Deep learning examples¶

This notebooks contains examples with neural network models.

Table of contents

Loading dataset
Architecture
Testing models
- Baseline
- DeepAR
- DeepARNative
- TFT
- TFTNative
- RNN
- MLP
- Deep State Model
- N-BEATS Model
- PatchTS Model

In [1]:

!pip install "etna[torch]" -q

In [2]:

import warnings

warnings.filterwarnings("ignore")

In [3]:

import random

import numpy as np
import pandas as pd
import torch

from etna.analysis import plot_backtest
from etna.datasets.tsdataset import TSDataset
from etna.metrics import MAE
from etna.metrics import MAPE
from etna.metrics import SMAPE
from etna.models import SeasonalMovingAverageModel
from etna.pipeline import Pipeline
from etna.transforms import DateFlagsTransform
from etna.transforms import LabelEncoderTransform
from etna.transforms import LagTransform
from etna.transforms import LinearTrendTransform
from etna.transforms import SegmentEncoderTransform
from etna.transforms import StandardScalerTransform

wandb: WARNING Disabling SSL verification.  Connections to this server are not verified and may be insecure!

In [4]:

def set_seed(seed: int = 42):
    """Set random seed for reproducibility."""
    random.seed(seed)
    np.random.seed(seed)
    torch.manual_seed(seed)
    torch.cuda.manual_seed_all(seed)

1. Loading dataset ¶

We are going to take some toy dataset. Let's load and look at it.

In [5]:

df = pd.read_csv("data/example_dataset.csv")
df.head()

Out[5]:

	timestamp	segment	target
0	2019-01-01	segment_a	170
1	2019-01-02	segment_a	243
2	2019-01-03	segment_a	267
3	2019-01-04	segment_a	287
4	2019-01-05	segment_a	279

Our library works with the special data structure TSDataset. Let's create it as it was done in "Get started" notebook.

In [6]:

ts = TSDataset(df, freq="D")
ts.head(5)

Out[6]:

segment	segment_a	segment_b	segment_c	segment_d
feature	target	target	target	target
timestamp
2019-01-01	170	102	92	238
2019-01-02	243	123	107	358
2019-01-03	267	130	103	366
2019-01-04	287	138	103	385
2019-01-05	279	137	104	384

2. Architecture ¶

Our library has two types of models:

Models from PyTorch Forecasting
Native models.

First, let's describe the pytorch-forecasting models, because they require a special handling. There are two ways to use these models: default one and via using PytorchForecastingDatasetBuilder for using extra features.

To include extra features we use PytorchForecastingDatasetBuilder class.

Let's look at it closer.

In [7]:

from etna.models.nn.utils import PytorchForecastingDatasetBuilder

In [8]:

?PytorchForecastingDatasetBuilder

We can see a pretty scary signature, but don't panic, we will look at the most important parameters.

time_varying_known_reals — known real values that change across the time (real regressors), now it it necessary to add "time_idx" variable to the list;
time_varying_unknown_reals — our real value target, set it to ["target"];
max_prediction_length — our horizon for forecasting;
max_encoder_length — length of past context to use;
static_categoricals — static categorical values, for example, if we use multiple segments it can be some its characteristics including identifier: "segment";
time_varying_known_categoricals — known categorical values that change across the time (categorical regressors);
target_normalizer — class for normalization targets across different segments.

Our library currently supports these pytorch-forecasting models:

DeepAR (will be removed in version 3.0),
TFT (will be removed in version 3.0).

As for the native neural network models, they are simpler to use, because they don't require PytorchForecastingTransform. We will see how to use them on examples.

3. Testing models ¶

In this section we will test our models on example.

In [9]:

HORIZON = 7
metrics = [SMAPE(), MAPE(), MAE()]

3.1 Baseline ¶

For comparison let's train some simple model as a baseline.

In [10]:

model_sma = SeasonalMovingAverageModel(window=5, seasonality=7)
linear_trend_transform = LinearTrendTransform(in_column="target")

pipeline_sma = Pipeline(model=model_sma, horizon=HORIZON, transforms=[linear_trend_transform])

In [11]:

metrics_sma, forecast_sma, fold_info_sma = pipeline_sma.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [12]:

metrics_sma

Out[12]:

	segment	SMAPE	MAPE	MAE	fold_number
0	segment_a	6.343943	6.124296	33.196532	0
0	segment_a	5.346946	5.192455	27.938101	1
0	segment_a	7.510347	7.189999	40.028565	2
1	segment_b	7.178822	6.920176	17.818102	0
1	segment_b	5.672504	5.554555	13.719200	1
1	segment_b	3.327846	3.359712	7.680919	2
2	segment_c	6.430429	6.200580	10.877718	0
2	segment_c	5.947090	5.727531	10.701336	1
2	segment_c	6.186545	5.943679	11.359563	2
3	segment_d	4.707899	4.644170	39.918646	0
3	segment_d	5.403426	5.600978	43.047332	1
3	segment_d	2.505279	2.543719	19.347565	2

In [13]:

score = metrics_sma["SMAPE"].mean()
print(f"Average SMAPE for Seasonal MA: {score:.3f}")

Average SMAPE for Seasonal MA: 5.547

In [14]:

plot_backtest(forecast_sma, ts, history_len=20)

3.2 DeepAR ¶

In [15]:

from etna.models.nn import DeepARModel

Before training let's fix seeds for reproducibility.

In [16]:

set_seed()

Default way¶

In [17]:

model_deepar = DeepARModel(
    encoder_length=HORIZON,
    decoder_length=HORIZON,
    trainer_params=dict(max_epochs=150, gradient_clip_val=0.1),
    lr=0.01,
    train_batch_size=64,
)
metrics = [SMAPE(), MAPE(), MAE()]

pipeline_deepar = Pipeline(model=model_deepar, horizon=HORIZON)

In [18]:

metrics_deepar, forecast_deepar, fold_info_deepar = pipeline_deepar.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name                   | Type                   | Params
------------------------------------------------------------------
0 | loss                   | NormalDistributionLoss | 0     
1 | logging_metrics        | ModuleList             | 0     
2 | embeddings             | MultiEmbedding         | 0     
3 | rnn                    | LSTM                   | 1.6 K 
4 | distribution_projector | Linear                 | 22    
------------------------------------------------------------------
1.6 K     Trainable params
0         Non-trainable params
1.6 K     Total params
0.006     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=150` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:  2.2min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name                   | Type                   | Params
------------------------------------------------------------------
0 | loss                   | NormalDistributionLoss | 0     
1 | logging_metrics        | ModuleList             | 0     
2 | embeddings             | MultiEmbedding         | 0     
3 | rnn                    | LSTM                   | 1.6 K 
4 | distribution_projector | Linear                 | 22    
------------------------------------------------------------------
1.6 K     Trainable params
0         Non-trainable params
1.6 K     Total params
0.006     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=150` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:  4.5min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name                   | Type                   | Params
------------------------------------------------------------------
0 | loss                   | NormalDistributionLoss | 0     
1 | logging_metrics        | ModuleList             | 0     
2 | embeddings             | MultiEmbedding         | 0     
3 | rnn                    | LSTM                   | 1.6 K 
4 | distribution_projector | Linear                 | 22    
------------------------------------------------------------------
1.6 K     Trainable params
0         Non-trainable params
1.6 K     Total params
0.006     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=150` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  6.9min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  6.9min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [19]:

metrics_deepar

Out[19]:

	segment	SMAPE	MAPE	MAE	fold_number
0	segment_a	11.457985	10.746764	58.296596	0
0	segment_a	3.176019	3.188004	16.515852	1
0	segment_a	7.292166	7.075430	38.055638	2
1	segment_b	8.014023	7.647102	20.117395	0
1	segment_b	4.404579	4.387297	10.633220	1
1	segment_b	5.720607	6.126162	13.026145	2
2	segment_c	6.136967	6.092227	10.315159	0
2	segment_c	4.311422	4.218119	7.638395	1
2	segment_c	9.405841	9.125036	16.484007	2
3	segment_d	5.807082	5.653967	50.962088	0
3	segment_d	4.531915	4.636140	36.712463	1
3	segment_d	3.950301	3.901850	31.104013	2

To summarize it we will take mean value of SMAPE metric because it is scale tolerant.

In [20]:

score = metrics_deepar["SMAPE"].mean()
print(f"Average SMAPE for DeepAR: {score:.3f}")

Average SMAPE for DeepAR: 6.184

Dataset Builder: creating dataset for DeepAR with etxtra features.¶

In [21]:

from pytorch_forecasting.data import GroupNormalizer

set_seed()

transform_date = DateFlagsTransform(day_number_in_week=True, day_number_in_month=False, out_column="dateflag")
num_lags = 10
transform_lag = LagTransform(
    in_column="target",
    lags=[HORIZON + i for i in range(num_lags)],
    out_column="target_lag",
)
lag_columns = [f"target_lag_{HORIZON+i}" for i in range(num_lags)]

dataset_builder_deepar = PytorchForecastingDatasetBuilder(
    max_encoder_length=HORIZON,
    max_prediction_length=HORIZON,
    time_varying_known_reals=["time_idx"] + lag_columns,
    time_varying_unknown_reals=["target"],
    time_varying_known_categoricals=["dateflag_day_number_in_week"],
    target_normalizer=GroupNormalizer(groups=["segment"]),
)

Now we are going to start backtest.

In [22]:

model_deepar = DeepARModel(
    dataset_builder=dataset_builder_deepar,
    trainer_params=dict(max_epochs=150, gradient_clip_val=0.1),
    lr=0.01,
    train_batch_size=64,
)

pipeline_deepar = Pipeline(
    model=model_deepar,
    horizon=HORIZON,
    transforms=[transform_lag, transform_date],
)

In [23]:

metrics_deepar, forecast_deepar, fold_info_deepar = pipeline_deepar.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name                   | Type                   | Params
------------------------------------------------------------------
0 | loss                   | NormalDistributionLoss | 0     
1 | logging_metrics        | ModuleList             | 0     
2 | embeddings             | MultiEmbedding         | 35    
3 | rnn                    | LSTM                   | 2.2 K 
4 | distribution_projector | Linear                 | 22    
------------------------------------------------------------------
2.3 K     Trainable params
0         Non-trainable params
2.3 K     Total params
0.009     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=150` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:  2.3min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name                   | Type                   | Params
------------------------------------------------------------------
0 | loss                   | NormalDistributionLoss | 0     
1 | logging_metrics        | ModuleList             | 0     
2 | embeddings             | MultiEmbedding         | 35    
3 | rnn                    | LSTM                   | 2.2 K 
4 | distribution_projector | Linear                 | 22    
------------------------------------------------------------------
2.3 K     Trainable params
0         Non-trainable params
2.3 K     Total params
0.009     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=150` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:  4.6min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name                   | Type                   | Params
------------------------------------------------------------------
0 | loss                   | NormalDistributionLoss | 0     
1 | logging_metrics        | ModuleList             | 0     
2 | embeddings             | MultiEmbedding         | 35    
3 | rnn                    | LSTM                   | 2.2 K 
4 | distribution_projector | Linear                 | 22    
------------------------------------------------------------------
2.3 K     Trainable params
0         Non-trainable params
2.3 K     Total params
0.009     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=150` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  7.0min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  7.0min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.5s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.5s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

Let's compare results across different segments.

In [24]:

metrics_deepar

Out[24]:

	segment	SMAPE	MAPE	MAE	fold_number
0	segment_a	7.796825	7.472601	39.812116	0
0	segment_a	3.667108	3.613067	18.643385	1
0	segment_a	4.231661	4.138719	22.416286	2
1	segment_b	6.644786	6.406091	16.496137	0
1	segment_b	3.708771	3.632007	9.208387	1
1	segment_b	3.485869	3.512980	8.107008	2
2	segment_c	4.850796	4.707044	8.339118	0
2	segment_c	5.969359	5.779788	10.466917	1
2	segment_c	5.508545	5.325093	10.010921	2
3	segment_d	4.996653	4.876972	42.090489	0
3	segment_d	3.922876	4.015897	31.788260	1
3	segment_d	3.240331	3.171267	27.756383	2

To summarize it we will take mean value of SMAPE metric because it is scale tolerant.

In [25]:

score = metrics_deepar["SMAPE"].mean()
print(f"Average SMAPE for DeepAR: {score:.3f}")

Average SMAPE for DeepAR: 4.835

Visualize results.

In [26]:

plot_backtest(forecast_deepar, ts, history_len=20)

3.3 DeepARNative ¶

It is recommended to use our native implementation of DeepAR, we will remove Pytorch Forecasting version in etna 3.0.0.

In [27]:

from etna.models.nn import DeepARNativeModel

In [28]:

scaler = StandardScalerTransform(in_column="target")
transform_date = DateFlagsTransform(day_number_in_week=True, day_number_in_month=False, out_column="dateflag")
segment_encoder = SegmentEncoderTransform()
label_encoder = LabelEncoderTransform(
    in_column="dateflag_day_number_in_week", strategy="none", out_column="dateflag_day_number_in_week_label"
)

embedding_sizes = {"dateflag_day_number_in_week": (7, 7), "segment_code": (4, 7)}

In [29]:

set_seed()

model_deepar_native = DeepARNativeModel(
    input_size=1,
    encoder_length=2 * HORIZON,
    decoder_length=HORIZON,
    embedding_sizes=embedding_sizes,
    lr=0.01,
    scale=False,
    n_samples=100,
    trainer_params=dict(max_epochs=20),
)

pipeline_deepar_native = Pipeline(
    model=model_deepar_native,
    horizon=HORIZON,
    transforms=[scaler, transform_date, segment_encoder, label_encoder],
)

In [30]:

metrics_deepar_native, forecast_deepar_native, fold_info_deepar_native = pipeline_deepar_native.backtest(
    ts, metrics=metrics, n_folds=3, n_jobs=1
)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | loss       | GaussianLoss   | 0     
1 | embedding  | MultiEmbedding | 91    
2 | rnn        | LSTM           | 4.3 K 
3 | projection | ModuleDict     | 34    
----------------------------------------------
4.4 K     Trainable params
0         Non-trainable params
4.4 K     Total params
0.018     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=20` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:   29.3s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | loss       | GaussianLoss   | 0     
1 | embedding  | MultiEmbedding | 91    
2 | rnn        | LSTM           | 4.3 K 
3 | projection | ModuleDict     | 34    
----------------------------------------------
4.4 K     Trainable params
0         Non-trainable params
4.4 K     Total params
0.018     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=20` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:   58.9s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | loss       | GaussianLoss   | 0     
1 | embedding  | MultiEmbedding | 91    
2 | rnn        | LSTM           | 4.3 K 
3 | projection | ModuleDict     | 34    
----------------------------------------------
4.4 K     Trainable params
0         Non-trainable params
4.4 K     Total params
0.018     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=20` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  1.5min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  1.5min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.8s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    1.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    1.3s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [31]:

score = metrics_deepar_native["SMAPE"].mean()
print(f"Average SMAPE for DeepARNative: {score:.3f}")

Average SMAPE for DeepARNative: 6.541

In [32]:

plot_backtest(forecast_deepar_native, ts, history_len=20)

3.4 TFT ¶

Let's move to the next model.

In [33]:

from etna.models.nn import TFTModel

In [34]:

set_seed()

Default way¶

In [35]:

model_tft = TFTModel(
    encoder_length=HORIZON,
    decoder_length=HORIZON,
    trainer_params=dict(max_epochs=200, gradient_clip_val=0.1),
    lr=0.01,
    train_batch_size=64,
)

pipeline_tft = Pipeline(
    model=model_tft,
    horizon=HORIZON,
)

In [36]:

metrics_tft, forecast_tft, fold_info_tft = pipeline_tft.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                               | Type                            | Params
----------------------------------------------------------------------------------------
0  | loss                               | QuantileLoss                    | 0     
1  | logging_metrics                    | ModuleList                      | 0     
2  | input_embeddings                   | MultiEmbedding                  | 0     
3  | prescalers                         | ModuleDict                      | 96    
4  | static_variable_selection          | VariableSelectionNetwork        | 1.7 K 
5  | encoder_variable_selection         | VariableSelectionNetwork        | 1.8 K 
6  | decoder_variable_selection         | VariableSelectionNetwork        | 1.2 K 
7  | static_context_variable_selection  | GatedResidualNetwork            | 1.1 K 
8  | static_context_initial_hidden_lstm | GatedResidualNetwork            | 1.1 K 
9  | static_context_initial_cell_lstm   | GatedResidualNetwork            | 1.1 K 
10 | static_context_enrichment          | GatedResidualNetwork            | 1.1 K 
11 | lstm_encoder                       | LSTM                            | 2.2 K 
12 | lstm_decoder                       | LSTM                            | 2.2 K 
13 | post_lstm_gate_encoder             | GatedLinearUnit                 | 544   
14 | post_lstm_add_norm_encoder         | AddNorm                         | 32    
15 | static_enrichment                  | GatedResidualNetwork            | 1.4 K 
16 | multihead_attn                     | InterpretableMultiHeadAttention | 676   
17 | post_attn_gate_norm                | GateAddNorm                     | 576   
18 | pos_wise_ff                        | GatedResidualNetwork            | 1.1 K 
19 | pre_output_gate_norm               | GateAddNorm                     | 576   
20 | output_layer                       | Linear                          | 119   
----------------------------------------------------------------------------------------
18.4 K    Trainable params
0         Non-trainable params
18.4 K    Total params
0.074     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=200` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:  4.6min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                               | Type                            | Params
----------------------------------------------------------------------------------------
0  | loss                               | QuantileLoss                    | 0     
1  | logging_metrics                    | ModuleList                      | 0     
2  | input_embeddings                   | MultiEmbedding                  | 0     
3  | prescalers                         | ModuleDict                      | 96    
4  | static_variable_selection          | VariableSelectionNetwork        | 1.7 K 
5  | encoder_variable_selection         | VariableSelectionNetwork        | 1.8 K 
6  | decoder_variable_selection         | VariableSelectionNetwork        | 1.2 K 
7  | static_context_variable_selection  | GatedResidualNetwork            | 1.1 K 
8  | static_context_initial_hidden_lstm | GatedResidualNetwork            | 1.1 K 
9  | static_context_initial_cell_lstm   | GatedResidualNetwork            | 1.1 K 
10 | static_context_enrichment          | GatedResidualNetwork            | 1.1 K 
11 | lstm_encoder                       | LSTM                            | 2.2 K 
12 | lstm_decoder                       | LSTM                            | 2.2 K 
13 | post_lstm_gate_encoder             | GatedLinearUnit                 | 544   
14 | post_lstm_add_norm_encoder         | AddNorm                         | 32    
15 | static_enrichment                  | GatedResidualNetwork            | 1.4 K 
16 | multihead_attn                     | InterpretableMultiHeadAttention | 676   
17 | post_attn_gate_norm                | GateAddNorm                     | 576   
18 | pos_wise_ff                        | GatedResidualNetwork            | 1.1 K 
19 | pre_output_gate_norm               | GateAddNorm                     | 576   
20 | output_layer                       | Linear                          | 119   
----------------------------------------------------------------------------------------
18.4 K    Trainable params
0         Non-trainable params
18.4 K    Total params
0.074     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=200` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:  9.4min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                               | Type                            | Params
----------------------------------------------------------------------------------------
0  | loss                               | QuantileLoss                    | 0     
1  | logging_metrics                    | ModuleList                      | 0     
2  | input_embeddings                   | MultiEmbedding                  | 0     
3  | prescalers                         | ModuleDict                      | 96    
4  | static_variable_selection          | VariableSelectionNetwork        | 1.7 K 
5  | encoder_variable_selection         | VariableSelectionNetwork        | 1.8 K 
6  | decoder_variable_selection         | VariableSelectionNetwork        | 1.2 K 
7  | static_context_variable_selection  | GatedResidualNetwork            | 1.1 K 
8  | static_context_initial_hidden_lstm | GatedResidualNetwork            | 1.1 K 
9  | static_context_initial_cell_lstm   | GatedResidualNetwork            | 1.1 K 
10 | static_context_enrichment          | GatedResidualNetwork            | 1.1 K 
11 | lstm_encoder                       | LSTM                            | 2.2 K 
12 | lstm_decoder                       | LSTM                            | 2.2 K 
13 | post_lstm_gate_encoder             | GatedLinearUnit                 | 544   
14 | post_lstm_add_norm_encoder         | AddNorm                         | 32    
15 | static_enrichment                  | GatedResidualNetwork            | 1.4 K 
16 | multihead_attn                     | InterpretableMultiHeadAttention | 676   
17 | post_attn_gate_norm                | GateAddNorm                     | 576   
18 | pos_wise_ff                        | GatedResidualNetwork            | 1.1 K 
19 | pre_output_gate_norm               | GateAddNorm                     | 576   
20 | output_layer                       | Linear                          | 119   
----------------------------------------------------------------------------------------
18.4 K    Trainable params
0         Non-trainable params
18.4 K    Total params
0.074     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=200` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed: 14.3min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed: 14.3min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [37]:

metrics_tft

Out[37]:

	segment	SMAPE	MAPE	MAE	fold_number
0	segment_a	40.672898	33.431255	181.536342	0
0	segment_a	9.250597	9.923689	47.444972	1
0	segment_a	9.813989	9.510262	51.294577	2
1	segment_b	32.807489	40.479604	96.606441	0
1	segment_b	29.624659	25.356150	64.590735	1
1	segment_b	7.350867	7.605594	16.847937	2
2	segment_c	67.610710	103.117201	175.320701	0
2	segment_c	7.182262	7.453978	12.599984	1
2	segment_c	9.692566	9.306065	17.481020	2
3	segment_d	83.180637	58.408386	509.964892	0
3	segment_d	37.934285	31.318080	263.853646	1
3	segment_d	22.102685	19.706220	174.857779	2

In [38]:

score = metrics_tft["SMAPE"].mean()
print(f"Average SMAPE for TFT: {score:.3f}")

Average SMAPE for TFT: 29.769

Dataset Builder¶

In [39]:

set_seed()

transform_date = DateFlagsTransform(day_number_in_week=True, day_number_in_month=False, out_column="dateflag")
num_lags = 10
transform_lag = LagTransform(
    in_column="target",
    lags=[HORIZON + i for i in range(num_lags)],
    out_column="target_lag",
)
lag_columns = [f"target_lag_{HORIZON+i}" for i in range(num_lags)]

dataset_builder_tft = PytorchForecastingDatasetBuilder(
    max_encoder_length=HORIZON,
    max_prediction_length=HORIZON,
    time_varying_known_reals=["time_idx"],
    time_varying_unknown_reals=["target"],
    time_varying_known_categoricals=["dateflag_day_number_in_week"],
    static_categoricals=["segment"],
    target_normalizer=GroupNormalizer(groups=["segment"]),
)

In [40]:

model_tft = TFTModel(
    dataset_builder=dataset_builder_tft,
    trainer_params=dict(max_epochs=200, gradient_clip_val=0.1),
    lr=0.01,
    train_batch_size=64,
)

pipeline_tft = Pipeline(
    model=model_tft,
    horizon=HORIZON,
    transforms=[transform_lag, transform_date],
)

In [41]:

metrics_tft, forecast_tft, fold_info_tft = pipeline_tft.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                               | Type                            | Params
----------------------------------------------------------------------------------------
0  | loss                               | QuantileLoss                    | 0     
1  | logging_metrics                    | ModuleList                      | 0     
2  | input_embeddings                   | MultiEmbedding                  | 47    
3  | prescalers                         | ModuleDict                      | 96    
4  | static_variable_selection          | VariableSelectionNetwork        | 1.8 K 
5  | encoder_variable_selection         | VariableSelectionNetwork        | 1.9 K 
6  | decoder_variable_selection         | VariableSelectionNetwork        | 1.3 K 
7  | static_context_variable_selection  | GatedResidualNetwork            | 1.1 K 
8  | static_context_initial_hidden_lstm | GatedResidualNetwork            | 1.1 K 
9  | static_context_initial_cell_lstm   | GatedResidualNetwork            | 1.1 K 
10 | static_context_enrichment          | GatedResidualNetwork            | 1.1 K 
11 | lstm_encoder                       | LSTM                            | 2.2 K 
12 | lstm_decoder                       | LSTM                            | 2.2 K 
13 | post_lstm_gate_encoder             | GatedLinearUnit                 | 544   
14 | post_lstm_add_norm_encoder         | AddNorm                         | 32    
15 | static_enrichment                  | GatedResidualNetwork            | 1.4 K 
16 | multihead_attn                     | InterpretableMultiHeadAttention | 676   
17 | post_attn_gate_norm                | GateAddNorm                     | 576   
18 | pos_wise_ff                        | GatedResidualNetwork            | 1.1 K 
19 | pre_output_gate_norm               | GateAddNorm                     | 576   
20 | output_layer                       | Linear                          | 119   
----------------------------------------------------------------------------------------
18.9 K    Trainable params
0         Non-trainable params
18.9 K    Total params
0.075     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=200` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:  4.9min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                               | Type                            | Params
----------------------------------------------------------------------------------------
0  | loss                               | QuantileLoss                    | 0     
1  | logging_metrics                    | ModuleList                      | 0     
2  | input_embeddings                   | MultiEmbedding                  | 47    
3  | prescalers                         | ModuleDict                      | 96    
4  | static_variable_selection          | VariableSelectionNetwork        | 1.8 K 
5  | encoder_variable_selection         | VariableSelectionNetwork        | 1.9 K 
6  | decoder_variable_selection         | VariableSelectionNetwork        | 1.3 K 
7  | static_context_variable_selection  | GatedResidualNetwork            | 1.1 K 
8  | static_context_initial_hidden_lstm | GatedResidualNetwork            | 1.1 K 
9  | static_context_initial_cell_lstm   | GatedResidualNetwork            | 1.1 K 
10 | static_context_enrichment          | GatedResidualNetwork            | 1.1 K 
11 | lstm_encoder                       | LSTM                            | 2.2 K 
12 | lstm_decoder                       | LSTM                            | 2.2 K 
13 | post_lstm_gate_encoder             | GatedLinearUnit                 | 544   
14 | post_lstm_add_norm_encoder         | AddNorm                         | 32    
15 | static_enrichment                  | GatedResidualNetwork            | 1.4 K 
16 | multihead_attn                     | InterpretableMultiHeadAttention | 676   
17 | post_attn_gate_norm                | GateAddNorm                     | 576   
18 | pos_wise_ff                        | GatedResidualNetwork            | 1.1 K 
19 | pre_output_gate_norm               | GateAddNorm                     | 576   
20 | output_layer                       | Linear                          | 119   
----------------------------------------------------------------------------------------
18.9 K    Trainable params
0         Non-trainable params
18.9 K    Total params
0.075     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=200` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed: 10.2min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                               | Type                            | Params
----------------------------------------------------------------------------------------
0  | loss                               | QuantileLoss                    | 0     
1  | logging_metrics                    | ModuleList                      | 0     
2  | input_embeddings                   | MultiEmbedding                  | 47    
3  | prescalers                         | ModuleDict                      | 96    
4  | static_variable_selection          | VariableSelectionNetwork        | 1.8 K 
5  | encoder_variable_selection         | VariableSelectionNetwork        | 1.9 K 
6  | decoder_variable_selection         | VariableSelectionNetwork        | 1.3 K 
7  | static_context_variable_selection  | GatedResidualNetwork            | 1.1 K 
8  | static_context_initial_hidden_lstm | GatedResidualNetwork            | 1.1 K 
9  | static_context_initial_cell_lstm   | GatedResidualNetwork            | 1.1 K 
10 | static_context_enrichment          | GatedResidualNetwork            | 1.1 K 
11 | lstm_encoder                       | LSTM                            | 2.2 K 
12 | lstm_decoder                       | LSTM                            | 2.2 K 
13 | post_lstm_gate_encoder             | GatedLinearUnit                 | 544   
14 | post_lstm_add_norm_encoder         | AddNorm                         | 32    
15 | static_enrichment                  | GatedResidualNetwork            | 1.4 K 
16 | multihead_attn                     | InterpretableMultiHeadAttention | 676   
17 | post_attn_gate_norm                | GateAddNorm                     | 576   
18 | pos_wise_ff                        | GatedResidualNetwork            | 1.1 K 
19 | pre_output_gate_norm               | GateAddNorm                     | 576   
20 | output_layer                       | Linear                          | 119   
----------------------------------------------------------------------------------------
18.9 K    Trainable params
0         Non-trainable params
18.9 K    Total params
0.075     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=200` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed: 15.4min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed: 15.4min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [42]:

metrics_tft

Out[42]:

	segment	SMAPE	MAPE	MAE	fold_number
0	segment_a	4.954594	4.861804	25.372825	0
0	segment_a	7.754915	7.631246	39.995815	1
0	segment_a	4.072187	3.931299	22.857274	2
1	segment_b	5.653733	5.452502	14.249708	0
1	segment_b	5.565292	5.428447	13.956488	1
1	segment_b	3.886476	3.999029	9.210266	2
2	segment_c	3.815528	3.743413	6.616340	0
2	segment_c	4.531915	4.425449	8.114482	1
2	segment_c	7.780429	7.491119	14.045940	2
3	segment_d	8.103217	7.994725	68.973964	0
3	segment_d	4.470993	4.635054	36.701948	1
3	segment_d	4.929895	4.782845	42.947946	2

In [43]:

score = metrics_tft["SMAPE"].mean()
print(f"Average SMAPE for TFT: {score:.3f}")

Average SMAPE for TFT: 5.460

In [44]:

plot_backtest(forecast_tft, ts, history_len=20)

3.5 TFTNative ¶

It is recommended to use our native implementation of TFT, we will remove Pytorch Forecasting version in etna 3.0.0.

In [45]:

from etna.models.nn import TFTNativeModel

In [46]:

num_lags = 6
lag_columns = [f"target_lag_{HORIZON+i}" for i in range(num_lags)]
transform_lag = LagTransform(
    in_column="target",
    lags=[HORIZON + i for i in range(num_lags)],
    out_column="target_lag",
)

transform_date = DateFlagsTransform(day_number_in_week=True, day_number_in_month=False, out_column="dateflag")

std = StandardScalerTransform(in_column=["target"])

encoder = SegmentEncoderTransform()
label_encoder = LabelEncoderTransform(
    in_column="dateflag_day_number_in_week", strategy="none", out_column="dateflag_day_number_in_week_label"
)

In [47]:

set_seed()

model_tft_native = TFTNativeModel(
    encoder_length=HORIZON,
    decoder_length=HORIZON,
    static_categoricals=["segment_code"],
    time_varying_categoricals_encoder=["dateflag_day_number_in_week_label"],
    time_varying_categoricals_decoder=["dateflag_day_number_in_week_label"],
    time_varying_reals_encoder=["target"] + lag_columns,
    time_varying_reals_decoder=lag_columns,
    num_embeddings={"segment_code": len(ts.segments), "dateflag_day_number_in_week_label": 7},
    n_heads=4,
    num_layers=2,
    hidden_size=64,
    lr=0.0001,
    train_batch_size=64,
    trainer_params=dict(max_epochs=15, gradient_clip_val=0.1),
)
pipeline_tft_native = Pipeline(
    model=model_tft_native, horizon=HORIZON, transforms=[std, transform_lag, transform_date, encoder, label_encoder]
)

In [48]:

metrics_tft_native, forecast_tft_native, fold_info_tft_native = pipeline_tft_native.backtest(
    ts, metrics=metrics, n_folds=3, n_jobs=1
)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                            | Type                     | Params
------------------------------------------------------------------------------
0  | loss                            | MSELoss                  | 0     
1  | static_scalers                  | ModuleDict               | 0     
2  | static_embeddings               | ModuleDict               | 320   
3  | time_varying_scalers_encoder    | ModuleDict               | 896   
4  | time_varying_embeddings_encoder | ModuleDict               | 512   
5  | time_varying_scalers_decoder    | ModuleDict               | 768   
6  | time_varying_embeddings_decoder | ModuleDict               | 512   
7  | static_variable_selection       | VariableSelectionNetwork | 25.3 K
8  | encoder_variable_selection      | VariableSelectionNetwork | 704 K 
9  | decoder_variable_selection      | VariableSelectionNetwork | 557 K 
10 | static_covariate_encoder        | StaticCovariateEncoder   | 67.1 K
11 | lstm_encoder                    | LSTM                     | 66.6 K
12 | lstm_decoder                    | LSTM                     | 66.6 K
13 | gated_norm1                     | GateAddNorm              | 8.4 K 
14 | temporal_fusion_decoder         | TemporalFusionDecoder    | 62.7 K
15 | gated_norm2                     | GateAddNorm              | 8.4 K 
16 | output_fc                       | Linear                   | 65    
------------------------------------------------------------------------------
1.6 M     Trainable params
0         Non-trainable params
1.6 M     Total params
6.282     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=15` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:   38.1s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                            | Type                     | Params
------------------------------------------------------------------------------
0  | loss                            | MSELoss                  | 0     
1  | static_scalers                  | ModuleDict               | 0     
2  | static_embeddings               | ModuleDict               | 320   
3  | time_varying_scalers_encoder    | ModuleDict               | 896   
4  | time_varying_embeddings_encoder | ModuleDict               | 512   
5  | time_varying_scalers_decoder    | ModuleDict               | 768   
6  | time_varying_embeddings_decoder | ModuleDict               | 512   
7  | static_variable_selection       | VariableSelectionNetwork | 25.3 K
8  | encoder_variable_selection      | VariableSelectionNetwork | 704 K 
9  | decoder_variable_selection      | VariableSelectionNetwork | 557 K 
10 | static_covariate_encoder        | StaticCovariateEncoder   | 67.1 K
11 | lstm_encoder                    | LSTM                     | 66.6 K
12 | lstm_decoder                    | LSTM                     | 66.6 K
13 | gated_norm1                     | GateAddNorm              | 8.4 K 
14 | temporal_fusion_decoder         | TemporalFusionDecoder    | 62.7 K
15 | gated_norm2                     | GateAddNorm              | 8.4 K 
16 | output_fc                       | Linear                   | 65    
------------------------------------------------------------------------------
1.6 M     Trainable params
0         Non-trainable params
1.6 M     Total params
6.282     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=15` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:  1.3min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

   | Name                            | Type                     | Params
------------------------------------------------------------------------------
0  | loss                            | MSELoss                  | 0     
1  | static_scalers                  | ModuleDict               | 0     
2  | static_embeddings               | ModuleDict               | 320   
3  | time_varying_scalers_encoder    | ModuleDict               | 896   
4  | time_varying_embeddings_encoder | ModuleDict               | 512   
5  | time_varying_scalers_decoder    | ModuleDict               | 768   
6  | time_varying_embeddings_decoder | ModuleDict               | 512   
7  | static_variable_selection       | VariableSelectionNetwork | 25.3 K
8  | encoder_variable_selection      | VariableSelectionNetwork | 704 K 
9  | decoder_variable_selection      | VariableSelectionNetwork | 557 K 
10 | static_covariate_encoder        | StaticCovariateEncoder   | 67.1 K
11 | lstm_encoder                    | LSTM                     | 66.6 K
12 | lstm_decoder                    | LSTM                     | 66.6 K
13 | gated_norm1                     | GateAddNorm              | 8.4 K 
14 | temporal_fusion_decoder         | TemporalFusionDecoder    | 62.7 K
15 | gated_norm2                     | GateAddNorm              | 8.4 K 
16 | output_fc                       | Linear                   | 65    
------------------------------------------------------------------------------
1.6 M     Trainable params
0         Non-trainable params
1.6 M     Total params
6.282     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=15` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  2.0min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  2.0min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [49]:

score = metrics_tft_native["SMAPE"].mean()
print(f"Average SMAPE for TFTNative: {score:.3f}")

Average SMAPE for TFTNative: 6.420

In [50]:

plot_backtest(forecast_tft_native, ts, history_len=20)

3.6 RNN ¶

We'll use RNN model based on LSTM cell

In [51]:

from etna.models.nn import RNNModel

In [52]:

num_lags = 10
scaler = StandardScalerTransform(in_column="target")
transform_lag = LagTransform(
    in_column="target",
    lags=[HORIZON + i for i in range(num_lags)],
    out_column="target_lag",
)
transform_date = DateFlagsTransform(day_number_in_week=True, day_number_in_month=False, out_column="dateflag")
segment_encoder = SegmentEncoderTransform()
label_encoder = LabelEncoderTransform(
    in_column="dateflag_day_number_in_week", strategy="none", out_column="dateflag_day_number_in_week_label"
)

embedding_sizes = {"dateflag_day_number_in_week": (7, 7), "segment_code": (4, 7)}

In [53]:

set_seed()

model_rnn = RNNModel(
    input_size=11,
    encoder_length=2 * HORIZON,
    decoder_length=HORIZON,
    embedding_sizes=embedding_sizes,
    trainer_params=dict(max_epochs=5),
    lr=1e-3,
)

pipeline_rnn = Pipeline(
    model=model_rnn,
    horizon=HORIZON,
    transforms=[scaler, transform_lag, transform_date, segment_encoder, label_encoder],
)

In [54]:

metrics_rnn, forecast_rnn, fold_info_rnn = pipeline_rnn.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | loss       | MSELoss        | 0     
1 | embedding  | MultiEmbedding | 91    
2 | rnn        | LSTM           | 4.9 K 
3 | projection | Linear         | 17    
----------------------------------------------
5.0 K     Trainable params
0         Non-trainable params
5.0 K     Total params
0.020     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=5` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    6.9s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | loss       | MSELoss        | 0     
1 | embedding  | MultiEmbedding | 91    
2 | rnn        | LSTM           | 4.9 K 
3 | projection | Linear         | 17    
----------------------------------------------
5.0 K     Trainable params
0         Non-trainable params
5.0 K     Total params
0.020     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=5` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:   13.8s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | loss       | MSELoss        | 0     
1 | embedding  | MultiEmbedding | 91    
2 | rnn        | LSTM           | 4.9 K 
3 | projection | Linear         | 17    
----------------------------------------------
5.0 K     Trainable params
0         Non-trainable params
5.0 K     Total params
0.020     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=5` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:   21.5s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:   21.5s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [55]:

score = metrics_rnn["SMAPE"].mean()
print(f"Average SMAPE for LSTM: {score:.3f}")

Average SMAPE for LSTM: 5.836

In [56]:

plot_backtest(forecast_rnn, ts, history_len=20)

3.7 MLP ¶

Base model with linear layers and activations.

In [57]:

from etna.models.nn import MLPModel

In [58]:

num_lags = 14
transform_lag = LagTransform(
    in_column="target",
    lags=[HORIZON + i for i in range(num_lags)],
    out_column="target_lag",
)
transform_date = DateFlagsTransform(day_number_in_week=True, day_number_in_month=False, out_column="dateflag")
segment_encoder = SegmentEncoderTransform()
label_encoder = LabelEncoderTransform(
    in_column="dateflag_day_number_in_week", strategy="none", out_column="dateflag_day_number_in_week_label"
)
lag_columns = [f"target_lag_{HORIZON+i}" for i in range(num_lags)]
embedding_sizes = {"dateflag_day_number_in_week": (7, 7), "segment_code": (4, 7), "dateflag_is_weekend": (2, 5)}

In [59]:

set_seed()

model_mlp = MLPModel(
    input_size=14,
    hidden_size=[16],
    embedding_sizes=embedding_sizes,
    decoder_length=HORIZON,
    trainer_params=dict(max_epochs=50, gradient_clip_val=0.1),
    lr=0.01,
    train_batch_size=64,
)
metrics = [SMAPE(), MAPE(), MAE()]

pipeline_mlp = Pipeline(
    model=model_mlp, transforms=[transform_lag, transform_date, segment_encoder, label_encoder], horizon=HORIZON
)

In [60]:

metrics_mlp, forecast_mlp, fold_info_mlp = pipeline_mlp.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name      | Type           | Params
---------------------------------------------
0 | loss      | MSELoss        | 0     
1 | embedding | MultiEmbedding | 106   
2 | mlp       | Sequential     | 561   
---------------------------------------------
667       Trainable params
0         Non-trainable params
667       Total params
0.003     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=50` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    2.6s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name      | Type           | Params
---------------------------------------------
0 | loss      | MSELoss        | 0     
1 | embedding | MultiEmbedding | 106   
2 | mlp       | Sequential     | 561   
---------------------------------------------
667       Trainable params
0         Non-trainable params
667       Total params
0.003     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=50` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    5.4s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name      | Type           | Params
---------------------------------------------
0 | loss      | MSELoss        | 0     
1 | embedding | MultiEmbedding | 106   
2 | mlp       | Sequential     | 561   
---------------------------------------------
667       Trainable params
0         Non-trainable params
667       Total params
0.003     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=50` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    8.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    8.1s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.3s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [61]:

score = metrics_mlp["SMAPE"].mean()
print(f"Average SMAPE for MLP: {score:.3f}")

Average SMAPE for MLP: 6.141

In [62]:

plot_backtest(forecast_mlp, ts, history_len=20)

3.8 Deep State Model ¶

Deep State Model works well with multiple similar time-series. It inffers shared patterns from them.

We have to determine the type of seasonality in data (based on data granularity), SeasonalitySSM class is responsible for this. In this example, we have daily data, so we use day-of-week (7 seasons) and day-of-month (31 seasons) models. We also set the trend component using the LevelTrendSSM class. Also in the model we use time-based features like day-of-week, day-of-month and time independent feature representing the segment of time series.

In [63]:

from etna.models.nn import DeepStateModel
from etna.models.nn.deepstate import CompositeSSM
from etna.models.nn.deepstate import LevelTrendSSM
from etna.models.nn.deepstate import SeasonalitySSM

In [64]:

num_lags = 7
transforms = [
    SegmentEncoderTransform(),
    StandardScalerTransform(in_column="target"),
    DateFlagsTransform(
        day_number_in_week=True,
        day_number_in_month=True,
        week_number_in_month=False,
        week_number_in_year=False,
        month_number_in_year=False,
        year_number=False,
        is_weekend=False,
        out_column="dateflag",
    ),
    LagTransform(
        in_column="target",
        lags=[HORIZON + i for i in range(num_lags)],
        out_column="target_lag",
    ),
]


embedding_sizes = {
    "dateflag_day_number_in_week": (7, 7),
    "dateflag_day_number_in_month": (31, 7),
    "segment_code": (4, 7),
}

In [65]:

monthly_smm = SeasonalitySSM(num_seasons=31, timestamp_transform=lambda x: x.day - 1)
weekly_smm = SeasonalitySSM(num_seasons=7, timestamp_transform=lambda x: x.weekday())

In [66]:

set_seed()

model_dsm = DeepStateModel(
    ssm=CompositeSSM(seasonal_ssms=[weekly_smm, monthly_smm], nonseasonal_ssm=LevelTrendSSM()),
    decoder_length=HORIZON,
    encoder_length=2 * HORIZON,
    embedding_sizes=embedding_sizes,
    input_size=7,
    trainer_params=dict(max_epochs=5),
    lr=1e-3,
)

pipeline_dsm = Pipeline(
    model=model_dsm,
    horizon=HORIZON,
    transforms=transforms,
)

In [67]:

metrics_dsm, forecast_dsm, fold_info_dsm = pipeline_dsm.backtest(ts, metrics=metrics, n_folds=3, n_jobs=1)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | embedding  | MultiEmbedding | 315   
1 | RNN        | LSTM           | 11.2 K
2 | projectors | ModuleDict     | 5.0 K 
----------------------------------------------
16.5 K    Trainable params
0         Non-trainable params
16.5 K    Total params
0.066     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=5` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:   15.7s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | embedding  | MultiEmbedding | 315   
1 | RNN        | LSTM           | 11.2 K
2 | projectors | ModuleDict     | 5.0 K 
----------------------------------------------
16.5 K    Trainable params
0         Non-trainable params
16.5 K    Total params
0.066     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=5` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:   31.8s
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type           | Params
----------------------------------------------
0 | embedding  | MultiEmbedding | 315   
1 | RNN        | LSTM           | 11.2 K
2 | projectors | ModuleDict     | 5.0 K 
----------------------------------------------
16.5 K    Trainable params
0         Non-trainable params
16.5 K    Total params
0.066     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=5` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:   48.6s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:   48.6s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.4s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [68]:

score = metrics_dsm["SMAPE"].mean()
print(f"Average SMAPE for DeepStateModel: {score:.3f}")

Average SMAPE for DeepStateModel: 5.309

In [69]:

plot_backtest(forecast_dsm, ts, history_len=20)

3.9 N-BEATS Model ¶

This architecture is based on backward and forward residual links and a deep stack of fully connected layers.

There are two types of models in the library. The NBeatsGenericModel class implements a generic deep learning model, while the NBeatsInterpretableModel is augmented with certain inductive biases to be interpretable (trend and seasonality).

In [70]:

from etna.models.nn import NBeatsGenericModel
from etna.models.nn import NBeatsInterpretableModel

In [71]:

set_seed()

model_nbeats_generic = NBeatsGenericModel(
    input_size=2 * HORIZON,
    output_size=HORIZON,
    loss="smape",
    stacks=30,
    layers=4,
    layer_size=256,
    trainer_params=dict(max_epochs=1000),
    lr=1e-3,
)

pipeline_nbeats_generic = Pipeline(
    model=model_nbeats_generic,
    horizon=HORIZON,
    transforms=[],
)

In [72]:

metrics_nbeats_generic, forecast_nbeats_generic, _ = pipeline_nbeats_generic.backtest(
    ts, metrics=metrics, n_folds=3, n_jobs=1
)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name  | Type        | Params
--------------------------------------
0 | model | NBeats      | 206 K 
1 | loss  | NBeatsSMAPE | 0     
--------------------------------------
206 K     Trainable params
0         Non-trainable params
206 K     Total params
0.826     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=1000` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:  1.2min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name  | Type        | Params
--------------------------------------
0 | model | NBeats      | 206 K 
1 | loss  | NBeatsSMAPE | 0     
--------------------------------------
206 K     Trainable params
0         Non-trainable params
206 K     Total params
0.826     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=1000` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:  2.4min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name  | Type        | Params
--------------------------------------
0 | model | NBeats      | 206 K 
1 | loss  | NBeatsSMAPE | 0     
--------------------------------------
206 K     Trainable params
0         Non-trainable params
206 K     Total params
0.826     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=1000` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  3.6min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  3.6min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [73]:

score = metrics_nbeats_generic["SMAPE"].mean()
print(f"Average SMAPE for N-BEATS Generic: {score:.3f}")

Average SMAPE for N-BEATS Generic: 5.545

In [74]:

plot_backtest(forecast_nbeats_generic, ts, history_len=20)

In [75]:

model_nbeats_interp = NBeatsInterpretableModel(
    input_size=4 * HORIZON,
    output_size=HORIZON,
    loss="smape",
    trend_layer_size=64,
    seasonality_layer_size=256,
    trainer_params=dict(max_epochs=2000),
    lr=1e-3,
)

pipeline_nbeats_interp = Pipeline(
    model=model_nbeats_interp,
    horizon=HORIZON,
    transforms=[],
)

In [76]:

metrics_nbeats_interp, forecast_nbeats_interp, _ = pipeline_nbeats_interp.backtest(
    ts, metrics=metrics, n_folds=3, n_jobs=1
)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name  | Type        | Params
--------------------------------------
0 | model | NBeats      | 224 K 
1 | loss  | NBeatsSMAPE | 0     
--------------------------------------
223 K     Trainable params
385       Non-trainable params
224 K     Total params
0.896     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=2000` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:  1.6min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name  | Type        | Params
--------------------------------------
0 | model | NBeats      | 224 K 
1 | loss  | NBeatsSMAPE | 0     
--------------------------------------
223 K     Trainable params
385       Non-trainable params
224 K     Total params
0.896     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=2000` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:  3.2min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name  | Type        | Params
--------------------------------------
0 | model | NBeats      | 224 K 
1 | loss  | NBeatsSMAPE | 0     
--------------------------------------
223 K     Trainable params
385       Non-trainable params
224 K     Total params
0.896     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=2000` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  4.8min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:  4.8min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [77]:

score = metrics_nbeats_interp["SMAPE"].mean()
print(f"Average SMAPE for N-BEATS Interpretable: {score:.3f}")

Average SMAPE for N-BEATS Interpretable: 5.512

In [78]:

plot_backtest(forecast_nbeats_interp, ts, history_len=20)

3.10 PatchTS Model ¶

Model with transformer encoder that uses patches of timeseries as input words and linear decoder.

In [79]:

from etna.models.nn import PatchTSModel

In [80]:

set_seed()

model_patchts = PatchTSModel(
    decoder_length=HORIZON,
    encoder_length=2 * HORIZON,
    patch_len=1,
    trainer_params=dict(max_epochs=100),
    lr=1e-3,
)

pipeline_patchts = Pipeline(
    model=model_patchts, horizon=HORIZON, transforms=[StandardScalerTransform(in_column="target")]
)

metrics_patchts, forecast_patchts, fold_info_patchs = pipeline_patchts.backtest(
    ts, metrics=metrics, n_folds=3, n_jobs=1
)

GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type       | Params
------------------------------------------
0 | loss       | MSELoss    | 0     
1 | model      | Sequential | 397 K 
2 | projection | Sequential | 1.8 K 
------------------------------------------
399 K     Trainable params
0         Non-trainable params
399 K     Total params
1.598     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=100` reached.
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:  9.0min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type       | Params
------------------------------------------
0 | loss       | MSELoss    | 0     
1 | model      | Sequential | 397 K 
2 | projection | Sequential | 1.8 K 
------------------------------------------
399 K     Trainable params
0         Non-trainable params
399 K     Total params
1.598     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=100` reached.
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed: 18.3min
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs

  | Name       | Type       | Params
------------------------------------------
0 | loss       | MSELoss    | 0     
1 | model      | Sequential | 397 K 
2 | projection | Sequential | 1.8 K 
------------------------------------------
399 K     Trainable params
0         Non-trainable params
399 K     Total params
1.598     Total estimated model params size (MB)

Training: 0it [00:00, ?it/s]

`Trainer.fit` stopped: `max_epochs=100` reached.
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed: 27.8min
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed: 27.8min
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.2s
[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:    0.0s
[Parallel(n_jobs=1)]: Done   2 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s
[Parallel(n_jobs=1)]: Done   3 tasks      | elapsed:    0.1s

In [81]:

score = metrics_patchts["SMAPE"].mean()
print(f"Average SMAPE for PatchTS: {score:.3f}")

Average SMAPE for PatchTS: 5.559

In [82]:

plot_backtest(forecast_patchts, ts, history_len=20)