Multi-Variable Linear Regression

H(x1,x2,x3)=w1x1+w2x2+w3x3+bH(x_1, x_2, x_3) = w_1x_1 + w_2x_2 + w_3x_3 + bH(x1​,x2​,x3​)=w1​x1​+w2​x2​+w3​x3​+b

Code

import tensorflow as tf

# data and label
x1 = [73., 93., 89., 96., 73.]
x2 = [80., 88., 91., 98., 66.]
x3 = [75., 93., 90., 100., 70.]
Y = [152., 185., 180., 196., 142.]

# weights and bias
w1 = tf.Variable(tf.random.normal([1]))
w2 = tf.Variable(tf.random.normal([1]))
w3 = tf.Variable(tf.random.normal([1]))
b = tf.Variable(tf.random.normal([1]))

learning_rate = 0.000001

for i in range(1001):
    # tf.GradientTape() to record the gradient of the cost function
    with tf.GradientTape() as tape:
        hypothesis = (w1 * x1) + (w2 * x2) + (w3 * x3) + b
        cost = tf.reduce_mean(tf.square(hypothesis - Y))

    # calculates the gradients of the cost
    w1_grad, w2_grad, w3_grad, b_grad = tape.gradient(cost, [w1, w2, w3, b])

    # update w1, w2, w3, and b
    #    w1.assign_sub(learning_rate * w1_grad)
    # => w1 = w1 - learning_rate * w1_grad
    w1.assign_sub(learning_rate * w1_grad)
    w2.assign_sub(learning_rate * w2_grad)
    w3.assign_sub(learning_rate * w3_grad)
    b.assign_sub(learning_rate * b_grad)
    
    if i % 50 == 0:
        print(f'{i:5} | {cost.numpy():12.4f}')

Output

costは非常に大きな値であり,更新された値によって徐々に減少することがわかる.ただし,変数(feature)が増えるにつれてweights値も一つ一つ記入する.

Using Matrix H(X)=XWH(X) = XWH(X)=XW

Code

import numpy as np

data = np.array([
    # x1,   x2,   x3,   y
    [ 73.,  80.,  75., 152.],
    [ 93.,  88.,  93., 185.],
    [ 89.,  91.,  90., 180.],
    [ 96.,  98., 100., 196.],
    [ 73.,  66.,  70., 142.]
], dtype=np.float32)

# slice data
X = data[:, :-1]
y = data[:, [-1]]

# X 의 변수(열)가 3개이므로 W의 행 값은 3개가 되어야 한다.
# 그리고 개별 인스턴스는 1개 이므로 W의 열의 값은 1개가 되어야 한다.
# y(출력값)은 하나이므로 1개가 되어야 한다.
W = tf.Variable(tf.random.normal([3, 1]))
b = tf.Variable(tf.random.normal([1]))

learning_rate = 0.000001

# hypothesis, prediction function
# 이후에 b 는 생략할 수도 있다.
def predict(X):
    return tf.matmul(X, W) + b

n_epochs = 2000
for i in range(n_epochs + 1):
    # record the gradient descent of the cost function
    with tf.GradientTape() as tape:
        cost = tf.reduce_mean(tf.square(predict(X) - y))

    # calculates the gradients of the cost
    W_grad, b_grad = tape.gradient(cost, [W, b])

    # update w1, w2, w3, and b
    #    w1.assign_sub(learning_rate * w1_grad)
    # => w1 = w1 - learning_rate * w1_grad
    W.assign_sub(learning_rate * W_grad)
    b.assign_sub(learning_rate * b_grad)
    
    if i % 100 == 0:
        print(f'{i:5} | {cost.numpy():10.4f}')

Output

With Matrix

行列を使用すると、変数の個数に応じて重み付けを使用する必要がなく、同じ式を使用できます.また、性能面でも有利である.