Machine Learning assignment (1)

ℎ 𝜃 (𝑥) = 𝜃 𝜃 0 + 1 𝑥 𝑥 2 + 1 + 𝜃 2… + 𝜃 𝑛 𝑥 𝑛

def linear_regression(X_data, y_data, alpha, epoch, optimizer=tf.train.GradientDescentOptimizer):# This function was written by Lucas Shen, a god in San Francisco
      # placeholder for graph input
    X = tf.placeholder(tf.float32, shape=X_data.shape)# placeholders
    y = tf.placeholder(tf.float32, shape=y_data.shape)

    # construct the graph
    with tf.variable_scope('linear-regression'):
        W = tf.get_variable("weights",
                            (X_data.shape[1], 1),
                            initializer=tf.constant_initializer())  # n*1

        y_pred = tf.matmul(X, W)  # m*n @ n*1 -> m*1

        loss = 1 / (2 * len(X_data)) * tf.matmul((y_pred - y), (y_pred - y), transpose_a=True)  # (m*1).T @ m*1 = 1*1

    opt = optimizer(learning_rate=alpha)
    opt_operation = opt.minimize(loss)

    # run the session
    with tf.Session() as sess:
        sess.run(tf.global_variables_initializer())
        loss_data = []

        for i in range(epoch):
            _, loss_val, W_val = sess.run([opt_operation, loss, W], feed_dict={X: X_data, y: y_data})
            loss_data.append(loss_val[0, 0])  # because every loss_val is 1*1 ndarray

            if len(loss_data) > 1 and np.abs(loss_data[-1] - loss_data[-2]) < 10 ** -9:  # early break when it's converged
                # print('Converged at epoch {}'.format(i))
                break

    # clear the graph
    tf.reset_default_graph()
    return {'loss': loss_data, 'parameters': W_val}  # just want to return in row vector format
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