机器学习实战：多变量线性回归的实现

多元线性回归其实方法和单变量线性回归差不多，我们这里直接给出算法：

computeCostMulti函数

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function J = computeCostMulti(X, y, theta)

    m = length(y); % number of training examples
    J = 0;
    predictions = X * theta;
    J = 1/(2*m)*(predictions - y)' * (predictions - y);

end

gradientDescentMulti函数

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function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)

    m = length(y); % number of training examples
    J_history = zeros(num_iters, 1);
    feature_number = size(X,2);
    temp = zeros(feature_number,1);
    for iter = 1:num_iters

        for i=1:feature_number
            temp(i) = theta(i) - (alpha / m) * sum((X * theta - y).* X(:,i));
        end
        for j=1:feature_number
            theta(j) = temp(j);
        end

        J_history(iter) = computeCostMulti(X, y, theta);

    end

end

但是其中还是有一些区别的，比如在开始梯度下降之前需要进行feature Scaling：

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function [X_norm, mu, sigma] = featureNormalize(X)

    X_norm = X;
    mu = zeros(1, size(X, 2));
    sigma = zeros(1, size(X, 2));
    mu = mean(X);
    sigma = std(X);
    for i=1:size(mu,2)
        X_norm(:,i) = (X(:,i).-mu(i))./sigma(i);
    end

end

Normal Equation算法的实现

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function [theta] = normalEqn(X, y)

theta = zeros(size(X, 2), 1);
theta = pinv(X'*X)*X'*y;

end

补充：综合编程 , 其他综合 ,