Machine_Learning（线性回归习题：matlab版）

野性酷女 2022-11-25 10:05 245阅读 0赞

## 线性回归习题：matlab版 ##

**单变量线性回归**  
**ex1.m**

data=load("E:\ML_exercise\ex1\ex1data1.txt");
    x=data(:,1);
    y=data(:,2);
    plotData(x,y,data);
    
    %predict
    predict1 = [1, 3.5] *theta;
    fprintf('population = 35,000, profit = %f\n',predict1*10000);
    predict2 = [1, 7] * theta;
    fprintf('population = 70,000, profit = %f\n',predict2*10000);
    
    %visualizing J(θ)
    theta0_vals = linspace(-10, 10, 100);%产生-10到10之间的100个数
    theta1_vals = linspace(-1, 4, 100);
    
    J_vals = zeros(length(theta0_vals), length(theta1_vals));
    
    for i = 1:length(theta0_vals)
        for j = 1:length(theta1_vals)
    	  t = [theta0_vals(i); theta1_vals(j)];
    	  J_vals(i,j) = computeCost(X, y, t);
        end
    end
    
    J_vals = J_vals';
    figure;
    surf(theta0_vals, theta1_vals, J_vals)
    xlabel('\theta_0'); ylabel('\theta_1');
    
    figure;
    contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
    xlabel('\theta_0'); ylabel('\theta_1');
    hold on;
    plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);

**plotData.m**

function plotData(x,y,data)
        m=length(y);
        plot(x,y,'rx','MarkerSize',10);
        hold on;
        ylabel('Profit in $10,000s');
        xlabel('Population of City in 10,000s');
    
        %构造X
        X=[ones(m,1),data(:,1)];
        %初始化参数
        theta=zeros(2,1);
        iterations=1500;
        alpha=0.01;
        %打印初始损失函数
        computeCost(X,y,theta);
    
        [theta,~]=gradientDescent(X,y,theta,alpha,iterations);
        plot(X(:,2),X*theta,'-b','MarkerSize',20);
        hold off;
        legend('Training data','Linear regression','Location','SouthEast');
    end

**computeCost.m**

function result = computeCost(X,y,theta)
    %损失函数
        inner=power((X*theta - y),2);
        result=sum(inner)/(2*length(X));
    end

**gradientDescent.m**

function [theta,costs] = gradientDescent(X,y,theta,alpha,iterations)
    %梯度下降函数
        costs=zeros(iterations,1);
        for i=1:iterations
            theta=theta-(X'*(X*theta - y))*alpha/length(X);
            costs(i)=computeCost(X,y,theta);
        end
    end

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