机器学习（一）------- 线性回归（Linear regression ）_机器学习线性回归怎么调库添加常数项

<pre name="code" class="python">def countCostFunc(X, y, theta, lamb):
    #X为训练集，y表示训练集上的lable，theta表示权重，lamb是正则常数
    #注意这里的X，theta都经过了扩充，X增加了一列1，theta增加了theta0，这主要是为了向量的统一运算
    m, n = np.shape(X)  #X矩阵行m，列n
    h = np.dot(X,  theta) #举证相乘
    regtheta = np.copy(theta)#深拷贝，因为，python是引用，
    regtheta[0,0] = 0
    J = ((np.dot((h-y).transpose(), (h - y))  +  lamb * np.dot(regtheta.transpose(), regtheta) )/ float(2 * m))
    grad = (1  / float(m)) * (np.dot(X.transpose(),  h-y) +  lamb * regtheta)  #对所有theta求导，这个就是J函数对theta分别求导后，然后变成一个列向量
    return J, grad

#theta多了theta0但是X还没有增加1列，用训练出来的模型，预测结果
def predict(X, theta):
    X = np.array(X)
    m,n = np.shape(X)
    X = np.hstack([np.ones((m, 1)), X]) #为X增加一列1
    h = np.dot(X, theta)
    return h
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#coding=utf-8
import numpy as np
import grandDescent
import costFunction
import loadData
import predict
import write2File
import rmse
import os
import random
import matplotlib.pyplot as plt
from pylab import plot,show
from scipy import stats
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def handle_data_self():
    X_train = np.array([0,1,2,3,4,5,6,7,8,9]).reshape(10, 1)
    y_train = np.array([0,2,3,4,5,6,7,4,9,10]).reshape(10, 1)
    X_cross = np.copy(X_train)
    y_cross = np.copy(y_train)
    X_test = np.array([0,1,2,3,4,5,6,7,8,9, 10,11,23,1]).reshape(14,1)
    plt.scatter(X_train, y_train, color="Red")
    # plt.show()
    return X_train,y_train,X_cross,y_cross,X_test

<pre name="code" class="python">#coding=utf-8
import numpy as np  #系统库
import grandDescent
import costFunction
import loadData
import predict
import write2File
import rmse
import os  #库 
import random #库
import matplotlib.pyplot as plt #库
 
 
 
def regression_simple(X, y, X1, y1, option):
    alpha = float(option["alpha"])
    maxCycles = int(option["maxCycle"])
    lamb = float(option["lamb"])
    save = bool(option["saveRecord"])
    add = bool(option["add"])
    optGoal = option["optGoal"]
    methods = option["method"]
    thetaPath = option["thetaWritePath"] if option.has_key("thetaWritePath") else None
    m,n = np.shape(X)
    J_train = None
    theta = None
    if methods == "stocGradDescent":
        J_train, theta = grandDescent.stocGradDescent(np.copy(X), y, maxCycles, alpha, lamb)
    elif methods == "grandDescent":
        J_train, theta = grandDescent.grandDescent(np.copy(X),  y, maxCycles, alpha, lamb)
    J_cross = costFunction.countCostFunc(np.hstack([np.ones((X1.shape[0], 1)), X1]), y1, theta, lamb)
    rmseResult = rmse.countrmse(np.copy(X1),y1,theta) #后面都是保存一些东西
    if save and thetaPath:
        if not add and os.path.exists(thetaPath):
            os.remove(thetaPath)
        file_object = None
        if not add:
            file_object = open(thetaPath, 'w')
        elif os.path.exists(thetaPath):
            file_object = open(thetaPath, 'a')
        else:
            file_object = open(thetaPath, 'w')
        file_object.write("J_traincost=>"+ str(J_train) + ",J_crosscost=>" + str(J_cross[0]) +  ",alpha=>" + str(alpha) + ",lamb=>" +  str(lamb) + ", Cycles=>"+ str(maxCycles) + ", rmse=>" + str(rmseResult) + "\n" + ",theata==>"+str(theta.transpose()) + "\n")
        file_object.close()
    J = None
    if optGoal == "J_train":
        J = J_train
    elif optGoal == "J_cross":
        J = J_cross
    elif optGoal == "rmse":
        J = rmseResult
    else:
        print "optGoal fault!!!"
    return J, theta
 
 
 
def handle_data_self():
    X_train = np.array([0,1,2,3,4,5,6,7,8,9]).reshape(10, 1)
    y_train = np.array([0,2,3,4,5,6,7,4,9,10]).reshape(10, 1)
    X_cross = np.copy(X_train)
    y_cross = np.copy(y_train)
    X_test = np.array([0,1,2,3,4,5,6,7,8,9, 10,11,23,1]).reshape(14,1)
    plt.scatter(X_train, y_train, color="Red")
    plt.show()
    return X_train,y_train,X_cross,y_cross,X_test
 
if __name__ == "__main__":
    print "load data..."
    X_train, y_train, X_cross, y_cross, X_test = handle_data_self()
    print "load data finished"
    print "进入traing..."
    action = "regression_grandDescent"
    J = None
    theta = None
    if action == "regression_grandDescent":
        option = {"maxCycle": 400, "alpha": 0.05, "lamb": 0.001, "saveRecord": 1,
                  "thetaWritePath": "./thetaSave.txt", "add":1, "optGoal":"J_train",
                  "method": "grandDescent"}
        J, theta = regression_simple(X_train.copy(), y_train.copy(), X_cross.copy(), y_cross.copy(), option)
        plt.plot(X_train, predict.predict(X_train, theta), color="Green")
        plt.show()
   
    print "完成traing"
 
    if action == "regression_grandDescent" or action == "regression_grandDescentWithBestAlphaAndLamb" or action == "regression_stocGradDescent":
        y_pre = predict.predict(X_test, theta)
        write2File.savePrediction(y_pre, path="sample_submission.csv")
    print "预测完毕","保存结果至sample_submission.csv"
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其中

X_train, y_train, X_cross, y_cross, X_test = handle_data_self()
这里分别是，原始数据集X，原始数据集y，交叉验证集X，交叉验证y，检测集X

原始数据集X：就是给你的训练样本的特征值，注意这里还没添加X0为一，后面会在其他地方加上，为什么要加一列，是为了统一后面的导数计算，

grandDescent.py文件
<pre name="code" class="python">#coding=utf-8
 
import numpy as np
import operator
import copy
import math
import costFunction
 
 
def grandDescent(X, y, maxCycles, alpha, lamb):
    m,n = np.shape(X)
    theta = np.zeros((n + 1, 1))
    X = np.hstack([np.ones((m,1)), X])
    J = 0
    for i in range(maxCycles):
        J, grad = costFunction.countCostFunc(np.copy(X), y, np.copy(theta), lamb)
        #print "J的第",i+1,"次==>" ,J
        theta = theta - alpha * grad
    return J, theta
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costFunction.py文件
<pre name="code" class="python">#coding=utf-8
 
import numpy as np
import operator
import copy
import math
 
 
 
 
 
def countCostFunc(X, y, theta, lamb):
    m, n = np.shape(X)
    h = np.dot(X,  theta)
    regtheta = np.copy(theta)
    regtheta[0,0] = 0
    J = ((np.dot((h-y).transpose(), (h - y))  +  lamb * np.dot(regtheta.transpose(), regtheta) )/ float(2 * m))
    grad = (1  / float(m)) * (np.dot(X.transpose(),  h-y) +  lamb * regtheta)
    return J, grad
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rmse.py 文件
#coding=utf-8
 
import numpy as np
import operator
import copy
import math
import costFunction
 
 
def countrmse(X, y, theta):
    m,n = np.shape(X)
    theta = theta
    #扩展1
    X = np.hstack([np.ones((m,1)), X])
    h = np.dot(X , theta)
    #按列求和
    sumDiffY = np.dot((h - y).transpose(), (h - y))
    J = sumDiffY / float(m)
    #print np.shape(J)
    return math.sqrt(J)
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predict.py文件

#coding=utf-8
import numpy as np
import costFunction
 
 
#theta多了theta0但是X还没有增加1列
def predict(X, theta):
    X = np.array(X)
    m,n = np.shape(X)
    X = np.hstack([np.ones((m, 1)), X])
    h = np.dot(X, theta)
    return h

write2File.py文件
def savePrediction(y_pre, path):
    file_object = open(path, 'w')
    file_object.write("Id,reference\n")
    for i in range(len(y_pre)):
        file_object.write(str(i) + "," + str(y_pre[i][0]) + "\n")

alphas = [0.1, 0.05, 0.01, 0.005, 0.001, 0.0005, 0.0001]
maxCycles = 200
lambs = [100,10,1,0.1,0.01, 0.001]