## Chase home lending mortgage trust 2019 atr1

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### Thematic video

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### Chase home lending mortgage trust 2019 atr1 -

Figure 1-5. Sample data and neural network–based estimations

Keras
The next example uses a sequential model with the Keras deep learning package.4 The
model is fitted, or trained, for 100 epochs. The procedure is repeated for five rounds.
After every such round, the approximation by the neural network is updated and
plotted. Figure 1-6 shows how the approximation gradually improves with every
round. This is also reflected in the decreasing MSE values. The end result is not per‐
fect, but again, it is quite good given the simplicity of the model:
In [35]: import tensorflow as tf
tf.random.set_seed(100)

### In [36]: from keras.layers import Dense

from keras.models import Sequential
Using TensorFlow backend.

### In [37]: model = Sequential()

model.compile(loss='mse', optimizer='rmsprop')

### In [38]: ((y - y_) ** 2).mean()

Out[38]: 0.021662355744355866

### In [39]: plt.figure(figsize=(10, 6))

plt.plot(x, y, 'ro', label='sample data')
for _ in range(1, 6):

### 4 For details, see Chollet (2017, ch. 3).

Neural Networks vii
Conclusions 391
References 392

### 14. Financial Singularity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

Notions and Definitions 396
What Is at Stake? 396
Paths to Financial Singularity 400
Orthogonal Skills and Resources 401
Scenarios Before and After 402
Star Trek or Star Wars 403
Conclusions 404
References 404

### Part VI. Appendixes

A. Interactive Neural Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

### C. Convolutional Neural Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447