optimal_theta = Result.x;

Question

我在Python中实现了线性回归的梯度下降，用于从csv文件读取数据。下面是代码：

import numpy as np
import scipy.optimize as op
from sklearn import preprocessing
import matplotlib.pyplot as plt
from matplotlib import style

def CostFunc(theta,x,y):
    m,n = x.shape; 
    theta = theta.reshape((n,1));
    #y = y.reshape((m,1));
    #x=x.reshape((m,1))
    J = 0.5*sum(np.square((X.dot(theta)-y)))[0]/m;
    return J;


def gradientDescent(X, y, theta, alpha, num_iters):
    m,n = X.shape;
    initial_iter = num_iters
    J = np.zeros((num_iters,1));
    while num_iters > 0:
        theta = theta - (alpha*np.sum(((X.dot(theta)-y)*X),axis=0)/m).reshape((n,1))
        J[initial_iter-num_iters][0]=CostFunc(theta,X,y)
        num_iters=num_iters-1

    return theta,J;


data = np.loadtxt(open("ex1data2.txt","rb"),delimiter=",",skiprows=1)
nr,nc = data.shape
X=data[:,0:nc - 1]
X=preprocessing.scale(X)
X=np.insert(X,0,1,axis=1)
y= data[:,[nc - 1]]
m , n = X.shape;
#initial_theta = np.zeros(len(n));
initial_theta = np.zeros((n,1));
theta,J=gradientDescent(X,y,initial_theta,0.01,400)
J=J.reshape(400)
count=0
grp=np.zeros((400,2));
for value in J:

    grp[count][0] = count+1
    grp[count][1] = value
    count = count+1



plt.plot(grp)
plt.legend(loc=4)
plt.xlabel('iter')
plt.ylabel('cost')
plt.show()



print(theta)

optimal_theta = Result.x;

我进行了400次迭代，得到了一个成本减少的情节，如下iteration vs cost plot

然后我使用以下代码

对同一数据使用了一种自定义算法

import numpy as np
import scipy.optimize as op
from sklearn import preprocessing

def Sigmoid(z):
    return 1/(1 + np.exp(-z));

def Gradient(theta,x,y):
    m , n = x.shape
    theta = theta.reshape((n,1));
    #y = y.reshape((m,1))
    #x=x.reshape((m,1))
    #sigmoid_x_theta = Sigmoid(x.dot(theta));
    grad = (np.sum(((X.dot(theta)-y)*X),axis=0)/m);
    return grad.flatten();

def CostFunc(theta,x,y):
    m,n = x.shape; 
    theta = theta.reshape((n,1));
    #y = y.reshape((m,1));
    #x=x.reshape((m,1))
    J = 0.5*sum(np.square((X.dot(theta)-y)))[0]/m;
    return J;


data = np.loadtxt(open("ex1data2.txt","rb"),delimiter=",",skiprows=1)
nr,nc = data.shape
X=data[:,0:nc - 1]
X=preprocessing.scale(X)
X=np.insert(X,0,1,axis=1)
y= data[:,[nc - 1]]
m , n = X.shape;
#initial_theta = np.zeros(len(n));
initial_theta = np.zeros((n,1));

Result = op.minimize(fun = CostFunc, 
                                x0 = initial_theta, 
                               args = (X, y),
                               method = 'TNC',
                               jac = Gradient);






print("====================")       
print(Result)        
#optimal_theta = Result.x;

第一个案例的theta值是 [[333032.07465084] [100130.7408761] [3699.66611303]]

从第二次开始，我得到以下输出好玩的：2066502781.7118049 jac：array（[-6.45345806e-11,7.84261236e-10，-2.42370452e-10]）消息：'达到了本地最小值（| pg |〜= 0）' nfev：27 尼特：13 状态：0 成功：是的 x：数组（[339119.45652174,110248.92165868，-6226.22670554]）

我假设x：array（[339119.45652174,110248.92165868，-6226.22670554]）是theta值。

为什么我在两种情况下得到不同的值？

线性回归（Python） - 为不同的算法保留不同的结果

optimal_theta = Result.x;

0 个答案: