PRML/prml_5_11.py at master · Alreschas/PRML · GitHub

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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Apr  2 10:52:30 2017

@author: Narifumi
"""

import numpy as np
import matplotlib.pyplot as plt
import copy

plt.clf()


def aFunc_l1(x):
    ret = np.tanh(x)
    return ret


def aFunc_l2(x):
    ret = x
    return ret


def out_l1(x, w_l1):
    ret = np.matrix(np.append(1, aFunc_l1(w_l1.T.dot(x)))).T
    return ret


def out_l2(x, w_l2):
    ret = np.matrix(aFunc_l2(w_l2.T.dot(x))).T
    return ret

# 正則化コスト関数


def J2(param, *args):
    """最小化を目指すコスト関数を返す"""
    w = param
    wl1 = w[:(N_in + 1) * N_hdn].reshape(N_in + 1, N_hdn)
    wl2 = w[(N_in + 1) * N_hdn:].reshape(N_hdn + 1, N_out)
    # パラメータ以外のデータはargsを通して渡す
    xt, yt, a, c = args
    N = xt.shape[0]
    E = 0
    lam1 = a**2 * 1
    lam2 = 1 / (c**2)
    for n in range(N):
        z_l0 = np.matrix(np.append(1, xt[n])).T
        z_l1 = out_l1(z_l0, wl1)
        z_l2 = out_l2(z_l1, wl2)
        y = z_l2[0, 0]
        E += (y - yt[n])**2
    E = E / 2 / (c**2) + lam1 * (w[N_hdn:(N_in + 1) * N_hdn]**2).sum(0) / 2 + lam2 * (w[(N_in + 1) * N_hdn + N_out:]**2).sum(0) / 2
    return E


def plot(w, xd):
    # プロット
    yd = np.zeros(xd.shape)
    w_l1 = w[:(N_in + 1) * N_hdn].reshape(N_in + 1, N_hdn)
    w_l2 = w[(N_in + 1) * N_hdn:].reshape(N_hdn + 1, N_out)

    for i in range(xd.shape[0]):
        z_l0 = np.matrix(np.append(1, xd[i])).T
        z_l1 = out_l1(z_l0, w_l1)
        z_l2 = out_l2(z_l1, w_l2)
        yd[i] = z_l2[0, 0]
    plt.plot(xd, yd)
    return np.max(yd), np.min(yd)


def addReg(w, alphaW1, alphaB1, alphaW2, alphaB2):
    w2 = copy.deepcopy(w)
    w2[:N_hdn] /= np.sqrt(alphaB1)
    w2[N_hdn:(N_in + 1) * N_hdn] /= np.sqrt(alphaW1)

    w2[(N_in + 1) * N_hdn:(N_in + 1) * N_hdn + N_in] /= np.sqrt(alphaB2)
    w2[(N_in + 1) * N_hdn + N_in:] /= np.sqrt(alphaW2)
    return w2


xd = np.arange(-1., 1., 0.001)
x_t = np.zeros(10)
y_t = np.zeros(10)
# 学習パラメータ
N_out = 1
N_in = 1
N_hdn = 12

# 無矛盾の検証
w = np.random.randn((N_in + 1) * N_hdn + (N_hdn + 1) * N_out) * np.sqrt(100)
w1 = copy.deepcopy(w)
w2 = copy.deepcopy(w)
w3 = copy.deepcopy(w)
a = 1 / np.sqrt(5)
b = 0.1
c = 10
d = 100

w2[:N_hdn] -= (b / a) * w3[N_hdn:(N_in + 1) * N_hdn]
w2[N_hdn:(N_in + 1) * N_hdn] /= a

w3[(N_in + 1) * N_hdn:] *= c
w3[(N_in + 1) * N_hdn:(N_in + 1) * N_hdn + N_out] += d


plt.subplot(4, 2, 1)
plt.title("orginal")
k, j = plot(w1, xd)
plt.text(-0.9, k - (k - j) / 10, "Err:%.2f" % J2(w1, *(x_t, y_t, 1, 1)))

plt.subplot(4, 2, 3)
plt.title("scale input")
k, j = plot(w2, xd)
plt.text(-0.9, k - (k - j) / 10, "Err:%.2f" % J2(w2, *(x_t * a + b, y_t, a, 1)))

plt.subplot(4, 2, 5)
plt.title("scale output")
k, j = plot(w3, xd)
plt.text(-0.9, k - (k - j) / 10, "Err:%.2f" % J2(w3, *(x_t, y_t * c + d, 1, c)))


# print(J2(w1,*(x_t,y_t,1,1)))
# print(J2(w2,*(x_t*a+b,y_t,a,1)))
# print(J2(w3,*(x_t,y_t*c+d,1,c)))

# 図5.11
param = [(1, 1, 1, 1),
         (1, 1, 1e-2, 1),  # W2は縦のスケール
         (1e-6, 1e-4, 1, 1),  # W1は横のスケール
         (1e-6, 1e-6, 1, 1),  # B1は変化の範囲
         (1, 1, 1, 1e-2)]  # B2は縦の位置
for j in range(5):
    w = np.random.randn((N_in + 1) * N_hdn + (N_hdn + 1) * N_out) * np.sqrt(1)
    for i in range(len(param) - 1):
        plt.subplot(4, 2, (i + 1) * 2)
        w2 = addReg(w, param[i][0], param[i][1], param[i][2], param[i][3])
        plot(w2, xd)

plt.show()