TF2.x: 02. Multi variable Linear Regression

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2-1. Simple Example (2 variables)

import tensorflow as tf
import numpy as np

tf.random.set_seed(1234)        # for reproducibility

x1_data = [1, 0, 3, 0, 5]
x2_data = [0, 2, 0, 4, 0]
y_data  = [1, 2, 3, 4, 5]

# tf.random.uniform(shape=[1], minval=-10.0, maxval=10.0)
W1 = tf.Variable(tf.random.uniform([1], -10.0, 10.0))   
W2 = tf.Variable(tf.random.uniform([1], -10.0, 10.0))
b  = tf.Variable(tf.random.uniform([1], -10.0, 10.0))

learning_rate = tf.Variable(0.001)

for i in range(1000+1):
    with tf.GradientTape() as tape:
        hypothesis = W1 * x1_data + W2 * x2_data + b
        cost = tf.reduce_mean(tf.square(hypothesis - y_data))
    W1_grad, W2_grad, b_grad = tape.gradient(cost, [W1, W2, b])
    W1.assign_sub(learning_rate * W1_grad)
    W2.assign_sub(learning_rate * W2_grad)
    b.assign_sub(learning_rate * b_grad)

    if i % 100 == 0:
        print("{:5} | {:10.6f} | {:10.4f} | {:10.4f} | {:10.6f}".format(
          i, cost.numpy(), W1.numpy()[0], W2.numpy()[0], b.numpy()[0]))

2-2. Simple Example (2 variables with Matrix)

x_data = [[1., 0., 3., 0., 5.],
          [0., 2., 0., 4., 0.]]
y_data  = [1, 2, 3, 4, 5]

print('x_data dim.:', tf.shape(x_data).numpy())
print('y_data dim.:', tf.shape(y_data).numpy())

가중치 설정

# W 차원 (1, 2) : W * (2, 5)  = (1, 5) 
W = tf.Variable(tf.random.uniform([1, 2], -1.0, 1.0))
b = tf.Variable(tf.random.uniform([1], -1.0, 1.0))

print(W.numpy())
print(b.numpy())

가중치 학습

learning_rate = tf.Variable(0.001)

for i in range(1000+1):
    with tf.GradientTape() as tape:
        hypothesis = tf.matmul(W, x_data) + b               # (1, 2) * (2, 5) = (1, 5)
        cost = tf.reduce_mean(tf.square(hypothesis - y_data))

        W_grad, b_grad = tape.gradient(cost, [W, b])
        W.assign_sub(learning_rate * W_grad)
        b.assign_sub(learning_rate * b_grad)
    
    if i % 100 == 0:
        print("{:5} | {:10.6f} | {:10.4f} | {:10.4f} | {:10.6f}".format(
            i, cost.numpy(), W.numpy()[0][0], W.numpy()[0][1], b.numpy()[0]))

2-3. Simple Example (Hypothesis without b)

별도의 bias 변수를 설정하지 않고, W 가중치 변수에 반영.
tf1.x 버전에서 optimizer로 사용된 tf.train.GradientDescentOptimizer는 tf.keras.optimizers.SGD로 변경됨

# 앞의 코드에서 bias(b)를 행렬에 추가
x_data = [[1., 1., 1., 1., 1.],     # bias를 '1'로 설정했으나, W가 곱해지고 열 원소가 더해지면
          [1., 0., 3., 0., 5.],     # 결과적으로 변수 b 원소가 더해진 것과 동일한 상황.
          [0., 2., 0., 4., 0.]]
y_data  = [1, 2, 3, 4, 5]

W = tf.Variable(tf.random.uniform([1, 3], -1.0, 1.0))  # [1, 3]으로 변경하고 X_data와 연산을 하면, bias가 반영됨.

learning_rate = 0.001
optimizer = tf.keras.optimizers.SGD(learning_rate)    #tf.1x버전의 tf.train.GradientDescentOptimizer를 대체

for i in range(1000+1):
    with tf.GradientTape() as tape:
        hypothesis = tf.matmul(W, x_data)                # bias 없음
        cost = tf.reduce_mean(tf.square(hypothesis - y_data))

    grads = tape.gradient(cost, [W])
    optimizer.apply_gradients(grads_and_vars=zip(grads,[W]))
    if i % 100 == 0:
        print("{:5} | {:10.6f} | {:10.4f} | {:10.4f} | {:10.4f}".format(
            i, cost.numpy(), W.numpy()[0][0], W.numpy()[0][1], W.numpy()[0][2]))

2.4 Simple Example (Custom Gradient)

tf1.x 버전에서 optimizer로 사용된 tf.train.GradientDescentOptimizer는 tf.keras.optimizers.SGD로 변경됨
optimizer.apply_gradients(): update

# Multi-variable linear regression (1)

X = tf.constant([[1., 2.], 
                 [3., 4.]])
y = tf.constant([[1.5], [3.5]])

W = tf.Variable(tf.random.normal([2, 1]))
b = tf.Variable(tf.random.normal([1]))

# Create an optimizer
optimizer = tf.keras.optimizers.SGD(learning_rate=0.01)   #tf.1x버전의 tf.train.GradientDescentOptimizer를 대체

n_epoch = 1000+1
print("epoch | cost")
for i in range(n_epoch):
    # Use tf.GradientTape() to record the gradient of the cost function
    with tf.GradientTape() as tape:
        y_pred = tf.matmul(X, W) + b
        cost = tf.reduce_mean(tf.square(y_pred - y))

    # calculates the gradients of the loss
    grads = tape.gradient(cost, [W, b])
    
    # updates parameters (W and b)
    optimizer.apply_gradients(grads_and_vars=zip(grads, [W, b]))
    if i % 100 == 0:
        print("{:5} | {:10.6f}".format(i, cost.numpy()))

2-5. More Examples (Predicting exam score)

hypothesis = w1 x1 + w2 x2 + w3 * x3 + b

# 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
w1 = tf.Variable(10.)
w2 = tf.Variable(10.)
w3 = tf.Variable(10.)
b  = tf.Variable(10.)

learning_rate = 0.000001

for i in range(1000+1):
    # 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)
    w2.assign_sub(learning_rate * w2_grad)
    w3.assign_sub(learning_rate * w3_grad)
    b.assign_sub(learning_rate * b_grad)

    if i % 100 == 0:
      print("{:5} | {:12.4f}".format(i, cost.numpy()))

Matrix 및 hypothesis 함수 사용

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]]

W = tf.Variable(tf.random.normal([3, 1]))
b = tf.Variable(tf.random.normal([1]))

learning_rate = 0.000001

# hypothesis, prediction function
def predict(X):
    return tf.matmul(X, W) + b

print("epoch | cost")

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

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

    # updates parameters (W and b)
    W.assign_sub(learning_rate * W_grad)
    b.assign_sub(learning_rate * b_grad)
    
    if i % 100 == 0:
        print("{:5} | {:10.4f}".format(i, cost.numpy()))

predict

Y # labels, 실제값

predict(X).numpy() # prediction, 예측값

# 새로운 데이터에 대한 예측
predict([[ 89.,  95.,  92.],[ 84.,  92.,  85.]]).numpy()

Reference

Ethan