TF2 0 Autoregressive Model
================ by Jawad Haider
Autoregressive Model¶
# Install TensorFlow
# !pip install -q tensorflow-gpu==2.0.0-beta1
try:
%tensorflow_version 2.x # Colab only.
except Exception:
pass
import tensorflow as tf
print(tf.__version__)
`%tensorflow_version` only switches the major version: `1.x` or `2.x`.
You set: `2.x # Colab only.`. This will be interpreted as: `2.x`.
TensorFlow 2.x selected.
2.1.0-rc1
from tensorflow.keras.layers import Input, Dense
from tensorflow.keras.models import Model
from tensorflow.keras.optimizers import SGD, Adam
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# make the original data
series = np.sin(0.1*np.arange(200)) #+ np.random.randn(200)*0.1
# plot it
plt.plot(series)
plt.show()
### build the dataset
# let's see if we can use T past values to predict the next value
T = 10
X = []
Y = []
for t in range(len(series) - T):
x = series[t:t+T]
X.append(x)
y = series[t+T]
Y.append(y)
X = np.array(X).reshape(-1, T)
Y = np.array(Y)
N = len(X)
print("X.shape", X.shape, "Y.shape", Y.shape)
X.shape (190, 10) Y.shape (190,)
### try autoregressive linear model
i = Input(shape=(T,))
x = Dense(1)(i)
model = Model(i, x)
model.compile(
loss='mse',
optimizer=Adam(lr=0.1),
)
# train the RNN
r = model.fit(
X[:-N//2], Y[:-N//2],
epochs=80,
validation_data=(X[-N//2:], Y[-N//2:]),
)
Train on 95 samples, validate on 95 samples
Epoch 1/80
95/95 [==============================] - 1s 6ms/sample - loss: 0.5928 - val_loss: 0.4919
Epoch 2/80
95/95 [==============================] - 0s 164us/sample - loss: 0.3797 - val_loss: 0.1337
Epoch 3/80
95/95 [==============================] - 0s 266us/sample - loss: 0.1297 - val_loss: 0.1125
Epoch 4/80
95/95 [==============================] - 0s 186us/sample - loss: 0.0874 - val_loss: 0.0243
Epoch 5/80
95/95 [==============================] - 0s 180us/sample - loss: 0.0316 - val_loss: 0.0582
Epoch 6/80
95/95 [==============================] - 0s 205us/sample - loss: 0.0388 - val_loss: 0.0208
Epoch 7/80
95/95 [==============================] - 0s 173us/sample - loss: 0.0353 - val_loss: 0.0687
Epoch 8/80
95/95 [==============================] - 0s 186us/sample - loss: 0.0416 - val_loss: 0.0304
Epoch 9/80
95/95 [==============================] - 0s 170us/sample - loss: 0.0305 - val_loss: 0.0277
Epoch 10/80
95/95 [==============================] - 0s 219us/sample - loss: 0.0195 - val_loss: 0.0061
Epoch 11/80
95/95 [==============================] - 0s 187us/sample - loss: 0.0101 - val_loss: 0.0063
Epoch 12/80
95/95 [==============================] - 0s 184us/sample - loss: 0.0045 - val_loss: 0.0042
Epoch 13/80
95/95 [==============================] - 0s 171us/sample - loss: 0.0056 - val_loss: 0.0061
Epoch 14/80
95/95 [==============================] - 0s 180us/sample - loss: 0.0038 - val_loss: 0.0053
Epoch 15/80
95/95 [==============================] - 0s 180us/sample - loss: 0.0058 - val_loss: 0.0037
Epoch 16/80
95/95 [==============================] - 0s 207us/sample - loss: 0.0033 - val_loss: 0.0032
Epoch 17/80
95/95 [==============================] - 0s 182us/sample - loss: 0.0026 - val_loss: 4.2511e-04
Epoch 18/80
95/95 [==============================] - 0s 179us/sample - loss: 7.7209e-04 - val_loss: 7.0560e-04
Epoch 19/80
95/95 [==============================] - 0s 204us/sample - loss: 5.4705e-04 - val_loss: 6.5394e-04
Epoch 20/80
95/95 [==============================] - 0s 181us/sample - loss: 9.3594e-04 - val_loss: 6.7224e-04
Epoch 21/80
95/95 [==============================] - 0s 169us/sample - loss: 5.9015e-04 - val_loss: 0.0013
Epoch 22/80
95/95 [==============================] - 0s 205us/sample - loss: 8.0676e-04 - val_loss: 5.2523e-04
Epoch 23/80
95/95 [==============================] - 0s 224us/sample - loss: 3.5637e-04 - val_loss: 2.0870e-04
Epoch 24/80
95/95 [==============================] - 0s 235us/sample - loss: 1.0215e-04 - val_loss: 5.3742e-05
Epoch 25/80
95/95 [==============================] - 0s 214us/sample - loss: 1.1322e-04 - val_loss: 8.9134e-05
Epoch 26/80
95/95 [==============================] - 0s 174us/sample - loss: 1.1851e-04 - val_loss: 2.4181e-04
Epoch 27/80
95/95 [==============================] - 0s 169us/sample - loss: 1.2587e-04 - val_loss: 9.3724e-05
Epoch 28/80
95/95 [==============================] - 0s 146us/sample - loss: 9.6006e-05 - val_loss: 4.7208e-05
Epoch 29/80
95/95 [==============================] - 0s 186us/sample - loss: 3.7994e-05 - val_loss: 2.2043e-05
Epoch 30/80
95/95 [==============================] - 0s 171us/sample - loss: 1.7351e-05 - val_loss: 8.1480e-06
Epoch 31/80
95/95 [==============================] - 0s 198us/sample - loss: 1.8036e-05 - val_loss: 1.2440e-05
Epoch 32/80
95/95 [==============================] - 0s 180us/sample - loss: 1.9975e-05 - val_loss: 2.8459e-05
Epoch 33/80
95/95 [==============================] - 0s 242us/sample - loss: 1.9230e-05 - val_loss: 1.5293e-05
Epoch 34/80
95/95 [==============================] - 0s 172us/sample - loss: 1.2585e-05 - val_loss: 6.7560e-06
Epoch 35/80
95/95 [==============================] - 0s 219us/sample - loss: 4.1914e-06 - val_loss: 3.5701e-06
Epoch 36/80
95/95 [==============================] - 0s 171us/sample - loss: 3.0705e-06 - val_loss: 3.9625e-06
Epoch 37/80
95/95 [==============================] - 0s 176us/sample - loss: 4.9658e-06 - val_loss: 4.9225e-06
Epoch 38/80
95/95 [==============================] - 0s 194us/sample - loss: 4.6270e-06 - val_loss: 3.9518e-06
Epoch 39/80
95/95 [==============================] - 0s 180us/sample - loss: 2.0241e-06 - val_loss: 1.9492e-06
Epoch 40/80
95/95 [==============================] - 0s 228us/sample - loss: 1.1528e-06 - val_loss: 7.1516e-07
Epoch 41/80
95/95 [==============================] - 0s 195us/sample - loss: 1.2629e-06 - val_loss: 7.8588e-07
Epoch 42/80
95/95 [==============================] - 0s 217us/sample - loss: 1.2023e-06 - val_loss: 8.7311e-07
Epoch 43/80
95/95 [==============================] - 0s 159us/sample - loss: 8.9838e-07 - val_loss: 1.4360e-06
Epoch 44/80
95/95 [==============================] - 0s 191us/sample - loss: 7.9823e-07 - val_loss: 4.8116e-07
Epoch 45/80
95/95 [==============================] - 0s 176us/sample - loss: 4.4251e-07 - val_loss: 4.6078e-08
Epoch 46/80
95/95 [==============================] - 0s 191us/sample - loss: 2.9620e-07 - val_loss: 1.3887e-07
Epoch 47/80
95/95 [==============================] - 0s 227us/sample - loss: 2.5926e-07 - val_loss: 2.5561e-07
Epoch 48/80
95/95 [==============================] - 0s 159us/sample - loss: 2.0303e-07 - val_loss: 3.1984e-07
Epoch 49/80
95/95 [==============================] - 0s 223us/sample - loss: 1.3438e-07 - val_loss: 2.8710e-08
Epoch 50/80
95/95 [==============================] - 0s 180us/sample - loss: 6.0148e-08 - val_loss: 2.4986e-08
Epoch 51/80
95/95 [==============================] - 0s 186us/sample - loss: 6.0143e-08 - val_loss: 4.7983e-08
Epoch 52/80
95/95 [==============================] - 0s 209us/sample - loss: 5.0851e-08 - val_loss: 5.6664e-08
Epoch 53/80
95/95 [==============================] - 0s 208us/sample - loss: 3.9499e-08 - val_loss: 5.2733e-08
Epoch 54/80
95/95 [==============================] - 0s 167us/sample - loss: 2.6937e-08 - val_loss: 8.6147e-09
Epoch 55/80
95/95 [==============================] - 0s 197us/sample - loss: 1.8057e-08 - val_loss: 3.7212e-09
Epoch 56/80
95/95 [==============================] - 0s 196us/sample - loss: 1.7351e-08 - val_loss: 9.4838e-09
Epoch 57/80
95/95 [==============================] - 0s 188us/sample - loss: 1.4201e-08 - val_loss: 1.2931e-08
Epoch 58/80
95/95 [==============================] - 0s 284us/sample - loss: 7.6740e-09 - val_loss: 1.9589e-08
Epoch 59/80
95/95 [==============================] - 0s 215us/sample - loss: 8.0834e-09 - val_loss: 3.3542e-09
Epoch 60/80
95/95 [==============================] - 0s 162us/sample - loss: 4.9637e-09 - val_loss: 2.0916e-09
Epoch 61/80
95/95 [==============================] - 0s 247us/sample - loss: 4.2822e-09 - val_loss: 2.6194e-09
Epoch 62/80
95/95 [==============================] - 0s 216us/sample - loss: 3.0952e-09 - val_loss: 2.4419e-09
Epoch 63/80
95/95 [==============================] - 0s 209us/sample - loss: 1.4149e-09 - val_loss: 3.5520e-09
Epoch 64/80
95/95 [==============================] - 0s 179us/sample - loss: 1.5010e-09 - val_loss: 1.6126e-09
Epoch 65/80
95/95 [==============================] - 0s 182us/sample - loss: 1.5736e-09 - val_loss: 1.0080e-09
Epoch 66/80
95/95 [==============================] - 0s 172us/sample - loss: 1.6310e-09 - val_loss: 5.8007e-10
Epoch 67/80
95/95 [==============================] - 0s 266us/sample - loss: 1.0262e-09 - val_loss: 7.7888e-11
Epoch 68/80
95/95 [==============================] - 0s 203us/sample - loss: 5.2353e-10 - val_loss: 2.4929e-10
Epoch 69/80
95/95 [==============================] - 0s 191us/sample - loss: 2.6591e-10 - val_loss: 3.0532e-10
Epoch 70/80
95/95 [==============================] - 0s 202us/sample - loss: 2.9230e-10 - val_loss: 3.4441e-10
Epoch 71/80
95/95 [==============================] - 0s 171us/sample - loss: 2.6945e-10 - val_loss: 3.9480e-10
Epoch 72/80
95/95 [==============================] - 0s 176us/sample - loss: 1.6047e-10 - val_loss: 2.6156e-10
Epoch 73/80
95/95 [==============================] - 0s 162us/sample - loss: 1.3762e-10 - val_loss: 7.6606e-11
Epoch 74/80
95/95 [==============================] - 0s 189us/sample - loss: 1.1569e-10 - val_loss: 3.6307e-11
Epoch 75/80
95/95 [==============================] - 0s 183us/sample - loss: 8.6744e-11 - val_loss: 2.3215e-11
Epoch 76/80
95/95 [==============================] - 0s 179us/sample - loss: 5.2023e-11 - val_loss: 1.7341e-11
Epoch 77/80
95/95 [==============================] - 0s 196us/sample - loss: 2.9296e-11 - val_loss: 4.5361e-11
Epoch 78/80
95/95 [==============================] - 0s 216us/sample - loss: 2.8942e-11 - val_loss: 3.2065e-11
Epoch 79/80
95/95 [==============================] - 0s 188us/sample - loss: 2.5990e-11 - val_loss: 2.9623e-11
Epoch 80/80
95/95 [==============================] - 0s 213us/sample - loss: 1.8977e-11 - val_loss: 3.0598e-11
# Plot loss per iteration
import matplotlib.pyplot as plt
plt.plot(r.history['loss'], label='loss')
plt.plot(r.history['val_loss'], label='val_loss')
plt.legend()
<matplotlib.legend.Legend at 0x7f64d4fa0278>
# "Wrong" forecast using true targets
validation_target = Y[-N//2:]
validation_predictions = []
# index of first validation input
i = -N//2
while len(validation_predictions) < len(validation_target):
p = model.predict(X[i].reshape(1, -1))[0,0] # 1x1 array -> scalar
i += 1
# update the predictions list
validation_predictions.append(p)
plt.plot(validation_target, label='forecast target')
plt.plot(validation_predictions, label='forecast prediction')
plt.legend()
<matplotlib.legend.Legend at 0x7f64d79f8f98>
# Forecast future values (use only self-predictions for making future predictions)
validation_target = Y[-N//2:]
validation_predictions = []
# first validation input
last_x = X[-N//2] # 1-D array of length T
while len(validation_predictions) < len(validation_target):
p = model.predict(last_x.reshape(1, -1))[0,0] # 1x1 array -> scalar
# update the predictions list
validation_predictions.append(p)
# make the new input
last_x = np.roll(last_x, -1)
last_x[-1] = p
plt.plot(validation_target, label='forecast target')
plt.plot(validation_predictions, label='forecast prediction')
plt.legend()
<matplotlib.legend.Legend at 0x7f64d7c15cf8>
