Time Series forecasting using Deep learning¶
Placeholder: To write in the future. Deadline before end of deep learning module
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
data = pd.read_csv('hyderabad-us consulate-air-quality.csv', parse_dates=['date'])
data = data.sort_values('date')
data.columns = ['date', 'pm25']
data = data.reset_index()
data
| index | date | pm25 | |
|---|---|---|---|
| 0 | 2295 | 2014-12-10 | 172 |
| 1 | 2296 | 2014-12-11 | 166 |
| 2 | 2297 | 2014-12-12 | 159 |
| 3 | 2298 | 2014-12-13 | 164 |
| 4 | 2299 | 2014-12-14 | 166 |
| ... | ... | ... | ... |
| 2309 | 0 | 2021-11-01 | 155 |
| 2310 | 1 | 2021-11-02 | 115 |
| 2311 | 2 | 2021-11-03 | 67 |
| 2312 | 3 | 2021-11-04 | 112 |
| 2313 | 4 | 2021-11-05 | 115 |
2314 rows × 3 columns
plt.figure(figsize=(20,10))
plt.plot(data.date, data.pm25, color='tab:red')
plt.gca().set(title='Pollution at Hyderabad', xlabel='Date', ylabel='PM25')
plt.show()
From this plot, we can see that pollution is higher during winter months while its lower during summer months. This effect is observed every year indicating a seasonal pattern in the data. There seems to be no increasing or decreasing trend in the data. This can be better visualised by decomposing the data into three components:
1. Seasonal component: The component that varies with season
2. Trend: Increasing or decreasing pattern
3. Random component: Remaining component that has no pattern
from statsmodels.tsa.seasonal import seasonal_decompose
result = seasonal_decompose(data.pm25, model='additive', period = 365)
fs, axs = plt.subplots(3, figsize=(20,10))
plt.suptitle('Pollution (PM25) at Hyderabad', fontsize = 20, y = 0.95)
axs[0].plot(data.date, result.trend)
axs[1].plot(data.date, result.seasonal)
axs[2].plot(data.date, result.resid)
axs[0].set_ylabel('Trend', fontsize=15)
axs[1].set_ylabel('Seasonality', fontsize=15)
axs[2].set_ylabel('Random component', fontsize=15)
plt.show()
Looking at the trend, we can see how the pollution decreased during 2020 (probably due to covid) and is slowly rising as the country is getting back to its feet.
data['year'] = data.date.dt.year
data['day'] = data.date.dt.dayofyear
plt.figure(figsize=(16,12), dpi= 80)
for i, y in enumerate(data.year.unique()):
plt.plot('day', 'pm25', data=data.loc[data.year==y, :], label = y)
plt.title("Seasonal Plot of Hyd AQ15", fontsize=20)
plt.legend(loc="upper left")
Simple Neural Net (Perceptron)¶
from keras.models import Sequential
from keras.layers import Dense, SimpleRNN, Lambda, LSTM
import tensorflow as tf
dataset = tf.data.Dataset.range(20)
dataset = dataset.window(15, shift=1, drop_remainder=True)
dataset = dataset.flat_map(lambda window: window.batch(15))
dataset = dataset.map(lambda window: (window[:-1], window[-1:]))
dataset = dataset.shuffle(buffer_size=3)
dataset = dataset.batch(1).prefetch(1)
for x,y in dataset:
print("x = ", x.numpy())
print("y = ", y.numpy())
x = [[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14]]
y = [[15]]
x = [[ 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
y = [[17]]
x = [[ 2 3 4 5 6 7 8 9 10 11 12 13 14 15]]
y = [[16]]
x = [[ 5 6 7 8 9 10 11 12 13 14 15 16 17 18]]
y = [[19]]
x = [[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13]]
y = [[14]]
x = [[ 4 5 6 7 8 9 10 11 12 13 14 15 16 17]]
y = [[18]]
def windowed_dataset(series, window_size, batch_size, shuffle_buffer):
dataset = tf.data.Dataset.from_tensor_slices(series)
dataset = dataset.window(window_size + 1, shift=1, drop_remainder=True)
dataset = dataset.flat_map(lambda window: window.batch(window_size + 1))
dataset = dataset.shuffle(shuffle_buffer).map(lambda window: (window[:-1], window[-1]))
dataset = dataset.batch(batch_size).prefetch(1)
return dataset
dataset = windowed_dataset(data.pm25, 14, 1, 3)
for x,y in dataset:
print("x = ", x.numpy())
print("y = ", y.numpy())
x = [[159 164 166 152 155 157 138 154 158 162 160 165 165 165]]
y = [163]
x = [[172 166 159 164 166 152 155 157 138 154 158 162 160 165]]
y = [165]
and so on
split_time = 2314-365*2
time_train = data.date[:split_time]
x_train = data.pm25[:split_time]
time_valid = data.date[split_time:]
x_valid = data.pm25[split_time:]
window_size = 14
batch_size = 1
shuffle_buffer_size = 2314-365*2
dataset = windowed_dataset(x_train, window_size, batch_size, shuffle_buffer_size)
l0 = tf.keras.layers.Dense(1, input_shape=[window_size])
model = tf.keras.models.Sequential([l0])
model.compile(loss="mse", optimizer=tf.keras.optimizers.SGD(learning_rate=1e-6, momentum=0.9), metrics=["mae"])
model.fit(dataset,epochs=100)
print("Layer weights {}".format(l0.get_weights()))
Epoch 1/100
1570/1570 [==============================] - 2s 764us/step - loss: 2513.6338 - mae: 36.4270
Epoch 2/100
1570/1570 [==============================] - 2s 1ms/step - loss: 2627.8843 - mae: 38.2651
Epoch 3/100
1570/1570 [==============================] - 1s 625us/step - loss: 4424.3721 - mae: 48.4370
Epoch 4/100
1570/1570 [==============================] - 1s 623us/step - loss: 5549.5840 - mae: 53.6082
Epoch 5/100
1570/1570 [==============================] - 1s 637us/step - loss: 2992.0337 - mae: 40.5288
Epoch 6/100
1570/1570 [==============================] - 1s 846us/step - loss: 3471.9915 - mae: 44.3860
Epoch 7/100
1570/1570 [==============================] - 3s 2ms/step - loss: 2531.1494 - mae: 34.7863
Epoch 8/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1852.7971 - mae: 32.0643
Epoch 9/100
1570/1570 [==============================] - 1s 661us/step - loss: 1253.9712 - mae: 26.1902
Epoch 10/100
1570/1570 [==============================] - 1s 618us/step - loss: 2161.4375 - mae: 35.7045
Epoch 11/100
1570/1570 [==============================] - 1s 767us/step - loss: 1726.3955 - mae: 30.9938
Epoch 12/100
1570/1570 [==============================] - 2s 967us/step - loss: 1668.6731 - mae: 31.8759
Epoch 13/100
1570/1570 [==============================] - 1s 662us/step - loss: 2064.4319 - mae: 34.0762
Epoch 14/100
1570/1570 [==============================] - 1s 630us/step - loss: 2944.2009 - mae: 39.0366
Epoch 15/100
1570/1570 [==============================] - 2s 1ms/step - loss: 2634.4287 - mae: 37.2135
Epoch 16/100
1570/1570 [==============================] - 1s 616us/step - loss: 2405.7512 - mae: 35.9506
Epoch 17/100
1570/1570 [==============================] - 1s 617us/step - loss: 3331.7898 - mae: 42.2314
Epoch 18/100
1570/1570 [==============================] - 2s 949us/step - loss: 1733.8339 - mae: 30.9589
Epoch 19/100
1570/1570 [==============================] - 1s 734us/step - loss: 2795.8682 - mae: 38.8242
Epoch 20/100
1570/1570 [==============================] - 1s 872us/step - loss: 3353.5576 - mae: 41.7762
Epoch 21/100
1570/1570 [==============================] - 1s 808us/step - loss: 1974.5398 - mae: 33.4402
Epoch 22/100
1570/1570 [==============================] - 1s 873us/step - loss: 1905.5634 - mae: 32.1671
Epoch 23/100
1570/1570 [==============================] - 2s 837us/step - loss: 2250.3162 - mae: 34.8362
Epoch 24/100
1570/1570 [==============================] - 2s 1ms/step - loss: 2360.7571 - mae: 36.5247
Epoch 25/100
1570/1570 [==============================] - 1s 705us/step - loss: 2153.8865 - mae: 35.0538
Epoch 26/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1548.2344 - mae: 29.6058
Epoch 27/100
1570/1570 [==============================] - 2s 942us/step - loss: 2877.3025 - mae: 39.9668
Epoch 28/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1990.7844 - mae: 32.4618
Epoch 29/100
1570/1570 [==============================] - 2s 831us/step - loss: 1433.8342 - mae: 28.8914
Epoch 30/100
1570/1570 [==============================] - 1s 680us/step - loss: 2065.6316 - mae: 34.1275
Epoch 31/100
1570/1570 [==============================] - 2s 977us/step - loss: 2812.8083 - mae: 38.1380
Epoch 32/100
1570/1570 [==============================] - 2s 814us/step - loss: 1840.2141 - mae: 32.0926
Epoch 33/100
1570/1570 [==============================] - 2s 970us/step - loss: 1858.1345 - mae: 32.9561
Epoch 34/100
1570/1570 [==============================] - 1s 735us/step - loss: 2243.5950 - mae: 33.8061
Epoch 35/100
1570/1570 [==============================] - 1s 624us/step - loss: 1999.2378 - mae: 33.1796
Epoch 36/100
1570/1570 [==============================] - 1s 609us/step - loss: 2803.6067 - mae: 37.3053
Epoch 37/100
1570/1570 [==============================] - 2s 1ms/step - loss: 3408.6633 - mae: 43.0755
Epoch 38/100
1570/1570 [==============================] - 1s 610us/step - loss: 7617.3584 - mae: 53.5411
Epoch 39/100
1570/1570 [==============================] - 2s 1ms/step - loss: 3608.6226 - mae: 41.9082
Epoch 40/100
1570/1570 [==============================] - 1s 622us/step - loss: 1665.9635 - mae: 30.1138
Epoch 41/100
1570/1570 [==============================] - 1s 664us/step - loss: 2472.9622 - mae: 34.7668
Epoch 42/100
1570/1570 [==============================] - 2s 1ms/step - loss: 4391.3267 - mae: 44.2831
Epoch 43/100
1570/1570 [==============================] - 1s 658us/step - loss: 3736.1123 - mae: 43.4484
Epoch 44/100
1570/1570 [==============================] - 2s 1ms/step - loss: 2405.3022 - mae: 37.2903
Epoch 45/100
1570/1570 [==============================] - 1s 637us/step - loss: 2640.0657 - mae: 37.7513
Epoch 46/100
1570/1570 [==============================] - 1s 624us/step - loss: 1698.6646 - mae: 30.3015
Epoch 47/100
1570/1570 [==============================] - 2s 904us/step - loss: 2157.7537 - mae: 34.5056
Epoch 48/100
1570/1570 [==============================] - 2s 850us/step - loss: 2351.3657 - mae: 36.3811
Epoch 49/100
1570/1570 [==============================] - 2s 923us/step - loss: 3389.1948 - mae: 42.5566
Epoch 50/100
1570/1570 [==============================] - 1s 753us/step - loss: 2557.7690 - mae: 36.7457
Epoch 51/100
1570/1570 [==============================] - 1s 866us/step - loss: 2274.4500 - mae: 35.3559
Epoch 52/100
1570/1570 [==============================] - 2s 814us/step - loss: 1476.2098 - mae: 29.2134
Epoch 53/100
1570/1570 [==============================] - 2s 895us/step - loss: 3051.8118 - mae: 41.4144
Epoch 54/100
1570/1570 [==============================] - 2s 837us/step - loss: 3997.4836 - mae: 42.0719
Epoch 55/100
1570/1570 [==============================] - 1s 632us/step - loss: 2640.8892 - mae: 37.8363
Epoch 56/100
1570/1570 [==============================] - 1s 676us/step - loss: 2127.0208 - mae: 33.5877
Epoch 57/100
1570/1570 [==============================] - 2s 1ms/step - loss: 2155.6133 - mae: 35.2079
Epoch 58/100
1570/1570 [==============================] - 1s 628us/step - loss: 2110.5273 - mae: 35.1694
Epoch 59/100
1570/1570 [==============================] - 2s 1ms/step - loss: 3205.5698 - mae: 41.6258
Epoch 60/100
1570/1570 [==============================] - 1s 681us/step - loss: 2516.9368 - mae: 37.6260
Epoch 61/100
1570/1570 [==============================] - 2s 1ms/step - loss: 3302.0437 - mae: 40.9913
Epoch 62/100
1570/1570 [==============================] - 1s 621us/step - loss: 2135.1140 - mae: 34.7838
Epoch 63/100
1570/1570 [==============================] - 1s 631us/step - loss: 1920.6626 - mae: 32.1499
Epoch 64/100
1570/1570 [==============================] - 2s 1ms/step - loss: 2632.5876 - mae: 37.2169
Epoch 65/100
1570/1570 [==============================] - 1s 642us/step - loss: 1719.2740 - mae: 30.8670
Epoch 66/100
1570/1570 [==============================] - 1s 618us/step - loss: 2797.1809 - mae: 38.1031
Epoch 67/100
1570/1570 [==============================] - 1s 821us/step - loss: 2052.6494 - mae: 33.3538
Epoch 68/100
1570/1570 [==============================] - 2s 826us/step - loss: 2140.2795 - mae: 33.2761
Epoch 69/100
1570/1570 [==============================] - 1s 810us/step - loss: 2568.9514 - mae: 35.5570
Epoch 70/100
1570/1570 [==============================] - 2s 916us/step - loss: 1741.9554 - mae: 31.4823
Epoch 71/100
1570/1570 [==============================] - 1s 640us/step - loss: 3985.8354 - mae: 41.0881
Epoch 72/100
1570/1570 [==============================] - 1s 625us/step - loss: 1813.1409 - mae: 31.6561
Epoch 73/100
1570/1570 [==============================] - 2s 1ms/step - loss: 4502.4375 - mae: 45.8338
Epoch 74/100
1570/1570 [==============================] - 1s 621us/step - loss: 2171.1902 - mae: 34.1269
Epoch 75/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1887.9999 - mae: 33.1114
Epoch 76/100
1570/1570 [==============================] - 1s 614us/step - loss: 1521.0691 - mae: 29.7172
Epoch 77/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1950.2441 - mae: 32.6277
Epoch 78/100
1570/1570 [==============================] - 1s 617us/step - loss: 1778.5680 - mae: 30.9782
Epoch 79/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1485.2815 - mae: 29.3998
Epoch 80/100
1570/1570 [==============================] - 1s 602us/step - loss: 1437.3258 - mae: 29.3189
Epoch 81/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1997.8091 - mae: 34.4411
Epoch 82/100
1570/1570 [==============================] - 1s 587us/step - loss: 2212.0806 - mae: 34.5182
Epoch 83/100
1570/1570 [==============================] - 1s 587us/step - loss: 2208.1921 - mae: 33.5488
Epoch 84/100
1570/1570 [==============================] - 1s 590us/step - loss: 2176.0520 - mae: 35.4611
Epoch 85/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1925.0211 - mae: 32.5826
Epoch 86/100
1570/1570 [==============================] - 1s 599us/step - loss: 3626.3096 - mae: 42.7268
Epoch 87/100
1570/1570 [==============================] - 2s 1ms/step - loss: 1902.9331 - mae: 33.2850
Epoch 88/100
1570/1570 [==============================] - 1s 588us/step - loss: 1713.0077 - mae: 31.0925
Epoch 89/100
1570/1570 [==============================] - 1s 584us/step - loss: 1231.0505 - mae: 26.7580
Epoch 90/100
1570/1570 [==============================] - 2s 902us/step - loss: 2903.7974 - mae: 39.2899
Epoch 91/100
1570/1570 [==============================] - 1s 704us/step - loss: 4899.5703 - mae: 49.9197
Epoch 92/100
1570/1570 [==============================] - 1s 720us/step - loss: 4719.0454 - mae: 45.7755
Epoch 93/100
1570/1570 [==============================] - 2s 915us/step - loss: 2016.2034 - mae: 33.3431
Epoch 94/100
1570/1570 [==============================] - 1s 746us/step - loss: 1934.7463 - mae: 32.4981
Epoch 95/100
1570/1570 [==============================] - 2s 930us/step - loss: 2149.3330 - mae: 34.3910
Epoch 96/100
1570/1570 [==============================] - 1s 583us/step - loss: 2434.7302 - mae: 36.1103
Epoch 97/100
1570/1570 [==============================] - 1s 585us/step - loss: 2350.9609 - mae: 35.0144
Epoch 98/100
1570/1570 [==============================] - 1s 612us/step - loss: 2069.1951 - mae: 33.9281
Epoch 99/100
1570/1570 [==============================] - 1s 596us/step - loss: 2446.0693 - mae: 36.7350
Epoch 100/100
1570/1570 [==============================] - 1s 626us/step - loss: 2440.7476 - mae: 33.8709
Layer weights [array([[-0.04500467],
[-0.05519092],
[ 0.09815453],
[-0.00597653],
[ 0.30430666],
[-0.00321147],
[ 0.07927534],
[ 0.00668947],
[ 0.04348003],
[ 0.11238142],
[-0.05560566],
[-0.29955685],
[ 0.01853935],
[ 0.76262796]], dtype=float32), array([0.7891302], dtype=float32)]
def plot_series(time, series, format="-", start=0, end=None):
plt.plot(time[start:end], series[start:end], format)
plt.xlabel("Time")
plt.ylabel("Value")
plt.grid(True)
forecast = []
for time in range(len(data.pm25) - window_size):
forecast.append(model.predict(np.array(data.pm25[time:time + window_size])[np.newaxis]))
forecast = forecast[split_time-window_size:]
results = np.array(forecast)[:, 0, 0]
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, results)
tf.keras.metrics.mean_absolute_error(x_valid, results).numpy()
15.45758
This model is currently deployed in Azure
Deep neural network¶
dataset = windowed_dataset(x_train, window_size, batch_size, shuffle_buffer_size)
model = tf.keras.models.Sequential([
tf.keras.layers.Dense(14, input_shape=[window_size], activation="relu"),
tf.keras.layers.Dense(14, activation="relu"),
tf.keras.layers.Dense(1)
])
model.compile(loss="mse", optimizer=tf.keras.optimizers.SGD(learning_rate=1e-6, momentum=0.9), metrics=["mae"])
model.fit(dataset,epochs=100)
Epoch 1/100
1570/1570 [==============================] - 1s 730us/step - loss: 845.5267 - mae: 21.9859
Epoch 2/100
1570/1570 [==============================] - 1s 724us/step - loss: 1019.4009 - mae: 24.1638
Epoch 3/100
1570/1570 [==============================] - 1s 717us/step - loss: 722.2228 - mae: 20.5732
Epoch 4/100
1570/1570 [==============================] - 1s 718us/step - loss: 701.0610 - mae: 20.4133
Epoch 5/100
1570/1570 [==============================] - 1s 716us/step - loss: 677.8721 - mae: 19.7713
Epoch 6/100
1570/1570 [==============================] - 1s 689us/step - loss: 897.4562 - mae: 22.3025
Epoch 7/100
1570/1570 [==============================] - 1s 698us/step - loss: 739.0591 - mae: 20.7214
Epoch 8/100
1570/1570 [==============================] - 1s 688us/step - loss: 659.6113 - mae: 19.5167
Epoch 9/100
1570/1570 [==============================] - 1s 749us/step - loss: 774.5299 - mae: 21.2334
Epoch 10/100
1570/1570 [==============================] - 1s 725us/step - loss: 732.1213 - mae: 20.3679
Epoch 11/100
1570/1570 [==============================] - 1s 727us/step - loss: 600.1824 - mae: 18.8780
Epoch 12/100
1570/1570 [==============================] - 1s 661us/step - loss: 717.2169 - mae: 20.2712
Epoch 13/100
1570/1570 [==============================] - 1s 685us/step - loss: 627.1095 - mae: 19.3082
Epoch 14/100
1570/1570 [==============================] - 1s 686us/step - loss: 713.9377 - mae: 19.4658
Epoch 15/100
1570/1570 [==============================] - 1s 696us/step - loss: 671.5330 - mae: 19.8928
Epoch 16/100
1570/1570 [==============================] - 1s 689us/step - loss: 809.9895 - mae: 21.1933
Epoch 17/100
1570/1570 [==============================] - 1s 697us/step - loss: 626.8463 - mae: 18.9511
Epoch 18/100
1570/1570 [==============================] - 1s 690us/step - loss: 664.7856 - mae: 19.5640
Epoch 19/100
1570/1570 [==============================] - 1s 702us/step - loss: 695.1313 - mae: 20.3170
Epoch 20/100
1570/1570 [==============================] - 1s 685us/step - loss: 844.7645 - mae: 21.5548
Epoch 21/100
1570/1570 [==============================] - 1s 749us/step - loss: 750.3210 - mae: 20.9530
Epoch 22/100
1570/1570 [==============================] - 1s 682us/step - loss: 631.6428 - mae: 19.1385
Epoch 23/100
1570/1570 [==============================] - 1s 694us/step - loss: 721.4250 - mae: 20.0112
Epoch 24/100
1570/1570 [==============================] - 1s 687us/step - loss: 879.2552 - mae: 22.0182
Epoch 25/100
1570/1570 [==============================] - 1s 684us/step - loss: 827.2421 - mae: 21.6464
Epoch 26/100
1570/1570 [==============================] - 1s 700us/step - loss: 701.4094 - mae: 20.2091
Epoch 27/100
1570/1570 [==============================] - 1s 691us/step - loss: 695.8590 - mae: 20.0878
Epoch 28/100
1570/1570 [==============================] - 1s 692us/step - loss: 703.5710 - mae: 20.0760
Epoch 29/100
1570/1570 [==============================] - 1s 699us/step - loss: 632.8063 - mae: 19.4138
Epoch 30/100
1570/1570 [==============================] - 1s 701us/step - loss: 653.7804 - mae: 19.7783
Epoch 31/100
1570/1570 [==============================] - 1s 691us/step - loss: 1016.0288 - mae: 23.3376
Epoch 32/100
1570/1570 [==============================] - 1s 701us/step - loss: 695.7961 - mae: 20.5422
Epoch 33/100
1570/1570 [==============================] - 1s 719us/step - loss: 642.6339 - mae: 19.6469
Epoch 34/100
1570/1570 [==============================] - 1s 753us/step - loss: 604.4878 - mae: 18.8055
Epoch 35/100
1570/1570 [==============================] - 1s 696us/step - loss: 669.7369 - mae: 20.0942
Epoch 36/100
1570/1570 [==============================] - 1s 697us/step - loss: 778.4235 - mae: 20.4621
Epoch 37/100
1570/1570 [==============================] - 1s 700us/step - loss: 697.3196 - mae: 19.9764
Epoch 38/100
1570/1570 [==============================] - 1s 697us/step - loss: 600.9893 - mae: 18.5254
Epoch 39/100
1570/1570 [==============================] - 1s 704us/step - loss: 710.3656 - mae: 20.0062
Epoch 40/100
1570/1570 [==============================] - 1s 697us/step - loss: 704.0516 - mae: 20.1501
Epoch 41/100
1570/1570 [==============================] - 1s 695us/step - loss: 733.9904 - mae: 20.4308
Epoch 42/100
1570/1570 [==============================] - 1s 697us/step - loss: 555.9091 - mae: 18.1039
Epoch 43/100
1570/1570 [==============================] - 1s 683us/step - loss: 647.9240 - mae: 18.9008
Epoch 44/100
1570/1570 [==============================] - 1s 708us/step - loss: 696.8072 - mae: 20.2532
Epoch 45/100
1570/1570 [==============================] - 1s 721us/step - loss: 639.6487 - mae: 19.3308
Epoch 46/100
1570/1570 [==============================] - 1s 726us/step - loss: 554.9702 - mae: 17.9829
Epoch 47/100
1570/1570 [==============================] - 1s 725us/step - loss: 605.5833 - mae: 18.8098
Epoch 48/100
1570/1570 [==============================] - 1s 745us/step - loss: 823.3652 - mae: 22.1876
Epoch 49/100
1570/1570 [==============================] - 1s 745us/step - loss: 700.0248 - mae: 20.3396
Epoch 50/100
1570/1570 [==============================] - 1s 763us/step - loss: 707.9413 - mae: 20.2279
Epoch 51/100
1570/1570 [==============================] - 1s 757us/step - loss: 700.5992 - mae: 19.8542
Epoch 52/100
1570/1570 [==============================] - 1s 702us/step - loss: 645.3628 - mae: 19.1472
Epoch 53/100
1570/1570 [==============================] - 1s 701us/step - loss: 636.1317 - mae: 19.1446
Epoch 54/100
1570/1570 [==============================] - 1s 778us/step - loss: 667.7475 - mae: 19.5081
Epoch 55/100
1570/1570 [==============================] - 1s 750us/step - loss: 676.5157 - mae: 19.5577
Epoch 56/100
1570/1570 [==============================] - 1s 709us/step - loss: 929.1287 - mae: 22.7297
Epoch 57/100
1570/1570 [==============================] - 1s 741us/step - loss: 804.6200 - mae: 21.4121
Epoch 58/100
1570/1570 [==============================] - 1s 750us/step - loss: 725.5538 - mae: 20.5640
Epoch 59/100
1570/1570 [==============================] - 1s 726us/step - loss: 732.9226 - mae: 20.6287
Epoch 60/100
1570/1570 [==============================] - 1s 774us/step - loss: 763.7737 - mae: 20.9384
Epoch 61/100
1570/1570 [==============================] - 1s 771us/step - loss: 598.0344 - mae: 18.4678
Epoch 62/100
1570/1570 [==============================] - 1s 731us/step - loss: 783.2723 - mae: 21.0092
Epoch 63/100
1570/1570 [==============================] - 1s 689us/step - loss: 613.8795 - mae: 18.4673
Epoch 64/100
1570/1570 [==============================] - 1s 689us/step - loss: 891.0996 - mae: 21.7655
Epoch 65/100
1570/1570 [==============================] - 1s 683us/step - loss: 680.8638 - mae: 19.8157
Epoch 66/100
1570/1570 [==============================] - 1s 705us/step - loss: 660.6561 - mae: 19.6660
Epoch 67/100
1570/1570 [==============================] - 1s 698us/step - loss: 768.7937 - mae: 21.4989
Epoch 68/100
1570/1570 [==============================] - 1s 688us/step - loss: 667.2055 - mae: 19.1970
Epoch 69/100
1570/1570 [==============================] - 1s 706us/step - loss: 735.8928 - mae: 20.3921
Epoch 70/100
1570/1570 [==============================] - 1s 696us/step - loss: 843.5947 - mae: 21.6246
Epoch 71/100
1570/1570 [==============================] - 1s 676us/step - loss: 612.9269 - mae: 18.9968
Epoch 72/100
1570/1570 [==============================] - 1s 745us/step - loss: 631.1614 - mae: 18.9914
Epoch 73/100
1570/1570 [==============================] - 1s 693us/step - loss: 713.9399 - mae: 20.2510
Epoch 74/100
1570/1570 [==============================] - 1s 635us/step - loss: 628.4302 - mae: 19.2150
Epoch 75/100
1570/1570 [==============================] - 1s 651us/step - loss: 740.0641 - mae: 20.8704
Epoch 76/100
1570/1570 [==============================] - 1s 622us/step - loss: 634.4455 - mae: 19.2745
Epoch 77/100
1570/1570 [==============================] - 1s 609us/step - loss: 716.5535 - mae: 20.6797
Epoch 78/100
1570/1570 [==============================] - 1s 639us/step - loss: 735.1273 - mae: 20.3919
Epoch 79/100
1570/1570 [==============================] - 1s 657us/step - loss: 630.1802 - mae: 19.2159
Epoch 80/100
1570/1570 [==============================] - 1s 616us/step - loss: 597.2530 - mae: 18.6527
Epoch 81/100
1570/1570 [==============================] - 1s 684us/step - loss: 662.5781 - mae: 19.5194
Epoch 82/100
1570/1570 [==============================] - 1s 699us/step - loss: 631.2231 - mae: 19.0265
Epoch 83/100
1570/1570 [==============================] - 1s 638us/step - loss: 719.9138 - mae: 20.2006
Epoch 84/100
1570/1570 [==============================] - 1s 613us/step - loss: 578.8290 - mae: 18.5974
Epoch 85/100
1570/1570 [==============================] - 1s 630us/step - loss: 833.9090 - mae: 21.5101
Epoch 86/100
1570/1570 [==============================] - 1s 689us/step - loss: 724.4709 - mae: 20.2260
Epoch 87/100
1570/1570 [==============================] - 1s 650us/step - loss: 659.7275 - mae: 19.9460
Epoch 88/100
1570/1570 [==============================] - 1s 655us/step - loss: 710.6397 - mae: 20.5307
Epoch 89/100
1570/1570 [==============================] - 1s 641us/step - loss: 703.9041 - mae: 20.2339
Epoch 90/100
1570/1570 [==============================] - 1s 641us/step - loss: 747.5262 - mae: 20.9598
Epoch 91/100
1570/1570 [==============================] - 1s 671us/step - loss: 803.8232 - mae: 21.4400
Epoch 92/100
1570/1570 [==============================] - 1s 637us/step - loss: 643.2718 - mae: 19.1185
Epoch 93/100
1570/1570 [==============================] - 1s 656us/step - loss: 735.5874 - mae: 20.7587
Epoch 94/100
1570/1570 [==============================] - 1s 646us/step - loss: 659.4421 - mae: 19.6404
Epoch 95/100
1570/1570 [==============================] - 1s 699us/step - loss: 632.8841 - mae: 19.2961
Epoch 96/100
1570/1570 [==============================] - 1s 702us/step - loss: 713.7954 - mae: 20.0682
Epoch 97/100
1570/1570 [==============================] - 1s 623us/step - loss: 650.3159 - mae: 19.1298
Epoch 98/100
1570/1570 [==============================] - 1s 642us/step - loss: 786.0706 - mae: 21.4033
Epoch 99/100
1570/1570 [==============================] - 1s 625us/step - loss: 687.3713 - mae: 19.8312
Epoch 100/100
1570/1570 [==============================] - 1s 683us/step - loss: 692.3904 - mae: 20.3091
forecast = []
for time in range(len(data.pm25) - window_size):
forecast.append(model.predict(np.array(data.pm25[time:time + window_size])[np.newaxis]))
forecast = forecast[split_time-window_size:]
results = np.array(forecast)[:, 0, 0]
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, results)
tf.keras.metrics.mean_absolute_error(x_valid, results).numpy()
13.240775
model.save('pm25_DL_model')
INFO:tensorflow:Assets written to: pm25_DL_model\assets
model = tf.keras.models.load_model('pm25_DL_model')
model.predict(np.array(data.pm25[1:15])[np.newaxis])
array([[163.71252]], dtype=float32)
This model is currently deployed as "Deep learning model" in Git actions
RNN¶
tf.keras.backend.clear_session()
tf.random.set_seed(51)
np.random.seed(51)
train_set = windowed_dataset(x_train, window_size, batch_size, shuffle_buffer_size)
model = tf.keras.models.Sequential([
tf.keras.layers.Lambda(lambda x: tf.expand_dims(x, axis=-1),
input_shape=[None]),
tf.keras.layers.SimpleRNN(14, return_sequences=True),
tf.keras.layers.SimpleRNN(14, return_sequences=True),
tf.keras.layers.Dense(1),
tf.keras.layers.Lambda(lambda x: x * 200.0)
])
lr_schedule = tf.keras.callbacks.LearningRateScheduler(
lambda epoch: 1e-8 * 10**(epoch / 20))
optimizer = tf.keras.optimizers.SGD(learning_rate=1e-8, momentum=0.9)
model.compile(loss=tf.keras.losses.Huber(),
optimizer=optimizer,
metrics=["mae"])
history = model.fit(train_set, epochs=25, callbacks=[lr_schedule])
Epoch 1/25
1570/1570 [==============================] - 7s 3ms/step - loss: 255.5130 - mae: 256.0130
Epoch 2/25
1570/1570 [==============================] - 6s 3ms/step - loss: 136.1440 - mae: 136.6439
Epoch 3/25
1570/1570 [==============================] - 5s 3ms/step - loss: 44.4807 - mae: 44.9783
Epoch 4/25
1570/1570 [==============================] - 5s 3ms/step - loss: 36.5102 - mae: 37.0077
Epoch 5/25
1570/1570 [==============================] - 5s 3ms/step - loss: 36.1142 - mae: 36.6120
Epoch 6/25
1570/1570 [==============================] - 5s 3ms/step - loss: 35.6905 - mae: 36.1887
Epoch 7/25
1570/1570 [==============================] - 5s 3ms/step - loss: 35.2254 - mae: 35.7231
Epoch 8/25
1570/1570 [==============================] - 5s 3ms/step - loss: 34.7579 - mae: 35.2558
Epoch 9/25
1570/1570 [==============================] - 5s 3ms/step - loss: 34.1971 - mae: 34.6951
Epoch 10/25
1570/1570 [==============================] - 5s 3ms/step - loss: 33.6498 - mae: 34.1480
Epoch 11/25
1570/1570 [==============================] - 5s 3ms/step - loss: 32.9927 - mae: 33.4904
Epoch 12/25
1570/1570 [==============================] - 5s 3ms/step - loss: 32.3265 - mae: 32.8238
Epoch 13/25
1570/1570 [==============================] - 5s 3ms/step - loss: 31.7288 - mae: 32.2260
Epoch 14/25
1570/1570 [==============================] - 5s 3ms/step - loss: 31.1841 - mae: 31.6818
Epoch 15/25
1570/1570 [==============================] - 5s 3ms/step - loss: 30.7113 - mae: 31.2086
Epoch 16/25
1570/1570 [==============================] - 5s 3ms/step - loss: 30.3737 - mae: 30.8711
Epoch 17/25
1570/1570 [==============================] - 5s 3ms/step - loss: 30.1141 - mae: 30.6113
Epoch 18/25
1570/1570 [==============================] - 5s 3ms/step - loss: 29.7798 - mae: 30.2774
Epoch 19/25
1570/1570 [==============================] - 5s 3ms/step - loss: 29.6268 - mae: 30.1236
Epoch 20/25
1570/1570 [==============================] - 5s 3ms/step - loss: 29.4335 - mae: 29.9309
Epoch 21/25
1570/1570 [==============================] - 5s 3ms/step - loss: 29.3501 - mae: 29.8474
Epoch 22/25
1570/1570 [==============================] - 5s 3ms/step - loss: 30.9055 - mae: 31.4033
Epoch 23/25
1570/1570 [==============================] - 5s 3ms/step - loss: 29.6605 - mae: 30.1580
Epoch 24/25
1570/1570 [==============================] - 5s 3ms/step - loss: 29.5224 - mae: 30.0199
Epoch 25/25
1570/1570 [==============================] - 5s 3ms/step - loss: 28.9797 - mae: 29.4764
plt.semilogx(history.history["lr"], history.history["loss"])
plt.axis([1e-8, 1e-6, 20, 300])
forecast = []
for time in range(len(data.pm25) - window_size):
forecast.append(model.predict(np.array(data.pm25[time:time + window_size])[np.newaxis]))
forecast = forecast[split_time-window_size:]
results = np.array(forecast)[:, 0, 0]
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, results)
tf.keras.metrics.mean_absolute_error(x_valid, results).numpy()
array([39.826717, 39.908363, 40.442093, ..., 39.340984, 39.340984], dtype=float32)
import matplotlib.image as mpimg
import matplotlib.pyplot as plt
#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
mae=history.history['mae']
loss=history.history['loss']
epochs=range(len(loss)) # Get number of epochs
#------------------------------------------------
# Plot MAE and Loss
#------------------------------------------------
plt.plot(epochs, mae, 'r')
plt.plot(epochs, loss, 'b')
plt.title('MAE and Loss')
plt.xlabel("Epochs")
plt.ylabel("Accuracy")
plt.legend(["MAE", "Loss"])
plt.figure()
epochs_zoom = epochs[200:]
mae_zoom = mae[200:]
loss_zoom = loss[200:]
#------------------------------------------------
# Plot Zoomed MAE and Loss
#------------------------------------------------
plt.plot(epochs_zoom, mae_zoom, 'r')
plt.plot(epochs_zoom, loss_zoom, 'b')
plt.title('MAE and Loss')
plt.xlabel("Epochs")
plt.ylabel("Accuracy")
plt.legend(["MAE", "Loss"])
plt.figure()
LSTM¶
def model_forecast(model, series, window_size):
ds = tf.data.Dataset.from_tensor_slices(series)
ds = ds.window(window_size, shift=1, drop_remainder=True)
ds = ds.flat_map(lambda w: w.batch(window_size))
ds = ds.batch(32).prefetch(1)
forecast = model.predict(ds)
return forecast
tf.keras.backend.clear_session()
tf.random.set_seed(51)
np.random.seed(51)
x_train_LSTM = tf.expand_dims(x_train, axis=-1)
train_set = windowed_dataset(x_train_LSTM, window_size, batch_size, shuffle_buffer_size)
train_set
model = tf.keras.models.Sequential([
tf.keras.layers.Conv1D(filters=32, kernel_size=5,
strides=1, padding="causal",
activation="relu",
input_shape=[None, 1]),
tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(32, return_sequences=True)),
tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(32, return_sequences=True)),
tf.keras.layers.Dense(1),
tf.keras.layers.Lambda(lambda x: x * 200)
])
lr_schedule = tf.keras.callbacks.LearningRateScheduler(
lambda epoch: 1e-8 * 10**(epoch / 20))
optimizer = tf.keras.optimizers.SGD(learning_rate=1e-8, momentum=0.9)
model.compile(loss=tf.keras.losses.Huber(),
optimizer=optimizer,
metrics=["mae"])
history = model.fit(train_set, epochs=25, callbacks=[lr_schedule])
Epoch 1/25
1570/1570 [==============================] - 27s 12ms/step - loss: 51.0839 - mae: 51.5817
Epoch 2/25
1570/1570 [==============================] - 21s 13ms/step - loss: 30.5634 - mae: 31.0600 0s - loss: 30.5700 - mae: 31.06
Epoch 3/25
1570/1570 [==============================] - 20s 13ms/step - loss: 28.5261 - mae: 29.0220
Epoch 4/25
1570/1570 [==============================] - 23s 14ms/step - loss: 27.1795 - mae: 27.6754
Epoch 5/25
1570/1570 [==============================] - 21s 13ms/step - loss: 25.9100 - mae: 26.4058
Epoch 6/25
1570/1570 [==============================] - 21s 13ms/step - loss: 24.7144 - mae: 25.2104
Epoch 7/25
1570/1570 [==============================] - 22s 14ms/step - loss: 23.5953 - mae: 24.0904
Epoch 8/25
1570/1570 [==============================] - 21s 13ms/step - loss: 22.6447 - mae: 23.1403
Epoch 9/25
1570/1570 [==============================] - 22s 14ms/step - loss: 21.7317 - mae: 22.2269
Epoch 10/25
1570/1570 [==============================] - 22s 14ms/step - loss: 20.8462 - mae: 21.3408
Epoch 11/25
1570/1570 [==============================] - 22s 14ms/step - loss: 20.1405 - mae: 20.6347
Epoch 12/25
1570/1570 [==============================] - 22s 14ms/step - loss: 19.4537 - mae: 19.9481
Epoch 13/25
1570/1570 [==============================] - 22s 14ms/step - loss: 18.8216 - mae: 19.3158
Epoch 14/25
1570/1570 [==============================] - 22s 14ms/step - loss: 18.2066 - mae: 18.7004
Epoch 15/25
1570/1570 [==============================] - 22s 14ms/step - loss: 17.5309 - mae: 18.0234
Epoch 16/25
1570/1570 [==============================] - 22s 14ms/step - loss: 17.3460 - mae: 17.8395
Epoch 17/25
1570/1570 [==============================] - 22s 14ms/step - loss: 16.8951 - mae: 17.3882
Epoch 18/25
1570/1570 [==============================] - 23s 15ms/step - loss: 16.5255 - mae: 17.0192
Epoch 19/25
1570/1570 [==============================] - 22s 14ms/step - loss: 16.4288 - mae: 16.9225
Epoch 20/25
1570/1570 [==============================] - 22s 14ms/step - loss: 16.1572 - mae: 16.6509
Epoch 21/25
1570/1570 [==============================] - 22s 14ms/step - loss: 15.7839 - mae: 16.2775
Epoch 22/25
1570/1570 [==============================] - 22s 14ms/step - loss: 15.7438 - mae: 16.2366
Epoch 23/25
1570/1570 [==============================] - 23s 15ms/step - loss: 15.6320 - mae: 16.1244
Epoch 24/25
1570/1570 [==============================] - 23s 14ms/step - loss: 15.7910 - mae: 16.2841
Epoch 25/25
1570/1570 [==============================] - 22s 14ms/step - loss: 15.5656 - mae: 16.0587
rnn_forecast = model_forecast(model, np.array(data.pm25)[..., np.newaxis], window_size)
rnn_forecast = rnn_forecast[split_time - window_size:-1, -1, 0]
plt.figure(figsize=(10, 6))
plot_series(time_valid, x_valid)
plot_series(time_valid, rnn_forecast)
tf.keras.metrics.mean_absolute_error(x_valid, rnn_forecast).numpy()
17.472342
import matplotlib.image as mpimg
import matplotlib.pyplot as plt
#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
mae=history.history['mae']
loss=history.history['loss']
epochs=range(len(loss)) # Get number of epochs
#------------------------------------------------
# Plot MAE and Loss
#------------------------------------------------
plt.plot(epochs, mae, 'r')
plt.plot(epochs, loss, 'b')
plt.title('MAE and Loss')
plt.xlabel("Epochs")
plt.ylabel("Accuracy")
plt.legend(["MAE", "Loss"])
plt.figure()
epochs_zoom = epochs[200:]
mae_zoom = mae[200:]
loss_zoom = loss[200:]
#------------------------------------------------
# Plot Zoomed MAE and Loss
#------------------------------------------------
plt.plot(epochs_zoom, mae_zoom, 'r')
plt.plot(epochs_zoom, loss_zoom, 'b')
plt.title('MAE and Loss')
plt.xlabel("Epochs")
plt.ylabel("Accuracy")
plt.legend(["MAE", "Loss"])
plt.figure()
