Why isn't my so simple linear regression working

Question

I am new to tensorflow-2 and I was starting my learning curve, with the follow simple Linear-Regression model:

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt


# Make data
num_samples, w, b = 20, 0.5, 2
xs = np.asarray(range(num_samples))
ys = np.asarray([x*w + b + np.random.normal() for x in range(num_samples)])
xts = tf.convert_to_tensor(xs, dtype=tf.float32)
yts = tf.convert_to_tensor(xs, dtype=tf.float32)
plt.plot(xs, ys, 'ro')

class Linear(tf.keras.Model):
    def __init__(self, name='linear', **kwargs):
        super().__init__(name='linear', **kwargs)
        self.w = tf.Variable(0, True, name="w", dtype=tf.float32)
        self.b = tf.Variable(1, True, name="b", dtype=tf.float32)   

    def call(self, inputs):
        return self.w*inputs + self.b

class Custom(tf.keras.callbacks.Callback):
    def on_epoch_end(self, epoch, logs=None):
        if epoch % 20 == 0:
            preds = self.model.predict(xts)
            plt.plot(xs, preds, label='{} {:7.2f}'.format(epoch, logs['loss']))
            print('The average loss for epoch {} is .'.format(epoch, logs['loss']))

x = tf.keras.Input(dtype=tf.float32, shape=[])
#model = tf.keras.Sequential([tf.keras.layers.Dense(units=1, input_shape=[1])])
model = Linear()
optimizer = tf.keras.optimizers.RMSprop(learning_rate=0.001)
model.compile(optimizer=optimizer, loss='MSE')
model.fit(x=xts, y=yts, verbose=1, batch_size=4, epochs=250, callbacks=[Custom()])

plt.legend()
plt.show()

For a reason I don't understand it seems like my model is not fitting the curve. I also tried with keras.layers.Dense(1) and I had the same exact result. Also it seems like the results don't correspond to a proper loss function, as around epoch 120 the model should have less loss than on 250.

Can you maybe help me understand what I am doing wrong? Thanks a lot!

Answer 1

There is a small bug in your code as xts and yts are identical to each other, ie you wrote

xts = tf.convert_to_tensor(xs, dtype=tf.float32)
yts = tf.convert_to_tensor(xs, dtype=tf.float32)

instead of

xts = tf.convert_to_tensor(xs, dtype=tf.float32)
yts = tf.convert_to_tensor(ys, dtype=tf.float32)

which is why the loss doesn't make sense. Once this has been fixed the results are as expected, see the plot below.