程式設計實現標準BP演算法（sgd）和累積BP演算法（fullbatch），在西瓜3.0上訓練一個單隱層網路，並進行比較。

需要先把字串轉成數字，這裡用one-hot。把二分類問題看成多分類問題的特例，然後用softmax。最終模型在訓練集上可達到100%準確率，並且在西瓜[email protected]上也可以達到100%，與前面的邏輯迴歸相比，多了一個隱層的非線性變換，模型的表達能力確實強大了很多!

經試驗，隱層大小至少為2，為1時很難訓練到百分之百準確率，隱層較大時，模型收斂更快。sgd和fullbatch相比，當模型還未收斂時，用同樣的epoch，sgd比fullbatch誤差高，但sgd時間更短。不過用同樣的時間訓練，sgd可能更容易達到收斂狀態。

程式碼如下：

# coding: utf-8
import pandas as pd 
from pandas import read_csv
import theano
import theano.tensor as T 
import numpy as np 
from theano.tensor.nnet import sigmoid, softmax, binary_crossentropy
import numpy.random as rng
import time 
import random

def one_hot_encoder(data):
	diff_type = []
	for i in data:
		if i not in diff_type:
			diff_type.append(i)
	ret = []
	for i in data:
		idx = diff_type.index(i)
		ret.append([1 if j==idx else 0 for j in range(len(diff_type))])
	return ret

pd = read_csv('西瓜資料集3.csv'.decode('utf-8'))
for i in pd.columns[1:-3]:
	pd[i] = one_hot_encoder(pd[i])

X = []
label = []
for raw in pd.values:
	tem = []
	for j in range(1, len(raw)-1):
		if type(raw[j]) is list:
			tem.extend(raw[j])
		else:
			tem.append(raw[j])
	X.append(tem)
	label.append(1 if raw[-1]=='是' else 0)
Y = one_hot_encoder(label)
# X = [raw[-2:] for raw in X] # 西瓜
 
[email protected]的資料
x = T.matrix('x')
y = T.matrix('y')
feats = len(X[0])
h1_size = 20
ou_size = 2
w1 = theano.shared(rng.normal(size=(feats,h1_size)), name='w1')
w2 = theano.shared(rng.normal(size=(h1_size,ou_size)), name='w2')
b1 = theano.shared(rng.normal(size=h1_size), name='b1')
b2 = theano.shared(rng.normal(size=ou_size), name='b2')

z1 = T.dot(x, w1) + b1
h1 = sigmoid(z1)
z2 = T.dot(h1, w2) + b2
h2 = softmax(z2)
pred_maxid = T.argmax(h2, axis=1)
cost = binary_crossentropy(h2, y).mean()
gw1, gb1, gw2, gb2 = theano.grad(cost, [w1, b1, w2, b2])

lrate = 1
max_epochs = 10000
fit = theano.function(inputs=[x, y], outputs=[cost], updates=(
	(w1, w1-lrate*gw1), (w2, w2-lrate*gw2), (b1, b1-lrate*gb1), (b2, b2-lrate*gb2))
)
predict = theano.function(inputs=[x], outputs=[pred_maxid])

t1 = time.time()
for i in range(max_epochs):
	# fit(X, Y) # full-batch
	choose = rng.randint(len(X))
	fit([X[choose]], [Y[choose]]) # sgd
	# if i%100==0:
	# 	print fit(X, Y)[0]
print 'training time:', time.time()-t1
print 'cost:', fit(X, Y)[0]	

maxid = predict(X)[0]
pred_res = [True if i==0 else False for i in maxid]
print 'predict result:'
print pred_res
print 'accuracy:'
print float(sum([1 if label[i]==pred_res[i] else 0 for i in range(len(label))])) / len(label)