一、前饋神經網路

 第三章： 編寫前饋神經網路的程式碼：

#Layer Neural Network for Regression

import autograd.numpy as np
import autograd.numpy.random as npr
from  autograd import  grad
import sklearn.metrics
import pylab

#Generate Dataset 初始化資料集
examples = 1000
features = 100
D = (npr.randn(examples,features),npr.randn(examples))

#specify the network 定義神經網路
layer1_units = 10
layer2_units = 1
w1 = npr.rand(features,layer1_units)  #定義w，b
b1 = npr.rand(layer1_units)
w2 = npr.rand(layer1_units,layer2_units)
b2 = 0.0
theta = (w1,b1,w2,b2)  #θ

#define the loss function 定義損失函式
def squared_loss(y,y_hat):    #y_hat：即為f函式
    return np.dot((y-y_hat),(y-y_hat))  #np.dot 矩陣的乘法

#output layer 輸出層
def binary_cross_entropy(y,y_hat):  #交叉熵
    return np.sum(-(y*np.log(y_hat))+(1-y)*np.log(1-y_hat))

#wraper around the  NN  包裝神經網路
def neural_network(x,theta):
    w1,b1,w2,b2 = theta
    return np.tanh(np.dot((np.tanh(np.dot(x,w1)+b1)),w2)+b2)

#wrapper around the bojective function  to be optimised 最優化
def objective(theta,idx):
    return  squared_loss(D[1][idx],neural_network(D[0][idx],theta))

#update  更新
def updata_theta(theta,delta,alpha):
    w1,b1,w2,b2 = theta
    w1_delta,b1_delta,w2_delta,b2_delta = delta #delta 增量  △

    w1_new = w1 - alpha * w1_delta
    b1_new = b1 - alpha * b1_delta
    w2_new = w2 - alpha * w2_delta
    b2_new = b2 - alpha * b2_delta

    new_theta = (w1_new,w2_new,b1_new,b2_new)
    return  new_theta

#compute gradient  計算梯度
grad_objective = grad(objective)

#Train the NN  訓練神經網路
epochs = 10
print("RMSE before traning:",sklearn.metrics.mean_squared_error(D[1],neural_network(D[0],theta))) #標準誤差
rmse = []

for i in range(0,epochs):
    for j in range(0,examples):
        delta = grad_objective(theta,j)
        theta = updata_theta(theta,delta,0.01)

rmse.append(sklearn.metrics.mean_squared_error(D[1],neural_network(D[0],theta)))
print("RMSE after traning",sklearn.metrics.mean_squared_error(D[1],neural_network(D[0],theta)))
pylab.plot(rmse)
pylab.show()
 

結果：

RMSE before traning: 1.89717170214

RMSE after traning 1.06282114173