线性回归之随机梯度下降（sgd）

梯度下降的原理：梯度下降
普通梯度下降bgd的方法简单暴力，但是调整速度比较慢。
如果不想等所有数据都计算完了才开始调整w，而是计算完数据的一部分(batch_size)后就立即调整w，说白了就是在训练过程中进行权重的更新。
这样就成了随机梯度下降
主要优点有：
* 收敛速度更快，
* 避免过拟合的问题。
代码更新如下：

'''
随机全梯度下降方法
改进：进行到一部分的时候即更新权重

'''
import numpy as np
import math


print(__doc__)

sample = 10
num_input = 5

#加入训练数据
np.random.seed(0)
normalRand = np.random.normal(0,0.1,sample)      # 10个均值为0方差为0.1 的随机数  (b)
weight = [7,99,-1,-333,0.06]                     # 1 * 5 权重
x_train = np.random.random((sample, num_input))  #x 数据（10 * 5）
y_train = np.zeros((sample,1))                   # y数据（10 * 1）


for i in range (0,len(x_train)):
    total = 0
    for j in range(0,len(x_train[i])):
        total += weight[j]*x_train[i,j]
    y_train[i] = total+ normalRand[i]


# 训练
np.random.seed(0)
weight = np.random.random(num_input+1)
rate = 0.04
batch = 3

def train(x_train,y_train):
    #计算损失
    global weight,rate
    predictY = np.zeros((len(x_train)))
    for i in range(0,len(x_train)):
        predictY[i] = np.dot(x_train[i],weight[0:num_input])+ weight[num_input]
        loss = 0
        for i in range(0,len(x_train)):
            loss += (predictY[i]-y_train[i])**2

    for i in range(0,len(weight)-1):
        grade = 0
        for j in range(0,len(x_train)):
            grade += 2*(predictY[j]-y_train[j])*x_train[j,i]
        weight[i] = weight[i] - rate*grade

    grade = 0
    for j in range(0,len(x_train)):
        grade += 2*(predictY[j]-y_train[j])
        weight[num_input] = weight[num_input] - rate*grade

    return loss


for epoch in range(0,100):
     begin = 0
     while begin < len(x_train):
          end = begin + batch
          if end > len(x_train):
               end = len(x_train)

          loss = train(x_train[begin:end],y_train[begin:end])

          begin = end

          print("epoch: %d-loss: %f"%(epoch,loss))      #打印迭代次数和损失函数
print(weight)