多项式回归

例1

%matplotlib inline

import tensorflow as tf

import numpy as np

import matplotlib.pyplot as plt

trX = np.linspace(-1, 1, 101)

num_coeffs = 6

trY_coeffs = [1, 2, 3, 4, 5, 6]

trY = 0

for i in range(num_coeffs):

trY += trY_coeffs[i] * np.power(trX, i)

trY += np.random.randn(*trX.shape) * 1.5

plt.scatter(trX, trY)

plt.show()

trX=tf.cast(trX,tf.float32)

trY=tf.cast(trY,tf.float32)

#y_model = model(X, w)

def model(X, w):

    terms = []

    for i in range(num_coeffs):

        term = tf.multiply(w[i], tf.pow(X, i))

        terms.append(term)

    return tf.add_n(terms)

def loss(x, y,w):

    err = model(x,w) - y

    return tf.reduce_mean(tf.square(err))

def grad(x,y,w):

    with tf.GradientTape() as tape:

        loss_ = loss(x,y,w)

    return tape.gradient(loss_,[w])

learning_rate = 0.01

training_epochs = 200

W = tf.Variable(np.random.randn(6),dtype=tf.float32)

loss_list_train = []

optimizer = tf.optimizers.Adam()

for i in range(training_epochs):

    for (x, y) in zip(trX, trY):

        grads=grad(trX, trY,W)

        optimizer.apply_gradients(zip(grads,[W]))

        loss_train =loss(x,y,W).numpy()

        loss_list_train.append(loss_train)

    if i % 20 == 0:

           print("Iteration {}, loss: {}".format(i, loss_train))

w_val = W

print(w_val.numpy())

plt.scatter(trX, trY)

trY2 = 0

for i in range(num_coeffs):

    trY2 += w_val[i] * np.power(trX, i)

plt.plot(trX, trY2, 'r')

plt.show()