一、lasso

二、前向逐步回归

前向逐步回归算法可以得到与lasso差不多的效果，但是前向逐步回归更加简单。这是一种贪心算法，在每一步尽量减少误差。

三、实验

1、Matlab实现

主程序

clear all;
clc;
%% 导入数据
data = load('abalone.txt');
x = data(:,1:8);
y = data(:,9);
%% 处理数据
yMean = mean(y);
yDeal = y-yMean;
xMean = mean(x);
xVar = var(x,1);
[m,n] = size(x);
xDeal = zeros(m,n);
for i = 1:m
    for j = 1:n
        xDeal(i,j) = (x(i,j)-xMean(j))/xVar(j);
    end
end

%% 训练
runtime  = 5000;%迭代的步数
eps = 0.001;%调整步长
wResult = stageWise(xDeal, yDeal, eps, runtime);

%% 根据wResult画出收敛曲线
hold on 
xAxis = 1:runtime;
for i = 1:n
    plot(xAxis, wResult(:,i));
end

前向逐步回归函数

function [ wResult ] = stageWise( x, y, eps, runtime)
    [m,n] = size(x);%数据集的大小
    wResult = zeros(runtime, n);%最终的结果
    w = zeros(n,1);
    wMax = zeros(n,1);
    for i = 1:runtime
        ws = w'%输出每一次计算出来的权重
        lowestError = inf;%定义最小值
        for j = 1:n
            for sign = -1:2:1
                wTest = w;%初始化
                wTest(j) = wTest(j)+eps*sign;%只改变一维变量
                yTest = x*wTest;
                %求误差
                rssE = rssError(y, yTest);
                if rssE < lowestError%如果好，就替换
                    lowestError = rssE;
                    wMax = wTest;
                end
            end
        end
        w = wMax;
        wResult(i,:) = w;
    end
end

误差函数

%% rssError函数主要是利用均方误差
function [ error ] = rssError( y, yTest )
    yDis = y-yTest;%误差
    [m,n] = size(yDis);
    %求平方
    for i = 1:m
        yDis(i) = yDis(i)^2;
    end
    error = sum(yDis);%求列和
end

2、收敛曲线

简单易学的机器学习算法——lasso

一、lasso

二、前向逐步回归

三、实验

1、Matlab实现

2、收敛曲线