In [18]:
import numpy as np
from scipy.io import loadmat
from sklearn.linear_model import LinearRegression
from sklearn.decomposition import PCA
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error,explained_variance_score
from lightgbm import LGBMRegressor
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import train_test_split
from sklearn.neural_network import MLPRegressor
from sklearn.datasets import load_boston
from keras.wrappers.scikit_learn import KerasRegressor
from keras.models import Sequential
from keras.layers import Dense,Dropout
import keras
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
In [19]:
scaler = StandardScaler()
forest = RandomForestRegressor(n_estimators=100,n_jobs=-1)
linreg = LinearRegression(normalize=True)
boosting = LGBMRegressor()
pca = PCA(3)
Цель вычислительного эксперимента:¶
Необходимо решить задачу регрессии с использованием моделей: линейная регрессия, линейная регрессия + метод главных компонент, простая нейросеть и критериями качества: квадратичная ошибка, число обусловленности.
Описание выборок:¶
Используется датасет ECoG (electrocorticographic data), уже разбитый на выборки обучение/контроль.
Блок загрузки и предобработки выборок:¶
In [20]:
X_train = loadmat('ECoG_X_train.mat')['X_train']
y_train = loadmat('ECoG_Y_train.mat')['Y_train']
X_test = loadmat('ECoG_X_test.mat')['X_hold_out']
y_test = loadmat('ECoG_Y_test.mat')['Y_hold_out']
In [21]:
X_train.shape
Out[21]:
(12801, 32, 27)
In [22]:
y_train.shape
Out[22]:
(12801, 3)
In [23]:
X_test.shape
Out[23]:
(6087, 32, 27)
In [24]:
y_test.shape
Out[24]:
(6087, 3)
Объектами X_train, X_test являются матрицы 32x27. Преобразуем их в одномерные векторы:
In [25]:
X_train = np.array([i.flatten() for i in X_train])
X_test = np.array([i.flatten() for i in X_test])
Анализ пропусков¶
In [26]:
np.isnan(X_train).any()
Out[26]:
False
In [27]:
np.isnan(y_train).any()
Out[27]:
False
Данная выборка не имеет пропусков.
Список моделей¶
Для решения поставленной задачи используются следующие модели:
- линейная регрессия
- PCA + линейная регрессия
- простая нейросеть
Список критериев качетсва:¶
- mean squared error
- variance score
Структурные параметры нейронной сети:¶
- число и состав признаков
- размерность скрытого пространства
- структура сети
Способ разбиения выборки на обучение-контроль:¶
Данные уже разбиты на 2 выборки.
Линейная регрессия:¶
In [28]:
model = linreg
pipe = Pipeline(steps=[('model', model)])
In [29]:
pipe.fit(X_train,y_train)
Out[29]:
Pipeline(memory=None,
steps=[('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True))])
In [30]:
res = pipe.predict(X_test)
mse = mean_squared_error(res,y_test)
varience = explained_variance_score(y_test,res)
print(mse,varience)
1786.7787691924393 0.0703714702511374
Линейная регрессия c PCA до 80 компонент¶
In [31]:
model = linreg
pca = PCA(n_components=80)
pipe = Pipeline(steps=[('pca',pca),('model', model)])
In [32]:
pipe.fit(X_train,y_train)
Out[32]:
Pipeline(memory=None,
steps=[('pca', PCA(copy=True, iterated_power='auto', n_components=80, random_state=None,
svd_solver='auto', tol=0.0, whiten=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True))])
In [33]:
res = pipe.predict(X_test)
mse = mean_squared_error(res,y_test)
varience = explained_variance_score(y_test,res)
print(mse,varience)
1634.9602130184223 0.1467494360544288
Нейронная сеть¶
In [34]:
def big_model():
model = Sequential()
model.add(Dense(512, input_dim=864, kernel_initializer='normal',
activation='relu',kernel_regularizer=keras.regularizers.l2(0.01)))
model.add(Dense(256, kernel_initializer='normal', activation='relu',
kernel_regularizer=keras.regularizers.l2(0.01)))
model.add(Dense(3, kernel_initializer='normal'))
# Compile model
model.compile(loss='mean_squared_error', optimizer='rmsprop')
return model
In [35]:
neural_net = KerasRegressor(big_model,epochs=100, batch_size=200,verbose=1)
model = neural_net
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
In [36]:
pipe.fit(X_train,y_train)
Epoch 1/100 12801/12801 [==============================] - 2s 178us/step - loss: 13826.9416 Epoch 2/100 12801/12801 [==============================] - 2s 145us/step - loss: 4106.8769 Epoch 3/100 12801/12801 [==============================] - 2s 143us/step - loss: 3307.4679 Epoch 4/100 12801/12801 [==============================] - 2s 145us/step - loss: 3014.8762 Epoch 5/100 12801/12801 [==============================] - 2s 142us/step - loss: 2704.6778 Epoch 6/100 12801/12801 [==============================] - 2s 147us/step - loss: 2511.1328 Epoch 7/100 12801/12801 [==============================] - 2s 146us/step - loss: 2389.2103 Epoch 8/100 12801/12801 [==============================] - 2s 146us/step - loss: 2233.0734 Epoch 9/100 12801/12801 [==============================] - 2s 149us/step - loss: 2113.7736 Epoch 10/100 12801/12801 [==============================] - 2s 158us/step - loss: 2028.6532 Epoch 11/100 12801/12801 [==============================] - 2s 147us/step - loss: 1898.8530 Epoch 12/100 12801/12801 [==============================] - 2s 148us/step - loss: 1864.5661 Epoch 13/100 12801/12801 [==============================] - 2s 162us/step - loss: 1776.9549 Epoch 14/100 12801/12801 [==============================] - 2s 156us/step - loss: 1701.9742 Epoch 15/100 12801/12801 [==============================] - 2s 170us/step - loss: 1652.2706 Epoch 16/100 12801/12801 [==============================] - 2s 140us/step - loss: 1591.3517 Epoch 17/100 12801/12801 [==============================] - 2s 139us/step - loss: 1516.2855 Epoch 18/100 12801/12801 [==============================] - 2s 169us/step - loss: 1479.7010 Epoch 19/100 12801/12801 [==============================] - 2s 133us/step - loss: 1395.4281 Epoch 20/100 12801/12801 [==============================] - 2s 180us/step - loss: 1366.5875 Epoch 21/100 12801/12801 [==============================] - 1s 112us/step - loss: 1285.3563 Epoch 22/100 12801/12801 [==============================] - 1s 110us/step - loss: 1267.7612 Epoch 23/100 12801/12801 [==============================] - 2s 160us/step - loss: 1239.2720 Epoch 24/100 12801/12801 [==============================] - 2s 156us/step - loss: 1162.5306 Epoch 25/100 12801/12801 [==============================] - 2s 193us/step - loss: 1151.1756 Epoch 26/100 12801/12801 [==============================] - 3s 224us/step - loss: 1139.7617 Epoch 27/100 12801/12801 [==============================] - 3s 211us/step - loss: 1074.3790 Epoch 28/100 12801/12801 [==============================] - 3s 213us/step - loss: 1066.1592 Epoch 29/100 12801/12801 [==============================] - 3s 213us/step - loss: 1013.9194 Epoch 30/100 12801/12801 [==============================] - 3s 214us/step - loss: 997.5742 Epoch 31/100 12801/12801 [==============================] - 2s 178us/step - loss: 990.0401 Epoch 32/100 12801/12801 [==============================] - 2s 180us/step - loss: 955.1419 Epoch 33/100 12801/12801 [==============================] - 2s 158us/step - loss: 930.7601 Epoch 34/100 12801/12801 [==============================] - 2s 169us/step - loss: 917.5061 Epoch 35/100 12801/12801 [==============================] - 2s 173us/step - loss: 876.6819 Epoch 36/100 12801/12801 [==============================] - 3s 272us/step - loss: 858.1280 Epoch 37/100 12801/12801 [==============================] - 3s 232us/step - loss: 825.9380 Epoch 38/100 12801/12801 [==============================] - 2s 183us/step - loss: 802.3470 Epoch 39/100 12801/12801 [==============================] - 3s 212us/step - loss: 800.9426 Epoch 40/100 12801/12801 [==============================] - 4s 278us/step - loss: 797.6517 Epoch 41/100 12801/12801 [==============================] - 2s 193us/step - loss: 775.5609 Epoch 42/100 12801/12801 [==============================] - 2s 189us/step - loss: 784.9142 Epoch 43/100 12801/12801 [==============================] - 3s 198us/step - loss: 730.1974 Epoch 44/100 12801/12801 [==============================] - 3s 214us/step - loss: 731.5533 Epoch 45/100 12801/12801 [==============================] - 3s 242us/step - loss: 724.2402 Epoch 46/100 12801/12801 [==============================] - 3s 243us/step - loss: 668.4577 Epoch 47/100 12801/12801 [==============================] - 3s 226us/step - loss: 682.9458 Epoch 48/100 12801/12801 [==============================] - 3s 199us/step - loss: 686.0351 Epoch 49/100 12801/12801 [==============================] - 2s 175us/step - loss: 669.5158 Epoch 50/100 12801/12801 [==============================] - 3s 213us/step - loss: 678.2515 Epoch 51/100 12801/12801 [==============================] - 3s 200us/step - loss: 648.4325 Epoch 52/100 12801/12801 [==============================] - 2s 190us/step - loss: 642.8736 Epoch 53/100 12801/12801 [==============================] - 2s 162us/step - loss: 637.3700 Epoch 54/100 12801/12801 [==============================] - 2s 159us/step - loss: 602.8367 Epoch 55/100 12801/12801 [==============================] - 2s 157us/step - loss: 619.3521 Epoch 56/100 12801/12801 [==============================] - 2s 161us/step - loss: 620.9534 Epoch 57/100 12801/12801 [==============================] - 3s 197us/step - loss: 586.6562 Epoch 58/100 12801/12801 [==============================] - 3s 219us/step - loss: 592.0330 Epoch 59/100 12801/12801 [==============================] - 3s 245us/step - loss: 591.1542 Epoch 60/100 12801/12801 [==============================] - 3s 234us/step - loss: 550.9516 Epoch 61/100 12801/12801 [==============================] - 3s 202us/step - loss: 579.5324 Epoch 62/100 12801/12801 [==============================] - 3s 202us/step - loss: 554.7284 Epoch 63/100 12801/12801 [==============================] - 2s 194us/step - loss: 535.0105 Epoch 64/100 12801/12801 [==============================] - 2s 195us/step - loss: 550.6192 Epoch 65/100 12801/12801 [==============================] - 3s 204us/step - loss: 555.5725 Epoch 66/100 12801/12801 [==============================] - 2s 182us/step - loss: 534.6731 Epoch 67/100 12801/12801 [==============================] - 2s 174us/step - loss: 533.0545 Epoch 68/100 12801/12801 [==============================] - 3s 203us/step - loss: 499.6661 Epoch 69/100 12801/12801 [==============================] - 3s 203us/step - loss: 528.4265 Epoch 70/100 12801/12801 [==============================] - 2s 172us/step - loss: 490.1835 Epoch 71/100 12801/12801 [==============================] - 2s 192us/step - loss: 515.8431 Epoch 72/100 12801/12801 [==============================] - 2s 157us/step - loss: 499.0169 Epoch 73/100 12801/12801 [==============================] - 2s 172us/step - loss: 487.5167 Epoch 74/100 12801/12801 [==============================] - 2s 165us/step - loss: 491.7562 Epoch 75/100 12801/12801 [==============================] - 2s 161us/step - loss: 478.5188 Epoch 76/100 12801/12801 [==============================] - 2s 174us/step - loss: 482.2381 Epoch 77/100 12801/12801 [==============================] - 2s 155us/step - loss: 487.5325 Epoch 78/100 12801/12801 [==============================] - 2s 173us/step - loss: 460.3936 Epoch 79/100 12801/12801 [==============================] - 2s 153us/step - loss: 442.9127 Epoch 80/100 12801/12801 [==============================] - 2s 184us/step - loss: 462.0990 Epoch 81/100 12801/12801 [==============================] - 2s 185us/step - loss: 457.4444 Epoch 82/100 12801/12801 [==============================] - 2s 155us/step - loss: 453.2949 Epoch 83/100 12801/12801 [==============================] - 3s 197us/step - loss: 440.8044 Epoch 84/100 12801/12801 [==============================] - 2s 171us/step - loss: 422.6709 Epoch 85/100 12801/12801 [==============================] - 2s 171us/step - loss: 445.0583 Epoch 86/100 12801/12801 [==============================] - 2s 166us/step - loss: 441.1010 Epoch 87/100 12801/12801 [==============================] - 2s 170us/step - loss: 416.9275 Epoch 88/100 12801/12801 [==============================] - 2s 177us/step - loss: 424.7273 Epoch 89/100 12801/12801 [==============================] - 2s 173us/step - loss: 442.3417 Epoch 90/100 12801/12801 [==============================] - 2s 152us/step - loss: 407.8288 Epoch 91/100 12801/12801 [==============================] - 2s 154us/step - loss: 411.6233 Epoch 92/100 12801/12801 [==============================] - 2s 179us/step - loss: 398.3094 Epoch 93/100 12801/12801 [==============================] - 2s 168us/step - loss: 415.3668 Epoch 94/100 12801/12801 [==============================] - 2s 172us/step - loss: 392.7755 Epoch 95/100 12801/12801 [==============================] - 2s 142us/step - loss: 385.8142 Epoch 96/100 12801/12801 [==============================] - 2s 144us/step - loss: 402.8084 Epoch 97/100 12801/12801 [==============================] - 2s 153us/step - loss: 390.5092 Epoch 98/100 12801/12801 [==============================] - 2s 159us/step - loss: 389.1342 Epoch 99/100 12801/12801 [==============================] - 2s 189us/step - loss: 397.8578 Epoch 100/100 12801/12801 [==============================] - 2s 188us/step - loss: 394.2945
Out[36]:
Pipeline(memory=None,
steps=[('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('model', <keras.wrappers.scikit_learn.KerasRegressor object at 0x7fd6ec452fd0>)])
In [37]:
res = pipe.predict(X_test)
mse = mean_squared_error(res,y_test)
varience = explained_variance_score(y_test,res)
print(mse,varience)
6087/6087 [==============================] - 1s 91us/step 2332.629741946544 -0.17965804136300276
Графики¶
Зависимость функции ошибки от количества эпох¶
In [47]:
results = np.zeros((5, 5))
N = 1218
for i, n_epoch in enumerate([1,5,10,20,50]):
model = KerasRegressor(big_model,epochs=n_epoch, batch_size=100,verbose=0)
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
pipe.fit(X_train,y_train)
res = pipe.predict(X_test)
for j in range(5):
results[i][j] = mean_squared_error(y_test[N * j: N * (j + 1)],
res[N * j: N * (j + 1)])
In [48]:
results
Out[48]:
array([[4569.91055308, 5012.51786228, 4277.85763436, 4546.70370505,
4328.95583161],
[2505.65580119, 2789.00047169, 2285.42403887, 3047.51039107,
2784.95535496],
[3187.45148495, 3263.25880654, 3078.71302404, 3242.64821162,
2757.90914865],
[2396.02436322, 3292.38280118, 2041.26333932, 2713.75580987,
2890.06975869],
[2601.56828163, 3753.07692081, 2202.77204714, 2998.7842833 ,
3507.00173318]])
In [50]:
x_ticks = [1,5,10,20,50]
results_mean = np.mean(results, axis=1)
results_std = np.std(results, axis=1)
plt.plot(x_ticks, results_mean, 'k-')
plt.plot(x_ticks, results_mean - results_std, 'b-')
plt.plot(x_ticks, results_mean + results_std, 'b-')
plt.fill_between(x_ticks, results_mean - results_std, results_mean + results_std)
plt.grid()
plt.title('Зависимость функции ошибки от количества эпох')
plt.xlabel("Количество эпох обучения")
plt.ylabel("Среднеквадратичное отклонение")
plt.show()
Зависимость функции ошибки от размера скрытого слоя¶
In [52]:
def variable_model():
model = Sequential()
model.add(Dense(64, input_dim=864, kernel_initializer='normal', activation='relu'))
for i in range(n_l-1):
model.add(Dense(64, kernel_initializer='normal', activation='relu'))
model.add(Dense(3, kernel_initializer='normal'))
# Compile model
model.compile(loss='mean_squared_error', optimizer='rmsprop')
return model
results1 = np.zeros((3,5))
n_layers = [1,2,3]
for i, n_l in enumerate(n_layers):
model = KerasRegressor(variable_model,epochs=10, batch_size=100,verbose=0)
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
pipe.fit(X_train,y_train)
res = pipe.predict(X_test)
for j in range(5):
results1[i][j] = mean_squared_error(y_test[N * j: N * (j + 1)], res[N * j: N * (j + 1)])
In [55]:
results1
Out[55]:
array([[4459.67106945, 4890.31655815, 3941.06789619, 4523.3945766 ,
4297.1579745 ],
[2392.58870991, 2882.90961967, 2121.09892981, 2700.03479441,
2798.22901469],
[2541.41769657, 2911.49202871, 2271.01093711, 2984.73926444,
2667.73825071]])
In [54]:
results1_mean = np.mean(results1, axis=1)
results1_std = np.std(results1, axis=1)
fig, ax = plt.subplots()
ax.set_xlabel("Количество скрытых слоев")
ax.set_ylabel("Среднеквадратичное отклонение")
ax.set_title('Зависимость функции ошибки от размера скрытого слоя')
ax.set_xticks(n_layers)
plt.plot(n_layers, results1_mean, 'k-')
plt.plot(n_layers, results1_mean - results1_std, 'b-')
plt.plot(n_layers, results1_mean + results1_std, 'b-')
plt.fill_between(n_layers, results1_mean - results1_std, results1_mean + results1_std)
plt.grid()
plt.show()
Зависимость функции ошибки от размера обучающей выборки¶
In [58]:
percents_of_data = [0.1,0.2,0.3,0.5,0.8,1.0]
results3 = np.zeros((6, 5))
for i, pod in enumerate(percents_of_data):
model = KerasRegressor(big_model,epochs=10, batch_size=100,verbose=0)
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
pipe.fit(X_train[:int(len(X_train)*pod)],y_train[:int(len(X_train)*pod)])
res = pipe.predict(X_test)
for j in range(5):
results3[i][j] = mean_squared_error(y_test[N * j: N * (j + 1)], res[N * j: N * (j + 1)])
In [59]:
results3
Out[59]:
array([[5446.2258489 , 4709.43085895, 5602.62709673, 5386.65219092,
4655.4724349 ],
[3791.06176671, 3598.5409162 , 3744.0984689 , 4104.49428603,
3550.56700095],
[3920.09423252, 3558.16307074, 3891.96906894, 3781.08513912,
3504.17818583],
[3670.57506937, 3750.95994031, 3456.65627776, 3560.79451291,
3628.13201099],
[2103.65891252, 2666.37717049, 1830.25414167, 2544.09178049,
2648.33948823],
[2667.3451799 , 2918.71788949, 2444.8128165 , 2768.48396353,
2550.68465311]])
In [60]:
results3_mean = np.mean(results3, axis=1)
results3_std = np.std(results3, axis=1)
fig, ax = plt.subplots()
#ax.set_ylim(0,60)
ax.set_xlabel("Процент от полной train выборки")
ax.set_ylabel("Среднеквадратичное отклонение")
ax.set_title('Зависимость функции ошибки от размера скрытого слоя')
ax.set_xticks(percents_of_data)
plt.plot(percents_of_data, results3_mean, 'k-')
plt.plot(percents_of_data, results3_mean - results3_std, 'b-')
plt.plot(percents_of_data, results3_mean + results3_std, 'b-')
plt.fill_between(percents_of_data, results3_mean - results3_std, results3_mean + results3_std)
plt.grid()
plt.show()
Синтетическая выборка¶
В качестве синтетической выборки для задачи регрессии возьмём Boston dataset.
In [61]:
dataset = load_boston()
In [62]:
dataset.data.shape
Out[62]:
(506, 13)
In [78]:
y = dataset.target
X = dataset.data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=228)
Линейная регрессия¶
In [64]:
model = linreg
pipe = Pipeline(steps=[('model', model)])
In [65]:
pipe.fit(X_train,y_train)
Out[65]:
Pipeline(memory=None,
steps=[('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True))])
In [66]:
res = pipe.predict(X_test)
mse = mean_squared_error(res,y_test)
varience = explained_variance_score(y_test,res)
print(mse,varience)
31.84400099655244 0.7013949934877279
Линейная регрессия c PCA до 8 компонент¶
In [67]:
model = linreg
pca = PCA(n_components=8)
pipe = Pipeline(steps=[('pca',pca),('model', model)])
In [68]:
pipe.fit(X_train,y_train)
Out[68]:
Pipeline(memory=None,
steps=[('pca', PCA(copy=True, iterated_power='auto', n_components=8, random_state=None,
svd_solver='auto', tol=0.0, whiten=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True))])
In [69]:
res = pipe.predict(X_test)
mse = mean_squared_error(res,y_test)
varience = explained_variance_score(y_test,res)
print(mse,varience)
49.06022977053876 0.5449917208136847
Нейронная сеть¶
In [70]:
def small_model():
model = Sequential()
model.add(Dense(128, input_dim=13, kernel_initializer='normal', activation='relu'))
model.add(Dense(64, kernel_initializer='normal', activation='relu'))
model.add(Dense(1, kernel_initializer='normal'))
# Compile model
model.compile(loss='mean_squared_error', optimizer='rmsprop')
return model
In [71]:
neural_net = KerasRegressor(small_model,epochs=200, batch_size=100,verbose=0)
model = neural_net
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
In [72]:
pipe.fit(X_train,y_train)
Out[72]:
Pipeline(memory=None,
steps=[('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('model', <keras.wrappers.scikit_learn.KerasRegressor object at 0x7fd6d360ba90>)])
In [73]:
res = pipe.predict(X_test)
mse = mean_squared_error(res,y_test)
varience = explained_variance_score(y_test,res)
print(mse,varience)
11.015076732376858 0.8960202502977511
Графики¶
Зависимость функции ошибки от количества эпох¶
In [81]:
results = np.zeros((8, 5))
N = 26
for i, n_epoch in enumerate([1,5,10,20,50,100,200,500]):
model = KerasRegressor(small_model,epochs=n_epoch, batch_size=100,verbose=0)
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
pipe.fit(X_train,y_train)
res = pipe.predict(X_test)
for j in range(5):
results[i][j] = mean_squared_error(y_test[N * j: N * (j + 1)],
res[N * j: N * (j + 1)])
In [82]:
results
Out[82]:
array([[588.55591617, 800.37676391, 541.50012345, 749.66211925,
570.88272409],
[508.42827134, 707.10844634, 472.86396325, 656.67109527,
501.77996136],
[296.32989856, 470.48872587, 307.76984998, 403.79549346,
319.74831032],
[ 74.0696805 , 155.49292005, 83.49085238, 109.01707561,
75.9354363 ],
[ 18.35862169, 64.41567193, 17.09276508, 11.94226864,
7.48491999],
[ 10.64446066, 31.28309395, 10.34166804, 6.75535306,
5.13119643],
[ 9.05678462, 20.23943936, 9.93137782, 6.50863175,
5.56096751],
[ 10.67959145, 10.31300342, 9.33933722, 6.88691065,
7.28555315]])
In [83]:
results_mean = np.mean(results, axis=1)
results_std = np.std(results, axis=1)
x_ticks = [1,5,10,20,50,100,200,500]
fig, ax = plt.subplots()
plt.plot(x_ticks, results_mean, 'k-')
plt.plot(x_ticks, results_mean - results_std, 'b-')
plt.plot(x_ticks, results_mean + results_std, 'b-')
plt.fill_between(x_ticks, results_mean - results_std, results_mean + results_std)
plt.grid()
ax.set_yscale('log')
ax.set_xscale('log')
ax.set_xticks(x_ticks)
ax.set_xticklabels(x_ticks)
ax.set_title('Зависимость функции ошибки от количества эпох')
ax.set_xlabel("Количество эпох обучения")
ax.set_ylabel("Среднеквадратичное отклонение")
plt.show()
Зависимость функции ошибки от размера скрытого слоя¶
In [85]:
def variable_model():
model = Sequential()
model.add(Dense(64, input_dim=13, kernel_initializer='normal', activation='relu'))
for i in range(n_l-1):
model.add(Dense(64, kernel_initializer='normal', activation='relu'))
model.add(Dense(1, kernel_initializer='normal'))
# Compile model
model.compile(loss='mean_squared_error', optimizer='rmsprop')
return model
results1 = np.zeros((5, 5))
n_layers = [1,2,3,5,10]
for i, n_l in enumerate(n_layers):
model = KerasRegressor(variable_model,epochs=200, batch_size=100,verbose=0)
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
pipe.fit(X_train,y_train)
res = pipe.predict(X_test)
for j in range(5):
results1[i][j] = mean_squared_error(y_test[N * j: N * (j + 1)], res[N * j: N * (j + 1)])
In [88]:
results1
Out[88]:
array([[17.59480924, 54.01601583, 12.71965805, 11.19683585, 6.58949272],
[11.86632501, 22.77298046, 10.72590175, 7.41086292, 5.56763962],
[10.70956175, 24.50284219, 9.90847772, 7.76224494, 5.09098941],
[ 9.26822945, 17.22824635, 12.05889931, 9.02318618, 9.70527924],
[ 8.88800241, 22.4141463 , 13.29210806, 12.69009511, 14.59686595]])
In [87]:
results1_mean = np.mean(results1, axis=1)
results1_std = np.std(results1, axis=1)
fig, ax = plt.subplots()
ax.set_ylim(0,30)
ax.set_xlabel("Количество скрытых слоев")
ax.set_ylabel("Среднеквадратичное отклонение")
ax.set_title('Зависимость функции ошибки от размера скрытого слоя')
ax.set_xticks(n_layers)
plt.plot(n_layers, results1_mean, 'k-')
plt.plot(n_layers, results1_mean - results1_std, 'b-')
plt.plot(n_layers, results1_mean + results1_std, 'b-')
plt.fill_between(n_layers, results1_mean - results1_std, results1_mean + results1_std)
plt.grid()
plt.show()
Зависимость функции ошибки от размера обучающей выборки¶
In [89]:
percents_of_data = [0.1,0.2,0.3,0.5,0.8,1.0]
results3 = np.zeros((6, 5))
for i, pod in enumerate(percents_of_data):
model = KerasRegressor(small_model,epochs=100, batch_size=100,verbose=0)
pipe = Pipeline(steps=[('scaler',scaler),('model', model)])
pipe.fit(X_train[:int(len(X_train)*pod)],y_train[:int(len(X_train)*pod)])
res = pipe.predict(X_test)
error = mean_squared_error(res,y_test)
for j in range(5):
results3[i][j] = mean_squared_error(y_test[N * j: N * (j + 1)], res[N * j: N * (j + 1)])
In [90]:
results3
Out[90]:
array([[ 39.26496364, 125.25234136, 28.80575555, 32.3160941 ,
31.61399156],
[ 45.71867795, 82.57181656, 29.47177725, 27.00505718,
30.71210084],
[ 23.73976423, 51.12091818, 16.76351469, 10.64888061,
12.67334685],
[ 15.25653084, 51.57973858, 12.16857357, 10.7065328 ,
6.5929573 ],
[ 9.90118696, 53.84111241, 11.18194535, 9.95077099,
4.9313148 ],
[ 10.90012465, 32.23885325, 9.8241123 , 7.94993799,
4.87686346]])
In [91]:
results3_mean = np.mean(results3, axis=1)
results3_std = np.std(results3, axis=1)
fig, ax = plt.subplots()
ax.set_ylim(0,60)
ax.set_xlabel("Процент от полной train выборки")
ax.set_ylabel("Среднеквадратичное отклонение")
ax.set_title('Зависимость функции ошибки от размера скрытого слоя')
ax.set_xticks(percents_of_data)
plt.plot(percents_of_data, results3_mean, 'k-')
plt.plot(percents_of_data, results3_mean - results3_std, 'b-')
plt.plot(percents_of_data, results3_mean + results3_std, 'b-')
plt.fill_between(percents_of_data, results3_mean - results3_std, results3_mean + results3_std)
plt.grid()
plt.show()
In [ ]: