파이썬 날코딩: 경사하강법(gradient descent), 선형 회귀

경사하강법은 가설 함수의 기울기(가중치)와 절편(편향)을 찾는 중 하나. 이를 옵티마이저라고 한다. 

단순 선형 회귀

순수 파이썬으로.. 

x = (2, 4, 6, 8)
y = (81, 93, 91, 97)

a = b = 0
lr = 0.03
epochs = 2001

for i in range(epochs):
    pred_y = [a * each_x + b for each_x in x]
    error = [each_y - each_pred_y for each_y, each_pred_y in zip(y, pred_y)]

    a_diff = 2 / len(x) * sum(-each_x * each_error for each_x, each_error in zip(x, error))
    b_diff = 2 / len(x) * sum(-each for each in error)

    a -= lr * a_diff  # a = a - lr * a_diff
    b -= lr * b_diff  # b = b - lr * b_diff

    if i % 100 == 0:
        print(i, a, b)

final_pred_y = [a * each + b for each in x]
print(final_pred_y)

넘파이로

import numpy as np

x = np.array([2, 4, 6, 8])
y = np.array([81, 93, 91, 97])

a = b = 0
lr = 0.03
epochs = 2001

for i in range(epochs):
    pred_y = a * x + b
    error = y - pred_y

    a_diff = 2 / len(x) * np.sum(-x * error)
    b_diff = 2 / len(x) * np.sum(-error)

    a -= lr * a_diff
    b -= lr * b_diff

    if i % 100 == 0:
        print(i, a, b)

final_pred_y = a * x + b
print(final_pred_y)

텐서 플로 / 케라스

import matplotlib.pyplot as plt
import numpy as np
from tensorflow import keras

x = np.array([2, 4, 6, 8])
y = np.array([81, 93, 91, 97])

model = keras.models.Sequential()

model.add(keras.layers.Dense(1, input_dim=1, activation='linear'))
model.compile(optimizer='sgd', loss='mse')
model.fit(x, y, epochs=2001)

plt.scatter(x, y)
plt.plot(x, model.predict(x), 'r')
plt.show()

print(model.predict([7]))