regression2_polynomial.py

import numpy as np
import matplotlib.pyplot as plt

# 学習データを読み込む
train = np.loadtxt('click.csv', delimiter=',', dtype='int', skiprows=1)
train_x = train[:,0]
train_y = train[:,1]

# 標準化
mu = train_x.mean()
sigma = train_x.std()
def standardize(x):
    return (x - mu) / sigma

train_z = standardize(train_x)

# パラメータを初期化
theta = np.random.rand(3)

# 学習データの行列を作る
def to_matrix(x):
    return np.vstack([np.ones(x.size), x, x ** 2]).T

X = to_matrix(train_z)

# 予測関数
def f(x):
    return np.dot(x, theta)

# 目的関数
def E(x, y):
    return 0.5 * np.sum((y - f(x)) ** 2)

# 学習率
ETA = 1e-2

# 誤差の差分
diff = 1

# 更新回数
count = 0

# 誤差の差分が0.01以下になるまでパラメータ更新を繰り返す
error = E(X, train_y)
while diff > 1e-3:
    # 更新結果を一時変数に保存
    theta = theta - ETA * np.dot(f(X) - train_y, X)

    # 前回の誤差との差分を計算
    current_error = E(X, train_y)
    diff = error - current_error
    error = current_error

    # ログの出力
    count += 1
    log = '{}回目: theta = {}, 差分 = {:.4f}'
    print(log.format(count, theta, diff))

# プロットして確認
x = np.linspace(-3, 3, 100)
plt.plot(train_z, train_y, 'o')
plt.plot(x, f(to_matrix(x)))
plt.show()