パーセプトロンの学習アルゴリズムについて

前提・実現したいこと

パーセプトロンの学習アルゴリズムの作成で，パラメータの更新の方法がわかりません.
パラメータの更新において, 学習率としてeta t = 0.01/t とします.

学習データ，テストデータはそれぞれデータ数10000，1000で以下のような786行からなるCSVファイルで与えられています.

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発生している問題・エラーメッセージ

パラメータ更新が想定通りに行えない.

該当のソースコード

python
1#!/usr/bin/env python3
2# -*- coding: utf-8 -*-
3
4import numpy as np
5import matplotlib.pyplot as plt
6
7np.random.seed(123)
8
9##### シグモイド関数, 誤差関数
10def sigmoid(x):
11    return 1.0 / (1.0 + np.exp(-x))
12
13def error_function(x, y):
14    return (-1)*y*logz(sigmoid(x)) - (1-y)*logz(1-sigmoid(x))
15
16# 0除算とINFを防ぐ
17def logz(x):
18    th = 1e-7
19    x = max( th, x )
20    x = min( x, 1 - th )
21    return np.log(x)
22    
23    
24##### データ数
25n = 10000
26n_test = 1000
27
28d = 28**2              #画素数
29
30##### パラメータ(重み)の初期値
31# 平均０，分散0.3の正規乱数をd+1件出力
32w = np.random.normal(0, 0.3, d+1)
33########## 確率的勾配降下法によるパラメータ推定
34e = []
35e_test = []
36error = []
37error_test = []
38
39step = 0
40num_epoch = 1
41
42eta = 0.01
43
44for epoch in range(0, num_epoch):
45    index = np.random.permutation(n) # indexはnを並び替えた配列
46    
47    step += 1
48    for i in index:
49        # テキストから数値の受け取り.　先頭は文字が入っているので飛ばす.
50        dat = np.genfromtxt("./train/{}.csv".format(i))[1:]
51        xi = np.append(1, dat[1:])
52        yi = dat[0]      
53
54############################# ここから  ###################### 
55
56        ##### 誤差評価
57        e.append(error_function(np.dot(w, xi), yi))
58        
59        for k in range(len(w)):
60            w[k] = w[k] + eta*(yi - ???)*xi[k]/step
61
62#################### ここまで ################################
63    
64    ##### エポックごとの訓練誤差
65    error.append(sum(e)/n)
66    e = []
67    
68    ##### テスト誤差
69    for j in range(0, n_test):        
70        dat = np.genfromtxt("./test/{}.csv".format(j))[1:]
71        
72        xi = np.append(1, dat[1:])
73        yi = dat[0]
74        
75        e_test.append(error_function(np.dot(w, xi), yi))
76    
77    error_test.append(sum(e_test)/n_test)
78    e_test = []
79    
80
81########## 誤差関数のプロット
82plt.plot(error, label="training", lw=3)     #青線
83plt.plot(error_test, label="test", lw=3)     #オレンジ線
84plt.grid()
85plt.legend(fontsize =16)
86plt.savefig("./error.pdf")
87