基于python中theano库的线性回归

theano库是做deep learning重要的一部分，其最吸引人的地方之一是你给出符号化的公式之后，能自动生成导数。本文使用梯度下降的方法，进行数据拟合，现在把代码贴在下方

代码块

import numpy as np 
import theano.tensor as T 
import theano 
import time 

class Linear_Reg(object): 
  def __init__(self,x): 
    self.a = theano.shared(value = np.zeros((1,), dtype=theano.config.floatX),name = 'a') 
    self.b = theano.shared(value = np.zeros((1,), 
dtype=theano.config.floatX),name = 'b') 
    self.result = self.a * x + self.b 
    self.params = [self.a,self.b] 
  def msl(self,y): 
    return T.mean((y - self.result)**2) 

def regrun(rate,data,labels): 

  X = theano.shared(np.asarray(data, 
                 dtype=theano.config.floatX),borrow = True) 
  Y = theano.shared(np.asarray(labels, 
                 dtype=theano.config.floatX),borrow = True) 

  index = T.lscalar() #定义符号化的公式
  x = T.dscalar('x')  #定义符号化的公式
  y = T.dscalar('y')  #定义符号化的公式

  reg = Linear_Reg(x = x) 
  cost = reg.msl(y) 


  a_g = T.grad(cost = cost,wrt = reg.a) #计算梯度 
  b_g = T.grad(cost = cost, wrt = reg.b) #计算梯度

  updates=[(reg.a,reg.a - rate * a_g),(reg.b,reg.b - rate * b_g)] #更新参数
  train_model = theano.function(inputs=[index], outputs = reg.msl(y),updates = updates,givens = {x:X[index], y:Y[index]}) 

  done = True 
  err = 0.0 
  count = 0 
  last = 0.0 
  start_time = time.clock() 
  while done: 
    #err_s = [train_model(i) for i in xrange(data.shape[0])] 
    for i in xxx:
      err_s = [train_model(i) ]
      err = np.mean(err_s)  

    #print err 
    count = count + 1 
    if count > 10000 or err <0.1: 
      done = False 
    last = err 
  end_time = time.clock() 
  print 'Total time is ：',end_time -start_time,' s' # 5.12s 
  print 'last error :',err 
  print 'a value : ',reg.a.get_value() # [ 2.92394467]  
  print 'b value : ',reg.b.get_value() # [ 1.81334458] 

if __name__ == '__main__':  
  rate = 0.01 
  data = np.linspace(1,10,10) 
  labels = data * 3 + np.ones(data.shape[0],dtype=np.float64) +np.random.rand(data.shape[0])
  regrun(rate,data,labels)

其基本思想是随机梯度下降。