [60]:
fit_and_evaluate(seq2seq_model, seq2seq_train, seq2seq_valid,
learning_rate=0.1)
Epoch 1/500 33/33 [==============================] - 1s 17ms/step - loss: 0.0754 - mae: 0.2785 - val_loss: 0.0163 - val_mae: 0.1379 Epoch 2/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0097 - mae: 0.1050 - val_loss: 0.0071 - val_mae: 0.0853 Epoch 3/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0069 - mae: 0.0846 - val_loss: 0.0063 - val_mae: 0.0790 Epoch 4/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0060 - mae: 0.0773 - val_loss: 0.0056 - val_mae: 0.0729 Epoch 5/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0055 - mae: 0.0722 - val_loss: 0.0049 - val_mae: 0.0662 Epoch 6/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0052 - mae: 0.0690 - val_loss: 0.0051 - val_mae: 0.0683 Epoch 7/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0049 - mae: 0.0663 - val_loss: 0.0046 - val_mae: 0.0626 Epoch 8/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0047 - mae: 0.0640 - val_loss: 0.0043 - val_mae: 0.0589 Epoch 9/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0046 - mae: 0.0627 - val_loss: 0.0041 - val_mae: 0.0560 Epoch 10/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0045 - mae: 0.0616 - val_loss: 0.0043 - val_mae: 0.0589 Epoch 11/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0044 - mae: 0.0608 - val_loss: 0.0042 - val_mae: 0.0580 Epoch 12/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0043 - mae: 0.0594 - val_loss: 0.0040 - val_mae: 0.0554 Epoch 13/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0042 - mae: 0.0584 - val_loss: 0.0041 - val_mae: 0.0572 Epoch 14/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0042 - mae: 0.0577 - val_loss: 0.0042 - val_mae: 0.0580 Epoch 15/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0042 - mae: 0.0579 - val_loss: 0.0038 - val_mae: 0.0530 Epoch 16/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0041 - mae: 0.0573 - val_loss: 0.0039 - val_mae: 0.0534 Epoch 17/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0041 - mae: 0.0566 - val_loss: 0.0038 - val_mae: 0.0530 Epoch 18/500 <<219 more lines>> Epoch 128/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0484 - val_loss: 0.0036 - val_mae: 0.0470 Epoch 129/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0489 - val_loss: 0.0036 - val_mae: 0.0472 Epoch 130/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0032 - mae: 0.0476 - val_loss: 0.0036 - val_mae: 0.0473 Epoch 131/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0032 - mae: 0.0483 - val_loss: 0.0036 - val_mae: 0.0479 Epoch 132/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0492 - val_loss: 0.0037 - val_mae: 0.0489 Epoch 133/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0499 - val_loss: 0.0036 - val_mae: 0.0480 Epoch 134/500 33/33 [==============================] - 0s 11ms/step - loss: 0.0033 - mae: 0.0486 - val_loss: 0.0035 - val_mae: 0.0469 Epoch 135/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0486 - val_loss: 0.0035 - val_mae: 0.0468 Epoch 136/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0491 - val_loss: 0.0035 - val_mae: 0.0467 Epoch 137/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0493 - val_loss: 0.0035 - val_mae: 0.0471 Epoch 138/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0486 - val_loss: 0.0036 - val_mae: 0.0476 Epoch 139/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0487 - val_loss: 0.0035 - val_mae: 0.0470 Epoch 140/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0492 - val_loss: 0.0035 - val_mae: 0.0467 Epoch 141/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0488 - val_loss: 0.0035 - val_mae: 0.0471 Epoch 142/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0493 - val_loss: 0.0035 - val_mae: 0.0468 Epoch 143/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0494 - val_loss: 0.0035 - val_mae: 0.0473 Epoch 144/500 33/33 [==============================] - 0s 10ms/step - loss: 0.0033 - mae: 0.0486 - val_loss: 0.0035 - val_mae: 0.0469 3/3 [==============================] - 0s 13ms/step - loss: 0.0034 - mae: 0.0459
Out[60]:
45928.88057231903
In [61]:
X = mulvar_valid.to_numpy()[np.newaxis, :seq_length]
y_pred_14 = seq2seq_model.predict(X)[0, -1] # only the last time step's output
In [62]:
Y_pred_valid = seq2seq_model.predict(seq2seq_valid)
for ahead in range(14):
preds = pd.Series(Y_pred_valid[:-1, -1, ahead],
index=mulvar_valid.index[56 + ahead : -14 + ahead])
mae = (preds - mulvar_valid["rail"]).abs().mean() * 1e6
print(f"MAE for +{ahead + 1}: {mae:,.0f}")
MAE for +1: 25,519 MAE for +2: 26,274 MAE for +3: 27,054 MAE for +4: 29,324 MAE for +5: 28,992 MAE for +6: 31,739 MAE for +7: 32,847 MAE for +8: 33,282 MAE for +9: 33,072 MAE for +10: 29,752 MAE for +11: 37,468 MAE for +12: 35,125 MAE for +13: 34,614 MAE for +14: 34,322
Deep RNNs with Layer Norm¶
In [63]:
class LNSimpleRNNCell(tf.keras.layers.Layer):
def __init__(self, units, activation="tanh", **kwargs):
super().__init__(**kwargs)
self.state_size = units
self.output_size = units
self.simple_rnn_cell = tf.keras.layers.SimpleRNNCell(units,
activation=None)
self.layer_norm = tf.keras.layers.LayerNormalization()
self.activation = tf.keras.activations.get(activation)
def call(self, inputs, states):
outputs, new_states = self.simple_rnn_cell(inputs, states)
norm_outputs = self.activation(self.layer_norm(outputs))
return norm_outputs, [norm_outputs]
In [64]:
tf.random.set_seed(42) # extra code – ensures reproducibility
custom_ln_model = tf.keras.Sequential([
tf.keras.layers.RNN(LNSimpleRNNCell(32), return_sequences=True,
input_shape=[None, 5]),
tf.keras.layers.Dense(14)
])
Just training for 5 epochs to show that it works (you can increase this if you want):
In [65]:
fit_and_evaluate(custom_ln_model, seq2seq_train, seq2seq_valid,
learning_rate=0.1, epochs=5)
Epoch 1/5 33/33 [==============================] - 2s 25ms/step - loss: 0.0809 - mae: 0.2898 - val_loss: 0.0178 - val_mae: 0.1511 Epoch 2/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0149 - mae: 0.1438 - val_loss: 0.0156 - val_mae: 0.1245 Epoch 3/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0120 - mae: 0.1281 - val_loss: 0.0131 - val_mae: 0.1160 Epoch 4/5 33/33 [==============================] - 1s 17ms/step - loss: 0.0105 - mae: 0.1167 - val_loss: 0.0118 - val_mae: 0.1095 Epoch 5/5 33/33 [==============================] - 1s 17ms/step - loss: 0.0093 - mae: 0.1067 - val_loss: 0.0105 - val_mae: 0.1038 3/3 [==============================] - 0s 14ms/step - loss: 0.0105 - mae: 0.1038
Out[65]:
103751.08569860458
Extra Material – Creating a Custom RNN Class¶
The RNN class is not magical. In fact, it's not too hard to implement your own RNN class:
In [66]:
class MyRNN(tf.keras.layers.Layer):
def __init__(self, cell, return_sequences=False, **kwargs):
super().__init__(**kwargs)
self.cell = cell
self.return_sequences = return_sequences
def get_initial_state(self, inputs):
try:
return self.cell.get_initial_state(inputs)
except AttributeError:
# fallback to zeros if self.cell has no get_initial_state() method
batch_size = tf.shape(inputs)[0]
return [tf.zeros([batch_size, self.cell.state_size],
dtype=inputs.dtype)]
@tf.function
def call(self, inputs):
states = self.get_initial_state(inputs)
shape = tf.shape(inputs)
batch_size = shape[0]
n_steps = shape[1]
sequences = tf.TensorArray(
inputs.dtype, size=(n_steps if self.return_sequences else 0))
outputs = tf.zeros(shape=[batch_size, self.cell.output_size],
dtype=inputs.dtype)
for step in tf.range(n_steps):
outputs, states = self.cell(inputs[:, step], states)
if self.return_sequences:
sequences = sequences.write(step, outputs)
if self.return_sequences:
# stack the outputs into an array of shape
# [time steps, batch size, dims], then transpose it to shape
# [batch size, time steps, dims]
return tf.transpose(sequences.stack(), [1, 0, 2])
else:
return outputs
Note that @tf.function requires the outputs variable to be created before the for loop, which is why we initialize its value to a zero tensor, even though we don't use that value at all. Once the function is converted to a graph, this unused value will be pruned from the graph, so it doesn't impact performance. Similarly, @tf.function requires the sequences variable to be created before the if statement where it is used, even if self.return_sequences is False, so we create a TensorArray of size 0 in this case.
In [67]:
tf.random.set_seed(42)
custom_model = tf.keras.Sequential([
MyRNN(LNSimpleRNNCell(32), return_sequences=True, input_shape=[None, 5]),
tf.keras.layers.Dense(14)
])
Just training for 5 epochs to show that it works (you can increase this if you want):
In [68]:
fit_and_evaluate(custom_model, seq2seq_train, seq2seq_valid,
learning_rate=0.1, epochs=5)
Epoch 1/5 33/33 [==============================] - 2s 26ms/step - loss: 0.0814 - mae: 0.2916 - val_loss: 0.0176 - val_mae: 0.1544 Epoch 2/5 33/33 [==============================] - 1s 20ms/step - loss: 0.0151 - mae: 0.1440 - val_loss: 0.0157 - val_mae: 0.1247 Epoch 3/5 33/33 [==============================] - 1s 19ms/step - loss: 0.0119 - mae: 0.1281 - val_loss: 0.0134 - val_mae: 0.1160 Epoch 4/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0105 - mae: 0.1162 - val_loss: 0.0111 - val_mae: 0.1084 Epoch 5/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0093 - mae: 0.1068 - val_loss: 0.0103 - val_mae: 0.1029 3/3 [==============================] - 0s 14ms/step - loss: 0.0103 - mae: 0.1029
Out[68]:
102874.92722272873
LSTMs¶
In [69]:
tf.random.set_seed(42) # extra code – ensures reproducibility
lstm_model = tf.keras.models.Sequential([
tf.keras.layers.LSTM(32, return_sequences=True, input_shape=[None, 5]),
tf.keras.layers.Dense(14)
])
Just training for 5 epochs to show that it works (you can increase this if you want):
In [70]:
fit_and_evaluate(lstm_model, seq2seq_train, seq2seq_valid,
learning_rate=0.1, epochs=5)
Epoch 1/5 33/33 [==============================] - 2s 29ms/step - loss: 0.0535 - mae: 0.2517 - val_loss: 0.0187 - val_mae: 0.1716 Epoch 2/5 33/33 [==============================] - 1s 16ms/step - loss: 0.0176 - mae: 0.1598 - val_loss: 0.0176 - val_mae: 0.1473 Epoch 3/5 33/33 [==============================] - 1s 16ms/step - loss: 0.0160 - mae: 0.1528 - val_loss: 0.0168 - val_mae: 0.1433 Epoch 4/5 33/33 [==============================] - 1s 16ms/step - loss: 0.0152 - mae: 0.1485 - val_loss: 0.0161 - val_mae: 0.1388 Epoch 5/5 33/33 [==============================] - 1s 16ms/step - loss: 0.0145 - mae: 0.1443 - val_loss: 0.0154 - val_mae: 0.1352 3/3 [==============================] - 0s 14ms/step - loss: 0.0154 - mae: 0.1352
Out[70]:
135186.25497817993
GRUs¶
In [71]:
tf.random.set_seed(42) # extra code – ensures reproducibility
gru_model = tf.keras.Sequential([
tf.keras.layers.GRU(32, return_sequences=True, input_shape=[None, 5]),
tf.keras.layers.Dense(14)
])
Just training for 5 epochs to show that it works (you can increase this if you want):
In [72]:
fit_and_evaluate(gru_model, seq2seq_train, seq2seq_valid,
learning_rate=0.1, epochs=5)
Epoch 1/5 33/33 [==============================] - 2s 29ms/step - loss: 0.0516 - mae: 0.2489 - val_loss: 0.0165 - val_mae: 0.1529 Epoch 2/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0145 - mae: 0.1386 - val_loss: 0.0139 - val_mae: 0.1260 Epoch 3/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0118 - mae: 0.1249 - val_loss: 0.0121 - val_mae: 0.1170 Epoch 4/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0106 - mae: 0.1166 - val_loss: 0.0111 - val_mae: 0.1109 Epoch 5/5 33/33 [==============================] - 1s 18ms/step - loss: 0.0098 - mae: 0.1107 - val_loss: 0.0104 - val_mae: 0.1071 3/3 [==============================] - 0s 14ms/step - loss: 0.0104 - mae: 0.1071
Out[72]:
107093.29694509506
Using One-Dimensional Convolutional Layers to Process Sequences¶
|-----0-----| |-----3----| |--... |-------52------|
|-----1----| |-----4----| ... | |-------53------|
|-----2----| |------5--...-51------| |-------54------|
X: 0 1 2 3 4 5 6 7 8 9 10 11 12 ... 104 105 106 107 108 109 110 111
Y: from 4 6 8 10 12 ... 106 108 110 112
to 17 19 21 23 25 ... 119 121 123 125
In [73]:
tf.random.set_seed(42) # extra code – ensures reproducibility
conv_rnn_model = tf.keras.Sequential([
tf.keras.layers.Conv1D(filters=32, kernel_size=4, strides=2,
activation="relu", input_shape=[None, 5]),
tf.keras.layers.GRU(32, return_sequences=True),
tf.keras.layers.Dense(14)
])
longer_train = to_seq2seq_dataset(mulvar_train, seq_length=112,
shuffle=True, seed=42)
longer_valid = to_seq2seq_dataset(mulvar_valid, seq_length=112)
downsampled_train = longer_train.map(lambda X, Y: (X, Y[:, 3::2]))
downsampled_valid = longer_valid.map(lambda X, Y: (X, Y[:, 3::2]))
Just training for 5 epochs to show that it works (you can increase this if you want):
In [74]:
fit_and_evaluate(conv_rnn_model, downsampled_train, downsampled_valid,
learning_rate=0.1, epochs=5)
Epoch 1/5 31/31 [==============================] - 2s 30ms/step - loss: 0.0482 - mae: 0.2420 - val_loss: 0.0214 - val_mae: 0.1616 Epoch 2/5 31/31 [==============================] - 1s 18ms/step - loss: 0.0165 - mae: 0.1532 - val_loss: 0.0171 - val_mae: 0.1423 Epoch 3/5 31/31 [==============================] - 1s 18ms/step - loss: 0.0144 - mae: 0.1447 - val_loss: 0.0157 - val_mae: 0.1342 Epoch 4/5 31/31 [==============================] - 1s 17ms/step - loss: 0.0130 - mae: 0.1361 - val_loss: 0.0141 - val_mae: 0.1254 Epoch 5/5 31/31 [==============================] - 1s 17ms/step - loss: 0.0115 - mae: 0.1256 - val_loss: 0.0124 - val_mae: 0.1159 1/1 [==============================] - 0s 88ms/step - loss: 0.0124 - mae: 0.1159
Out[74]:
115850.42625665665
WaveNet¶
⋮
C2 /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\...
\ / \ / \ / \ / \ / \ / \
/ \ / \ / \
C1 /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /...\
X: 0 1 2 3 4 5 6 7 8 9 10 11 12 ... 111
Y: 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 112
/14 15 16 17 18 19 20 21 22 23 24 25 26 ... 125
In [75]:
tf.random.set_seed(42) # extra code – ensures reproducibility
wavenet_model = tf.keras.Sequential()
wavenet_model.add(tf.keras.layers.InputLayer(input_shape=[None, 5]))
for rate in (1, 2, 4, 8) * 2:
wavenet_model.add(tf.keras.layers.Conv1D(
filters=32, kernel_size=2, padding="causal", activation="relu",
dilation_rate=rate))
wavenet_model.add(tf.keras.layers.Conv1D(filters=14, kernel_size=1))
Just training for 5 epochs to show that it works (you can increase this if you want):
In [76]:
fit_and_evaluate(wavenet_model, longer_train, longer_valid,
learning_rate=0.1, epochs=5)
Epoch 1/5 31/31 [==============================] - 2s 26ms/step - loss: 0.0796 - mae: 0.3159 - val_loss: 0.0239 - val_mae: 0.1723 Epoch 2/5 31/31 [==============================] - 1s 16ms/step - loss: 0.0172 - mae: 0.1585 - val_loss: 0.0182 - val_mae: 0.1545 Epoch 3/5 31/31 [==============================] - 1s 16ms/step - loss: 0.0159 - mae: 0.1561 - val_loss: 0.0181 - val_mae: 0.1505 Epoch 4/5 31/31 [==============================] - 1s 16ms/step - loss: 0.0155 - mae: 0.1535 - val_loss: 0.0175 - val_mae: 0.1479 Epoch 5/5 31/31 [==============================] - 1s 17ms/step - loss: 0.0147 - mae: 0.1488 - val_loss: 0.0166 - val_mae: 0.1407 1/1 [==============================] - 0s 74ms/step - loss: 0.0166 - mae: 0.1407
Out[76]:
140713.95993232727
Extra Material – Wavenet Implementation¶
Here is the original WaveNet defined in the paper: it uses Gated Activation Units instead of ReLU and parametrized skip connections, plus it pads with zeros on the left to avoid getting shorter and shorter sequences:
In [77]:
class GatedActivationUnit(tf.keras.layers.Layer):
def __init__(self, activation="tanh", **kwargs):
super().__init__(**kwargs)
self.activation = tf.keras.activations.get(activation)
def call(self, inputs):
n_filters = inputs.shape[-1] // 2
linear_output = self.activation(inputs[..., :n_filters])
gate = tf.keras.activations.sigmoid(inputs[..., n_filters:])
return self.activation(linear_output) * gate
In [78]:
def wavenet_residual_block(inputs, n_filters, dilation_rate):
z = tf.keras.layers.Conv1D(2 * n_filters, kernel_size=2, padding="causal",
dilation_rate=dilation_rate)(inputs)
z = GatedActivationUnit()(z)
z = tf.keras.layers.Conv1D(n_filters, kernel_size=1)(z)
return tf.keras.layers.Add()([z, inputs]), z
In [79]:
tf.random.set_seed(42)
n_layers_per_block = 3 # 10 in the paper
n_blocks = 1 # 3 in the paper
n_filters = 32 # 128 in the paper
n_outputs = 14 # 256 in the paper
inputs = tf.keras.layers.Input(shape=[None, 5])
z = tf.keras.layers.Conv1D(n_filters, kernel_size=2, padding="causal")(inputs)
skip_to_last = []
for dilation_rate in [2**i for i in range(n_layers_per_block)] * n_blocks:
z, skip = wavenet_residual_block(z, n_filters, dilation_rate)
skip_to_last.append(skip)
z = tf.keras.activations.relu(tf.keras.layers.Add()(skip_to_last))
z = tf.keras.layers.Conv1D(n_filters, kernel_size=1, activation="relu")(z)
Y_preds = tf.keras.layers.Conv1D(n_outputs, kernel_size=1)(z)
full_wavenet_model = tf.keras.Model(inputs=[inputs], outputs=[Y_preds])
Just training for 5 epochs to show that it works (you can increase this if you want):
In [80]:
fit_and_evaluate(full_wavenet_model, longer_train, longer_valid,
learning_rate=0.1, epochs=5)
Epoch 1/5 31/31 [==============================] - 2s 26ms/step - loss: 0.0706 - mae: 0.2861 - val_loss: 0.0209 - val_mae: 0.1630 Epoch 2/5 31/31 [==============================] - 1s 18ms/step - loss: 0.0137 - mae: 0.1398 - val_loss: 0.0140 - val_mae: 0.1273 Epoch 3/5 31/31 [==============================] - 1s 20ms/step - loss: 0.0104 - mae: 0.1190 - val_loss: 0.0116 - val_mae: 0.1125 Epoch 4/5 31/31 [==============================] - 1s 18ms/step - loss: 0.0086 - mae: 0.1048 - val_loss: 0.0096 - val_mae: 0.1020 Epoch 5/5 31/31 [==============================] - 1s 19ms/step - loss: 0.0073 - mae: 0.0942 - val_loss: 0.0087 - val_mae: 0.0953 1/1 [==============================] - 0s 71ms/step - loss: 0.0087 - mae: 0.0953
Out[80]:
95349.08086061478
In this chapter we explored the fundamentals of RNNs and used them to process sequences (namely, time series). In the process we also looked at other ways to process sequences, including CNNs. In the next chapter we will use RNNs for Natural Language Processing, and we will learn more about RNNs (bidirectional RNNs, stateful vs stateless RNNs, Encoder–Decoders, and Attention-augmented Encoder-Decoders). We will also look at the Transformer, an Attention-only architecture.
Exercise solutions¶
1. to 8.¶
- Here are a few RNN applications:
- For a sequence-to-sequence RNN: predicting the weather (or any other time series), machine translation (using an Encoder–Decoder architecture), video captioning, speech to text, music generation (or other sequence generation), identifying the chords of a song
- For a sequence-to-vector RNN: classifying music samples by music genre, analyzing the sentiment of a book review, predicting what word an aphasic patient is thinking of based on readings from brain implants, predicting the probability that a user will want to watch a movie based on their watch history (this is one of many possible implementations of collaborative filtering for a recommender system)
- For a vector-to-sequence RNN: image captioning, creating a music playlist based on an embedding of the current artist, generating a melody based on a set of parameters, locating pedestrians in a picture (e.g., a video frame from a self-driving car's camera)
- An RNN layer must have three-dimensional inputs: the first dimension is the batch dimension (its size is the batch size), the second dimension represents the time (its size is the number of time steps), and the third dimension holds the inputs at each time step (its size is the number of input features per time step). For example, if you want to process a batch containing 5 time series of 10 time steps each, with 2 values per time step (e.g., the temperature and the wind speed), the shape will be [5, 10, 2]. The outputs are also three-dimensional, with the same first two dimensions, but the last dimension is equal to the number of neurons. For example, if an RNN layer with 32 neurons processes the batch we just discussed, the output will have a shape of [5, 10, 32].
- To build a deep sequence-to-sequence RNN using Keras, you must set
return_sequences=Truefor all RNN layers. To build a sequence-to-vector RNN, you must setreturn_sequences=Truefor all RNN layers except for the top RNN layer, which must havereturn_sequences=False(or do not set this argument at all, sinceFalseis the default). - If you have a daily univariate time series, and you want to forecast the next seven days, the simplest RNN architecture you can use is a stack of RNN layers (all with
return_sequences=Trueexcept for the top RNN layer), using seven neurons in the output RNN layer. You can then train this model using random windows from the time series (e.g., sequences of 30 consecutive days as the inputs, and a vector containing the values of the next 7 days as the target). This is a sequence-to-vector RNN. Alternatively, you could setreturn_sequences=Truefor all RNN layers to create a sequence-to-sequence RNN. You can train this model using random windows from the time series, with sequences of the same length as the inputs as the targets. Each target sequence should have seven values per time step (e.g., for time step t, the target should be a vector containing the values at time steps t + 1 to t + 7). - The two main difficulties when training RNNs are unstable gradients (exploding or vanishing) and a very limited short-term memory. These problems both get worse when dealing with long sequences. To alleviate the unstable gradients problem, you can use a smaller learning rate, use a saturating activation function such as the hyperbolic tangent (which is the default), and possibly use gradient clipping, Layer Normalization, or dropout at each time step. To tackle the limited short-term memory problem, you can use
LSTMorGRUlayers (this also helps with the unstable gradients problem). - An LSTM cell's architecture looks complicated, but it's actually not too hard if you understand the underlying logic. The cell has a short-term state vector and a long-term state vector. At each time step, the inputs and the previous short-term state are fed to a simple RNN cell and three gates: the forget gate decides what to remove from the long-term state, the input gate decides which part of the output of the simple RNN cell should be added to the long-term state, and the output gate decides which part of the long-term state should be output at this time step (after going through the tanh activation function). The new short-term state is equal to the output of the cell. See Figure 15–12.
- An RNN layer is fundamentally sequential: in order to compute the outputs at time step t, it has to first compute the outputs at all earlier time steps. This makes it impossible to parallelize. On the other hand, a 1D convolutional layer lends itself well to parallelization since it does not hold a state between time steps. In other words, it has no memory: the output at any time step can be computed based only on a small window of values from the inputs without having to know all the past values. Moreover, since a 1D convolutional layer is not recurrent, it suffers less from unstable gradients. One or more 1D convolutional layers can be useful in an RNN to efficiently preprocess the inputs, for example to reduce their temporal resolution (downsampling) and thereby help the RNN layers detect long-term patterns. In fact, it is possible to use only convolutional layers, for example by building a WaveNet architecture.
- To classify videos based on their visual content, one possible architecture could be to take (say) one frame per second, then run every frame through the same convolutional neural network (e.g., a pretrained Xception model, possibly frozen if your dataset is not large), feed the sequence of outputs from the CNN to a sequence-to-vector RNN, and finally run its output through a softmax layer, giving you all the class probabilities. For training you would use cross entropy as the cost function. If you wanted to use the audio for classification as well, you could use a stack of strided 1D convolutional layers to reduce the temporal resolution from thousands of audio frames per second to just one per second (to match the number of images per second), and concatenate the output sequence to the inputs of the sequence-to-vector RNN (along the last dimension).
9. Tackling the SketchRNN Dataset¶
Exercise: Train a classification model for the SketchRNN dataset, available in TensorFlow Datasets.
The dataset is not available in TFDS yet, the pull request is still work in progress. Luckily, the data is conveniently available as TFRecords, so let's download it (it might take a while, as it's about 1 GB large, with 3,450,000 training sketches and 345,000 test sketches):
In [81]:
tf_download_root = "http://download.tensorflow.org/data/"
filename = "quickdraw_tutorial_dataset_v1.tar.gz"
filepath = tf.keras.utils.get_file(filename,
tf_download_root + filename,
cache_dir=".",
extract=True)
Downloading data from http://download.tensorflow.org/data/quickdraw_tutorial_dataset_v1.tar.gz 1065304064/1065301781 [==============================] - 230s 0us/step 1065312256/1065301781 [==============================] - 230s 0us/step
In [82]:
quickdraw_dir = Path(filepath).parent
train_files = sorted(
[str(path) for path in quickdraw_dir.glob("training.tfrecord-*")]
)
eval_files = sorted(
[str(path) for path in quickdraw_dir.glob("eval.tfrecord-*")]
)
In [83]:
train_files
Out[83]:
['datasets/training.tfrecord-00000-of-00010', 'datasets/training.tfrecord-00001-of-00010', 'datasets/training.tfrecord-00002-of-00010', 'datasets/training.tfrecord-00003-of-00010', 'datasets/training.tfrecord-00004-of-00010', 'datasets/training.tfrecord-00005-of-00010', 'datasets/training.tfrecord-00006-of-00010', 'datasets/training.tfrecord-00007-of-00010', 'datasets/training.tfrecord-00008-of-00010', 'datasets/training.tfrecord-00009-of-00010']
In [84]:
eval_files
Out[84]:
['datasets/eval.tfrecord-00000-of-00010', 'datasets/eval.tfrecord-00001-of-00010', 'datasets/eval.tfrecord-00002-of-00010', 'datasets/eval.tfrecord-00003-of-00010', 'datasets/eval.tfrecord-00004-of-00010', 'datasets/eval.tfrecord-00005-of-00010', 'datasets/eval.tfrecord-00006-of-00010', 'datasets/eval.tfrecord-00007-of-00010', 'datasets/eval.tfrecord-00008-of-00010', 'datasets/eval.tfrecord-00009-of-00010']
In [85]:
with open(quickdraw_dir / "eval.tfrecord.classes") as test_classes_file:
test_classes = test_classes_file.readlines()
with open(quickdraw_dir / "training.tfrecord.classes") as train_classes_file:
train_classes = train_classes_file.readlines()
In [86]:
assert train_classes == test_classes
class_names = [name.strip().lower() for name in train_classes]
In [87]:
sorted(class_names)
Out[87]:
['aircraft carrier', 'airplane', 'alarm clock', 'ambulance', 'angel', 'animal migration', 'ant', 'anvil', 'apple', 'arm', 'asparagus', 'axe', 'backpack', 'banana', 'bandage', 'barn', 'baseball', 'baseball bat', 'basket', 'basketball', 'bat', 'bathtub', 'beach', 'bear', 'beard', 'bed', 'bee', 'belt', 'bench', 'bicycle', 'binoculars', 'bird', 'birthday cake', 'blackberry', 'blueberry', 'book', 'boomerang', 'bottlecap', 'bowtie', 'bracelet', 'brain', 'bread', 'bridge', 'broccoli', 'broom', 'bucket', 'bulldozer', 'bus', 'bush', 'butterfly', 'cactus', 'cake', 'calculator', 'calendar', 'camel', 'camera', 'camouflage', 'campfire', 'candle', 'cannon', 'canoe', 'car', 'carrot', 'castle', 'cat', 'ceiling fan', 'cell phone', 'cello', 'chair', 'chandelier', 'church', 'circle', 'clarinet', 'clock', 'cloud', 'coffee cup', 'compass', 'computer', 'cookie', 'cooler', 'couch', 'cow', 'crab', 'crayon', 'crocodile', 'crown', 'cruise ship', 'cup', 'diamond', 'dishwasher', 'diving board', 'dog', 'dolphin', 'donut', 'door', 'dragon', 'dresser', 'drill', 'drums', 'duck', 'dumbbell', 'ear', 'elbow', 'elephant', 'envelope', 'eraser', 'eye', 'eyeglasses', 'face', 'fan', 'feather', 'fence', 'finger', 'fire hydrant', 'fireplace', 'firetruck', 'fish', 'flamingo', 'flashlight', 'flip flops', 'floor lamp', 'flower', 'flying saucer', 'foot', 'fork', 'frog', 'frying pan', 'garden', 'garden hose', 'giraffe', 'goatee', 'golf club', 'grapes', 'grass', 'guitar', 'hamburger', 'hammer', 'hand', 'harp', 'hat', 'headphones', 'hedgehog', 'helicopter', 'helmet', 'hexagon', 'hockey puck', 'hockey stick', 'horse', 'hospital', 'hot air balloon', 'hot dog', 'hot tub', 'hourglass', 'house', 'house plant', 'hurricane', 'ice cream', 'jacket', 'jail', 'kangaroo', 'key', 'keyboard', 'knee', 'knife', 'ladder', 'lantern', 'laptop', 'leaf', 'leg', 'light bulb', 'lighter', 'lighthouse', 'lightning', 'line', 'lion', 'lipstick', 'lobster', 'lollipop', 'mailbox', 'map', 'marker', 'matches', 'megaphone', 'mermaid', 'microphone', 'microwave', 'monkey', 'moon', 'mosquito', 'motorbike', 'mountain', 'mouse', 'moustache', 'mouth', 'mug', 'mushroom', 'nail', 'necklace', 'nose', 'ocean', 'octagon', 'octopus', 'onion', 'oven', 'owl', 'paint can', 'paintbrush', 'palm tree', 'panda', 'pants', 'paper clip', 'parachute', 'parrot', 'passport', 'peanut', 'pear', 'peas', 'pencil', 'penguin', 'piano', 'pickup truck', 'picture frame', 'pig', 'pillow', 'pineapple', 'pizza', 'pliers', 'police car', 'pond', 'pool', 'popsicle', 'postcard', 'potato', 'power outlet', 'purse', 'rabbit', 'raccoon', 'radio', 'rain', 'rainbow', 'rake', 'remote control', 'rhinoceros', 'rifle', 'river', 'roller coaster', 'rollerskates', 'sailboat', 'sandwich', 'saw', 'saxophone', 'school bus', 'scissors', 'scorpion', 'screwdriver', 'sea turtle', 'see saw', 'shark', 'sheep', 'shoe', 'shorts', 'shovel', 'sink', 'skateboard', 'skull', 'skyscraper', 'sleeping bag', 'smiley face', 'snail', 'snake', 'snorkel', 'snowflake', 'snowman', 'soccer ball', 'sock', 'speedboat', 'spider', 'spoon', 'spreadsheet', 'square', 'squiggle', 'squirrel', 'stairs', 'star', 'steak', 'stereo', 'stethoscope', 'stitches', 'stop sign', 'stove', 'strawberry', 'streetlight', 'string bean', 'submarine', 'suitcase', 'sun', 'swan', 'sweater', 'swing set', 'sword', 'syringe', 't-shirt', 'table', 'teapot', 'teddy-bear', 'telephone', 'television', 'tennis racquet', 'tent', 'the eiffel tower', 'the great wall of china', 'the mona lisa', 'tiger', 'toaster', 'toe', 'toilet', 'tooth', 'toothbrush', 'toothpaste', 'tornado', 'tractor', 'traffic light', 'train', 'tree', 'triangle', 'trombone', 'truck', 'trumpet', 'umbrella', 'underwear', 'van', 'vase', 'violin', 'washing machine', 'watermelon', 'waterslide', 'whale', 'wheel', 'windmill', 'wine bottle', 'wine glass', 'wristwatch', 'yoga', 'zebra', 'zigzag']
In [88]:
def parse(data_batch):
feature_descriptions = {
"ink": tf.io.VarLenFeature(dtype=tf.float32),
"shape": tf.io.FixedLenFeature([2], dtype=tf.int64),
"class_index": tf.io.FixedLenFeature([1], dtype=tf.int64)
}
examples = tf.io.parse_example(data_batch, feature_descriptions)
flat_sketches = tf.sparse.to_dense(examples["ink"])
sketches = tf.reshape(flat_sketches, shape=[tf.size(data_batch), -1, 3])
lengths = examples["shape"][:, 0]
labels = examples["class_index"][:, 0]
return sketches, lengths, labels
In [89]:
def quickdraw_dataset(filepaths, batch_size=32, shuffle_buffer_size=None,
n_parse_threads=5, n_read_threads=5, cache=False):
dataset = tf.data.TFRecordDataset(filepaths,
num_parallel_reads=n_read_threads)
if cache:
dataset = dataset.cache()
if shuffle_buffer_size:
dataset = dataset.shuffle(shuffle_buffer_size)
dataset = dataset.batch(batch_size)
dataset = dataset.map(parse, num_parallel_calls=n_parse_threads)
return dataset.prefetch(1)
In [90]:
train_set = quickdraw_dataset(train_files, shuffle_buffer_size=10000)
valid_set = quickdraw_dataset(eval_files[:5])
test_set = quickdraw_dataset(eval_files[5:])
In [91]:
for sketches, lengths, labels in train_set.take(1):
print("sketches =", sketches)
print("lengths =", lengths)
print("labels =", labels)
sketches = tf.Tensor( [[[-0.08627451 0.11764706 0. ] [-0.01176471 0.16806725 0. ] [ 0.02352941 0.07563025 0. ] ... [ 0. 0. 0. ] [ 0. 0. 0. ] [ 0. 0. 0. ]] [[-0.04705882 -0.06696428 0. ] [-0.09019607 -0.07142857 0. ] [-0.0862745 -0.04464286 0. ] ... [ 0. 0. 0. ] [ 0. 0. 0. ] [ 0. 0. 0. ]] [[ 0. 0. 1. ] [ 0. 0. 0. ] [ 0.00784314 0.11320752 0. ] ... [ 0.11764708 0.01886791 0. ] [-0.03529412 0.12264156 0. ] [-0.19215688 0.33962262 1. ]] ... [[-0.21276593 -0.01960784 0. ] [-0.31382978 0.00784314 0. ] [-0.37234044 0.13725491 0. ] ... [ 0. 0. 0. ] [ 0. 0. 0. ] [ 0. 0. 0. ]] [[ 0. 0.4677419 0. ] [-0.01176471 0.15053767 0. ] [ 0.16470589 0.05376345 0. ] ... [ 0. 0. 0. ] [ 0. 0. 0. ] [ 0. 0. 0. ]] [[-0.04819274 0.01568627 0. ] [-0.07228917 -0.01176471 0. ] [-0.05622491 -0.03921568 0. ] ... [ 0. 0. 0. ] [ 0. 0. 0. ] [ 0. 0. 0. ]]], shape=(32, 104, 3), dtype=float32) lengths = tf.Tensor( [ 29 48 104 34 29 35 28 40 95 26 23 41 47 17 37 47 12 13 17 41 36 23 8 15 60 32 54 38 68 30 89 36], shape=(32,), dtype=int64) labels = tf.Tensor( [ 95 190 163 12 77 213 216 278 25 202 310 33 327 204 260 181 337 233 299 186 61 157 274 150 7 34 47 319 213 292 312 282], shape=(32,), dtype=int64)
In [92]:
def draw_sketch(sketch, label=None):
origin = np.array([[0., 0., 0.]])
sketch = np.r_[origin, sketch]
stroke_end_indices = np.argwhere(sketch[:, -1]==1.)[:, 0]
coordinates = sketch[:, :2].cumsum(axis=0)
strokes = np.split(coordinates, stroke_end_indices + 1)
title = class_names[label.numpy()] if label is not None else "Try to guess"
plt.title(title)
plt.plot(coordinates[:, 0], -coordinates[:, 1], "y:")
for stroke in strokes:
plt.plot(stroke[:, 0], -stroke[:, 1], ".-")
plt.axis("off")
def draw_sketches(sketches, lengths, labels):
n_sketches = len(sketches)
n_cols = 4
n_rows = (n_sketches - 1) // n_cols + 1
plt.figure(figsize=(n_cols * 3, n_rows * 3.5))
for index, sketch, length, label in zip(range(n_sketches), sketches, lengths, labels):
plt.subplot(n_rows, n_cols, index + 1)
draw_sketch(sketch[:length], label)
plt.show()
for sketches, lengths, labels in train_set.take(1):
draw_sketches(sketches, lengths, labels)
Most sketches are composed of less than 100 points:
In [93]:
lengths = np.concatenate([lengths for _, lengths, _ in train_set.take(1000)])
plt.hist(lengths, bins=150, density=True)
plt.axis([0, 200, 0, 0.03])
plt.xlabel("length")
plt.ylabel("density")
plt.show()
In [94]:
def crop_long_sketches(dataset, max_length=100):
return dataset.map(lambda inks, lengths, labels: (inks[:, :max_length], labels))
cropped_train_set = crop_long_sketches(train_set)
cropped_valid_set = crop_long_sketches(valid_set)
cropped_test_set = crop_long_sketches(test_set)
In [95]:
model = tf.keras.Sequential([
tf.keras.layers.Conv1D(32, kernel_size=5, strides=2, activation="relu"),
tf.keras.layers.BatchNormalization(),
tf.keras.layers.Conv1D(64, kernel_size=5, strides=2, activation="relu"),
tf.keras.layers.BatchNormalization(),
tf.keras.layers.Conv1D(128, kernel_size=3, strides=2, activation="relu"),
tf.keras.layers.BatchNormalization(),
tf.keras.layers.LSTM(128, return_sequences=True),
tf.keras.layers.LSTM(128),
tf.keras.layers.Dense(len(class_names), activation="softmax")
])
optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2, clipnorm=1.)
model.compile(loss="sparse_categorical_crossentropy",
optimizer=optimizer,
metrics=["accuracy", "sparse_top_k_categorical_accuracy"])
history = model.fit(cropped_train_set, epochs=2,
validation_data=cropped_valid_set)
Epoch 1/2 107813/107813 [==============================] - 2048s 19ms/step - loss: 4.0817 - accuracy: 0.1705 - sparse_top_k_categorical_accuracy: 0.3747 - val_loss: 3.0628 - val_accuracy: 0.3127 - val_sparse_top_k_categorical_accuracy: 0.5969 Epoch 2/2 107813/107813 [==============================] - 3975s 37ms/step - loss: 2.7176 - accuracy: 0.3771 - sparse_top_k_categorical_accuracy: 0.6660 - val_loss: 2.4580 - val_accuracy: 0.4253 - val_sparse_top_k_categorical_accuracy: 0.7143
In [96]:
y_test = np.concatenate([labels for _, _, labels in test_set])
y_probas = model.predict(test_set)
WARNING:tensorflow:5 out of the last 18 calls to <function Model.make_predict_function.<locals>.predict_function at 0x7fd0e07f7a60> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has experimental_relax_shapes=True option that relaxes argument shapes that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for more details.
In [97]:
np.mean(tf.keras.metrics.sparse_top_k_categorical_accuracy(y_test, y_probas))
Out[97]:
0.60668993
In [98]:
n_new = 10
Y_probas = model.predict(sketches)
top_k = tf.nn.top_k(Y_probas, k=5)
for index in range(n_new):
plt.figure(figsize=(3, 3.5))
draw_sketch(sketches[index])
plt.show()
print("Top-5 predictions:".format(index + 1))
for k in range(5):
class_name = class_names[top_k.indices[index, k]]
proba = 100 * top_k.values[index, k]
print(" {}. {} {:.3f}%".format(k + 1, class_name, proba))
print("Answer: {}".format(class_names[labels[index].numpy()]))
Top-5 predictions: 1. popsicle 13.105% 2. computer 7.943% 3. television 7.032% 4. laptop 6.640% 5. cell phone 5.520% Answer: picture frame
Top-5 predictions: 1. garden hose 15.217% 2. trumpet 10.083% 3. rifle 8.203% 4. spoon 5.367% 5. moustache 4.533% Answer: boomerang
Top-5 predictions: 1. wine bottle 24.326% 2. hexagon 22.632% 3. octagon 13.903% 4. lipstick 2.759% 5. blackberry 2.112% Answer: square
Top-5 predictions: 1. ear 62.866% 2. moon 17.284% 3. boomerang 3.729% 4. knee 2.912% 5. squiggle 2.257% Answer: ear
Top-5 predictions: 1. monkey 34.293% 2. mermaid 8.274% 3. blueberry 7.341% 4. camouflage 4.992% 5. bear 4.961% Answer: monkey
Top-5 predictions: 1. fork 8.643% 2. shovel 7.149% 3. syringe 6.684% 4. screwdriver 5.352% 5. stitches 4.247% Answer: line
Top-5 predictions: 1. snowflake 22.972% 2. yoga 10.533% 3. matches 6.915% 4. candle 4.574% 5. syringe 3.947% Answer: trumpet
Top-5 predictions: 1. shovel 15.070% 2. floor lamp 10.788% 3. screwdriver 10.516% 4. lipstick 9.559% 5. lantern 7.887% Answer: anvil
Top-5 predictions: 1. blueberry 13.230% 2. submarine 11.078% 3. bicycle 9.777% 4. motorbike 9.246% 5. eyeglasses 8.239% Answer: pickup truck
Top-5 predictions: 1. stereo 21.389% 2. radio 16.453% 3. yoga 9.803% 4. ant 6.983% 5. power outlet 4.575% Answer: calendar
In [99]:
model.save("my_sketchrnn", save_format="tf")
2022-02-18 16:47:16.114014: W tensorflow/python/util/util.cc:368] Sets are not currently considered sequences, but this may change in the future, so consider avoiding using them. WARNING:absl:Found untraced functions such as lstm_cell_1_layer_call_fn, lstm_cell_1_layer_call_and_return_conditional_losses, lstm_cell_2_layer_call_fn, lstm_cell_2_layer_call_and_return_conditional_losses, lstm_cell_1_layer_call_fn while saving (showing 5 of 10). These functions will not be directly callable after loading.
INFO:tensorflow:Assets written to: my_sketchrnn/assets
INFO:tensorflow:Assets written to: my_sketchrnn/assets WARNING:absl:<keras.layers.recurrent.LSTMCell object at 0x7fd0e0822610> has the same name 'LSTMCell' as a built-in Keras object. Consider renaming <class 'keras.layers.recurrent.LSTMCell'> to avoid naming conflicts when loading with `tf.keras.models.load_model`. If renaming is not possible, pass the object in the `custom_objects` parameter of the load function. WARNING:absl:<keras.layers.recurrent.LSTMCell object at 0x7fd0e080f070> has the same name 'LSTMCell' as a built-in Keras object. Consider renaming <class 'keras.layers.recurrent.LSTMCell'> to avoid naming conflicts when loading with `tf.keras.models.load_model`. If renaming is not possible, pass the object in the `custom_objects` parameter of the load function.
10. Bach Chorales¶
Exercise: Download the Bach chorales dataset and unzip it. It is composed of 382 chorales composed by Johann Sebastian Bach. Each chorale is 100 to 640 time steps long, and each time step contains 4 integers, where each integer corresponds to a note's index on a piano (except for the value 0, which means that no note is played). Train a model—recurrent, convolutional, or both—that can predict the next time step (four notes), given a sequence of time steps from a chorale. Then use this model to generate Bach-like music, one note at a time: you can do this by giving the model the start of a chorale and asking it to predict the next time step, then appending these time steps to the input sequence and asking the model for the next note, and so on. Also make sure to check out Google's Coconet model, which was used for a nice Google doodle about Bach.
In [100]:
tf.keras.utils.get_file(
"jsb_chorales.tgz",
"https://github.com/ageron/data/raw/main/jsb_chorales.tgz",
cache_dir=".",
extract=True)
Downloading data from https://github.com/ageron/data/raw/main/jsb_chorales.tgz 122880/117793 [===============================] - 0s 0us/step 131072/117793 [=================================] - 0s 0us/step
Out[100]:
'./datasets/jsb_chorales.tgz'
In [101]:
jsb_chorales_dir = Path("datasets/jsb_chorales")
train_files = sorted(jsb_chorales_dir.glob("train/chorale_*.csv"))
valid_files = sorted(jsb_chorales_dir.glob("valid/chorale_*.csv"))
test_files = sorted(jsb_chorales_dir.glob("test/chorale_*.csv"))
In [102]:
import pandas as pd
def load_chorales(filepaths):
return [pd.read_csv(filepath).values.tolist() for filepath in filepaths]
train_chorales = load_chorales(train_files)
valid_chorales = load_chorales(valid_files)
test_chorales = load_chorales(test_files)
In [103]:
train_chorales[0]
Out[103]:
[[74, 70, 65, 58], [74, 70, 65, 58], [74, 70, 65, 58], [74, 70, 65, 58], [75, 70, 58, 55], [75, 70, 58, 55], [75, 70, 60, 55], [75, 70, 60, 55], [77, 69, 62, 50], [77, 69, 62, 50], [77, 69, 62, 50], [77, 69, 62, 50], [77, 70, 62, 55], [77, 70, 62, 55], [77, 69, 62, 55], [77, 69, 62, 55], [75, 67, 63, 48], [75, 67, 63, 48], [75, 69, 63, 48], [75, 69, 63, 48], [74, 70, 65, 46], [74, 70, 65, 46], [74, 70, 65, 46], [74, 70, 65, 46], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [74, 70, 65, 46], [74, 70, 65, 46], [74, 70, 65, 46], [74, 70, 65, 46], [75, 69, 63, 48], [75, 69, 63, 48], [75, 67, 63, 48], [75, 67, 63, 48], [77, 65, 62, 50], [77, 65, 62, 50], [77, 65, 60, 50], [77, 65, 60, 50], [74, 67, 58, 55], [74, 67, 58, 55], [74, 67, 58, 53], [74, 67, 58, 53], [72, 67, 58, 51], [72, 67, 58, 51], [72, 67, 58, 51], [72, 67, 58, 51], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [72, 69, 65, 53], [74, 71, 53, 50], [74, 71, 53, 50], [74, 71, 53, 50], [74, 71, 53, 50], [75, 72, 55, 48], [75, 72, 55, 48], [75, 72, 55, 50], [75, 72, 55, 50], [75, 67, 60, 51], [75, 67, 60, 51], [75, 67, 60, 53], [75, 67, 60, 53], [74, 67, 60, 55], [74, 67, 60, 55], [74, 67, 57, 55], [74, 67, 57, 55], [74, 65, 59, 43], [74, 65, 59, 43], [72, 63, 59, 43], [72, 63, 59, 43], [72, 63, 55, 48], [72, 63, 55, 48], [72, 63, 55, 48], [72, 63, 55, 48], [72, 63, 55, 48], [72, 63, 55, 48], [72, 63, 55, 48], [72, 63, 55, 48], [75, 67, 60, 60], [75, 67, 60, 60], [75, 67, 60, 60], [75, 67, 60, 60], [77, 70, 62, 58], [77, 70, 62, 58], [77, 70, 62, 56], [77, 70, 62, 56], [79, 70, 62, 55], [79, 70, 62, 55], [79, 70, 62, 53], [79, 70, 62, 53], [79, 70, 63, 51], [79, 70, 63, 51], [79, 70, 63, 51], [79, 70, 63, 51], [77, 70, 63, 58], [77, 70, 63, 58], [77, 70, 60, 58], [77, 70, 60, 58], [77, 70, 62, 46], [77, 70, 62, 46], [77, 68, 62, 46], [75, 68, 62, 46], [75, 67, 58, 51], [75, 67, 58, 51], [75, 67, 58, 51], [75, 67, 58, 51], [75, 67, 58, 51], [75, 67, 58, 51], [75, 67, 58, 51], [75, 67, 58, 51], [74, 67, 58, 55], [74, 67, 58, 55], [74, 67, 58, 55], [74, 67, 58, 55], [75, 67, 58, 53], [75, 67, 58, 53], [75, 67, 58, 51], [75, 67, 58, 51], [77, 65, 58, 50], [77, 65, 58, 50], [77, 65, 56, 50], [77, 65, 56, 50], [70, 63, 55, 51], [70, 63, 55, 51], [70, 63, 55, 51], [70, 63, 55, 51], [75, 65, 60, 45], [75, 65, 60, 45], [75, 65, 60, 45], [75, 65, 60, 45], [74, 65, 58, 46], [74, 65, 58, 46], [74, 65, 58, 46], [74, 65, 58, 46], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [74, 65, 58, 58], [74, 65, 58, 58], [74, 65, 58, 58], [74, 65, 58, 58], [75, 67, 58, 57], [75, 67, 58, 57], [75, 67, 58, 55], [75, 67, 58, 55], [77, 65, 60, 57], [77, 65, 60, 57], [77, 65, 60, 53], [77, 65, 60, 53], [74, 65, 58, 58], [74, 65, 58, 58], [74, 65, 58, 58], [74, 65, 58, 58], [72, 67, 58, 51], [72, 67, 58, 51], [72, 67, 58, 51], [72, 67, 58, 51], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [72, 65, 57, 53], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46], [70, 65, 62, 46]]
Notes range from 36 (C1 = C on octave 1) to 81 (A5 = A on octave 5), plus 0 for silence:
In [104]:
notes = set()
for chorales in (train_chorales, valid_chorales, test_chorales):
for chorale in chorales:
for chord in chorale:
notes |= set(chord)
n_notes = len(notes)
min_note = min(notes - {0})
max_note = max(notes)
assert min_note == 36
assert max_note == 81
Let's write a few functions to listen to these chorales (you don't need to understand the details here, and in fact there are certainly simpler ways to do this, for example using MIDI players, but I just wanted to have a bit of fun writing a synthesizer):
In [105]:
from IPython.display import Audio
def notes_to_frequencies(notes):
# Frequency doubles when you go up one octave; there are 12 semi-tones
# per octave; Note A on octave 4 is 440 Hz, and it is note number 69.
return 2 ** ((np.array(notes) - 69) / 12) * 440
def frequencies_to_samples(frequencies, tempo, sample_rate):
note_duration = 60 / tempo # the tempo is measured in beats per minutes
# To reduce click sound at every beat, we round the frequencies to try to
# get the samples close to zero at the end of each note.
frequencies = (note_duration * frequencies).round() / note_duration
n_samples = int(note_duration * sample_rate)
time = np.linspace(0, note_duration, n_samples)
sine_waves = np.sin(2 * np.pi * frequencies.reshape(-1, 1) * time)
# Removing all notes with frequencies ≤ 9 Hz (includes note 0 = silence)
sine_waves *= (frequencies > 9.).reshape(-1, 1)
return sine_waves.reshape(-1)
def chords_to_samples(chords, tempo, sample_rate):
freqs = notes_to_frequencies(chords)
freqs = np.r_[freqs, freqs[-1:]] # make last note a bit longer
merged = np.mean([frequencies_to_samples(melody, tempo, sample_rate)
for melody in freqs.T], axis=0)
n_fade_out_samples = sample_rate * 60 // tempo # fade out last note
fade_out = np.linspace(1., 0., n_fade_out_samples)**2
merged[-n_fade_out_samples:] *= fade_out
return merged
def play_chords(chords, tempo=160, amplitude=0.1, sample_rate=44100, filepath=None):
samples = amplitude * chords_to_samples(chords, tempo, sample_rate)
if filepath:
from scipy.io import wavfile
samples = (2**15 * samples).astype(np.int16)
wavfile.write(filepath, sample_rate, samples)
return display(Audio(filepath))
else:
return display(Audio(samples, rate=sample_rate))
Now let's listen to a few chorales:
In [106]:
for index in range(3):
play_chords(train_chorales[index])
Divine! :)
In order to be able to generate new chorales, we want to train a model that can predict the next chord given all the previous chords. If we naively try to predict the next chord in one shot, predicting all 4 notes at once, we run the risk of getting notes that don't go very well together (believe me, I tried). It's much better and simpler to predict one note at a time. So we will need to preprocess every chorale, turning each chord into an arpegio (i.e., a sequence of notes rather than notes played simultaneuously). So each chorale will be a long sequence of notes (rather than chords), and we can just train a model that can predict the next note given all the previous notes. We will use a sequence-to-sequence approach, where we feed a window to the neural net, and it tries to predict that same window shifted one time step into the future.
We will also shift the values so that they range from 0 to 46, where 0 represents silence, and values 1 to 46 represent notes 36 (C1) to 81 (A5).
And we will train the model on windows of 128 notes (i.e., 32 chords).
Since the dataset fits in memory, we could preprocess the chorales in RAM using any Python code we like, but I will demonstrate here how to do all the preprocessing using tf.data (there will be more details about creating windows using tf.data in the next chapter).
In [107]:
def create_target(batch):
X = batch[:, :-1]
Y = batch[:, 1:] # predict next note in each arpegio, at each step
return X, Y
def preprocess(window):
window = tf.where(window == 0, window, window - min_note + 1) # shift values
return tf.reshape(window, [-1]) # convert to arpegio
def bach_dataset(chorales, batch_size=32, shuffle_buffer_size=None,
window_size=32, window_shift=16, cache=True):
def batch_window(window):
return window.batch(window_size + 1)
def to_windows(chorale):
dataset = tf.data.Dataset.from_tensor_slices(chorale)
dataset = dataset.window(window_size + 1, window_shift, drop_remainder=True)
return dataset.flat_map(batch_window)
chorales = tf.ragged.constant(chorales, ragged_rank=1)
dataset = tf.data.Dataset.from_tensor_slices(chorales)
dataset = dataset.flat_map(to_windows).map(preprocess)
if cache:
dataset = dataset.cache()
if shuffle_buffer_size:
dataset = dataset.shuffle(shuffle_buffer_size)
dataset = dataset.batch(batch_size)
dataset = dataset.map(create_target)
return dataset.prefetch(1)
Now let's create the training set, the validation set and the test set:
In [108]:
train_set = bach_dataset(train_chorales, shuffle_buffer_size=1000)
valid_set = bach_dataset(valid_chorales)
test_set = bach_dataset(test_chorales)
Now let's create the model:
- We could feed the note values directly to the model, as floats, but this would probably not give good results. Indeed, the relationships between notes are not that simple: for example, if you replace a C3 with a C4, the melody will still sound fine, even though these notes are 12 semi-tones apart (i.e., one octave). Conversely, if you replace a C3 with a C#3, it's very likely that the chord will sound horrible, despite these notes being just next to each other. So we will use an
Embeddinglayer to convert each note to a small vector representation (see Chapter 16 for more details on embeddings). We will use 5-dimensional embeddings, so the output of this first layer will have a shape of[batch_size, window_size, 5]. - We will then feed this data to a small WaveNet-like neural network, composed of a stack of 4
Conv1Dlayers with doubling dilation rates. We will intersperse these layers withBatchNormalizationlayers for faster better convergence. - Then one
LSTMlayer to try to capture long-term patterns. - And finally a
Denselayer to produce the final note probabilities. It will predict one probability for each chorale in the batch, for each time step, and for each possible note (including silence). So the output shape will be[batch_size, window_size, 47].
In [109]:
n_embedding_dims = 5
model = tf.keras.Sequential([
tf.keras.layers.Embedding(input_dim=n_notes, output_dim=n_embedding_dims,
input_shape=[None]),
tf.keras.layers.Conv1D(32, kernel_size=2, padding="causal", activation="relu"),
tf.keras.layers.BatchNormalization(),
tf.keras.layers.Conv1D(48, kernel_size=2, padding="causal", activation="relu", dilation_rate=2),
tf.keras.layers.BatchNormalization(),
tf.keras.layers.Conv1D(64, kernel_size=2, padding="causal", activation="relu", dilation_rate=4),
tf.keras.layers.BatchNormalization(),
tf.keras.layers.Conv1D(96, kernel_size=2, padding="causal", activation="relu", dilation_rate=8),
tf.keras.layers.BatchNormalization(),
tf.keras.layers.LSTM(256, return_sequences=True),
tf.keras.layers.Dense(n_notes, activation="softmax")
])
model.summary()
Model: "sequential_19"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
embedding (Embedding) (None, None, 5) 235
conv1d_22 (Conv1D) (None, None, 32) 352
batch_normalization_3 (Batc (None, None, 32) 128
hNormalization)
conv1d_23 (Conv1D) (None, None, 48) 3120
batch_normalization_4 (Batc (None, None, 48) 192
hNormalization)
conv1d_24 (Conv1D) (None, None, 64) 6208
batch_normalization_5 (Batc (None, None, 64) 256
hNormalization)
conv1d_25 (Conv1D) (None, None, 96) 12384
batch_normalization_6 (Batc (None, None, 96) 384
hNormalization)
lstm_3 (LSTM) (None, None, 256) 361472
dense_17 (Dense) (None, None, 47) 12079
=================================================================
Total params: 396,810
Trainable params: 396,330
Non-trainable params: 480
_________________________________________________________________
Now we're ready to compile and train the model!
In [110]:
optimizer = tf.keras.optimizers.Nadam(learning_rate=1e-3)
model.compile(loss="sparse_categorical_crossentropy", optimizer=optimizer,
metrics=["accuracy"])
model.fit(train_set, epochs=20, validation_data=valid_set)
Epoch 1/20 98/98 [==============================] - 25s 208ms/step - loss: 1.8695 - accuracy: 0.5301 - val_loss: 3.7034 - val_accuracy: 0.1226 Epoch 2/20 98/98 [==============================] - 22s 225ms/step - loss: 0.9034 - accuracy: 0.7638 - val_loss: 3.4941 - val_accuracy: 0.1050 Epoch 3/20 98/98 [==============================] - 23s 233ms/step - loss: 0.7523 - accuracy: 0.7916 - val_loss: 3.3243 - val_accuracy: 0.1938 Epoch 4/20 98/98 [==============================] - 23s 232ms/step - loss: 0.6756 - accuracy: 0.8074 - val_loss: 2.5097 - val_accuracy: 0.3022 Epoch 5/20 98/98 [==============================] - 22s 223ms/step - loss: 0.6188 - accuracy: 0.8193 - val_loss: 1.7532 - val_accuracy: 0.4628 Epoch 6/20 98/98 [==============================] - 23s 237ms/step - loss: 0.5788 - accuracy: 0.8280 - val_loss: 1.0323 - val_accuracy: 0.6826 Epoch 7/20 98/98 [==============================] - 25s 256ms/step - loss: 0.5396 - accuracy: 0.8374 - val_loss: 0.7257 - val_accuracy: 0.7910 Epoch 8/20 98/98 [==============================] - 27s 278ms/step - loss: 0.5079 - accuracy: 0.8451 - val_loss: 0.8296 - val_accuracy: 0.7497 Epoch 9/20 98/98 [==============================] - 26s 267ms/step - loss: 0.4796 - accuracy: 0.8523 - val_loss: 0.6217 - val_accuracy: 0.8162 Epoch 10/20 98/98 [==============================] - 26s 270ms/step - loss: 0.4543 - accuracy: 0.8594 - val_loss: 0.6307 - val_accuracy: 0.8136 Epoch 11/20 98/98 [==============================] - 28s 285ms/step - loss: 0.4291 - accuracy: 0.8665 - val_loss: 0.6203 - val_accuracy: 0.8183 Epoch 12/20 98/98 [==============================] - 28s 284ms/step - loss: 0.4062 - accuracy: 0.8732 - val_loss: 0.6111 - val_accuracy: 0.8210 Epoch 13/20 98/98 [==============================] - 24s 247ms/step - loss: 0.3846 - accuracy: 0.8798 - val_loss: 0.6185 - val_accuracy: 0.8167 Epoch 14/20 98/98 [==============================] - 24s 247ms/step - loss: 0.3647 - accuracy: 0.8856 - val_loss: 0.6036 - val_accuracy: 0.8244 Epoch 15/20 98/98 [==============================] - 24s 248ms/step - loss: 0.3454 - accuracy: 0.8918 - val_loss: 0.6400 - val_accuracy: 0.8149 Epoch 16/20 98/98 [==============================] - 24s 243ms/step - loss: 0.3299 - accuracy: 0.8969 - val_loss: 0.6517 - val_accuracy: 0.8099 Epoch 17/20 98/98 [==============================] - 23s 240ms/step - loss: 0.3100 - accuracy: 0.9027 - val_loss: 0.6472 - val_accuracy: 0.8148 Epoch 18/20 98/98 [==============================] - 23s 238ms/step - loss: 0.2952 - accuracy: 0.9080 - val_loss: 0.6446 - val_accuracy: 0.8167 Epoch 19/20 98/98 [==============================] - 22s 221ms/step - loss: 0.2781 - accuracy: 0.9136 - val_loss: 0.6774 - val_accuracy: 0.8104 Epoch 20/20 98/98 [==============================] - 23s 234ms/step - loss: 0.2642 - accuracy: 0.9179 - val_loss: 0.6484 - val_accuracy: 0.8199
Out[110]:
<keras.callbacks.History at 0x7fd121a6bdf0>
I have not done much hyperparameter search, so feel free to iterate on this model now and try to optimize it. For example, you could try removing the LSTM layer and replacing it with Conv1D layers. You could also play with the number of layers, the learning rate, the optimizer, and so on.
Once you're satisfied with the performance of the model on the validation set, you can save it and evaluate it one last time on the test set:
In [111]:
model.save("my_bach_model", save_format="tf")
model.evaluate(test_set)
34/34 [==============================] - 3s 74ms/step - loss: 0.6631 - accuracy: 0.8164
Out[111]:
[0.6630987524986267, 0.8163789510726929]
Note: There's no real need for a test set in this exercise, since we will perform the final evaluation by just listening to the music produced by the model. So if you want, you can add the test set to the train set, and train the model again, hopefully getting a slightly better model.
Now let's write a function that will generate a new chorale. We will give it a few seed chords, it will convert them to arpegios (the format expected by the model), and use the model to predict the next note, then the next, and so on. In the end, it will group the notes 4 by 4 to create chords again, and return the resulting chorale.
In [112]:
def generate_chorale(model, seed_chords, length):
arpegio = preprocess(tf.constant(seed_chords, dtype=tf.int64))
arpegio = tf.reshape(arpegio, [1, -1])
for chord in range(length):
for note in range(4):
next_note = model.predict(arpegio, verbose=0).argmax(axis=-1)[:1, -1:]
arpegio = tf.concat([arpegio, next_note], axis=1)
arpegio = tf.where(arpegio == 0, arpegio, arpegio + min_note - 1)
return tf.reshape(arpegio, shape=[-1, 4])
To test this function, we need some seed chords. Let's use the first 8 chords of one of the test chorales (it's actually just 2 different chords, each played 4 times):
In [113]:
seed_chords = test_chorales[2][:8]
play_chords(seed_chords, amplitude=0.2)
Now we are ready to generate our first chorale! Let's ask the function to generate 56 more chords, for a total of 64 chords, i.e., 16 bars (assuming 4 chords per bar, i.e., a 4/4 signature):
In [114]:
new_chorale = generate_chorale(model, seed_chords, 56)
play_chords(new_chorale)
This approach has one major flaw: it is often too conservative. Indeed, the model will not take any risk, it will always choose the note with the highest score, and since repeating the previous note generally sounds good enough, it's the least risky option, so the algorithm will tend to make notes last longer and longer. Pretty boring. Plus, if you run the model multiple times, it will always generate the same melody.
So let's spice things up a bit! Instead of always picking the note with the highest score, we will pick the next note randomly, according to the predicted probabilities. For example, if the model predicts a C3 with 75% probability, and a G3 with a 25% probability, then we will pick one of these two notes randomly, with these probabilities. We will also add a temperature parameter that will control how "hot" (i.e., daring) we want the system to feel. A high temperature will bring the predicted probabilities closer together, reducing the probability of the likely notes and increasing the probability of the unlikely ones.
In [115]:
def generate_chorale_v2(model, seed_chords, length, temperature=1):
arpegio = preprocess(tf.constant(seed_chords, dtype=tf.int64))
arpegio = tf.reshape(arpegio, [1, -1])
for chord in range(length):
for note in range(4):
next_note_probas = model.predict(arpegio)[0, -1:]
rescaled_logits = tf.math.log(next_note_probas) / temperature
next_note = tf.random.categorical(rescaled_logits, num_samples=1)
arpegio = tf.concat([arpegio, next_note], axis=1)
arpegio = tf.where(arpegio == 0, arpegio, arpegio + min_note - 1)
return tf.reshape(arpegio, shape=[-1, 4])
Let's generate 3 chorales using this new function: one cold, one medium, and one hot (feel free to experiment with other seeds, lengths and temperatures). The code saves each chorale to a separate file. You can run these cells over an over again until you generate a masterpiece!
Please share your most beautiful generated chorale with me on Twitter @aureliengeron, I would really appreciate it! :))
In [116]:
new_chorale_v2_cold = generate_chorale_v2(model, seed_chords, 56, temperature=0.8)
play_chords(new_chorale_v2_cold, filepath="bach_cold.wav")
In [117]:
new_chorale_v2_medium = generate_chorale_v2(model, seed_chords, 56, temperature=1.0)
play_chords(new_chorale_v2_medium, filepath="bach_medium.wav")
In [118]:
new_chorale_v2_hot = generate_chorale_v2(model, seed_chords, 56, temperature=1.5)
play_chords(new_chorale_v2_hot, filepath="bach_hot.wav")
Lastly, you can try a fun social experiment: send your friends a few of your favorite generated chorales, plus the real chorale, and ask them to guess which one is the real one!
In [119]:
play_chords(test_chorales[2][:64], filepath="bach_test_4.wav")