机器学习——正则化线性回归和偏差/方差(Matlab代码实现)

           目录

💥1 概述

📚2 运行结果

🎉3 参考文献

👨‍💻4 Matlab代码


💥1 概述

本文使用水库水位的变化来实现正则化线性回归,以预测大坝流出的水量。后续本文将对调试学习算法进行一些诊断,并检查偏差与方差的影响。

第 1 部分:正则化线性回归

我们将实现正则化线性回归,以利用水库水位的变化来预测从大坝流出的水量。

第 1.1 部分:加载和可视化数据

我们将首先可视化包含有关水位变化 x 和从大坝流出的水量 y 的历史记录的数据集。

此数据集分为三个部分:

  • 模型将学习的训练集:X, y
  • 用于确定正则化参数的交叉验证集:Xval、yval
  • 用于评估性能的测试集。这些是你的模型在训练过程中没有看到的“看不见的”例子:Xtest,ytest。

📚2 运行结果

 

 

 

🎉3 参考文献

[1]刘建伟,崔立鹏,刘泽宇,罗雄麟.正则化稀疏模型[J].计算机学报,2015,38(07):1307-1325.

👨‍💻4 Matlab代码

主函数部分代码:

%% Initialization
clear ; close all; clc

%% =========== Part 1: Loading and Visualizing Data =============
%  We start the exercise by first loading and visualizing the dataset. 
%  The following code will load the dataset into your environment and plot
%  the data.
%

% Load Training Data
fprintf('Loading and Visualizing Data ...\n')

% Load from ex5data1: 
% You will have X, y, Xval, yval, Xtest, ytest in your environment
load ('ex5data1.mat');

% m = Number of examples
m = size(X, 1);

% Plot training data
plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5);
xlabel('Change in water level (x)');
ylabel('Water flowing out of the dam (y)');

fprintf('Program paused. Press enter to continue.\n');
pause;

%% =========== Part 2: Regularized Linear Regression Cost =============
%  You should now implement the cost function for regularized linear 
%  regression. 
%

theta = [1 ; 1];
J = linearRegCostFunction([ones(m, 1) X], y, theta, 1);

fprintf(['Cost at theta = [1 ; 1]: %f '...
         '\n(this value should be about 303.993192)\n'], J);

fprintf('Program paused. Press enter to continue.\n');
pause;

%% =========== Part 3: Regularized Linear Regression Gradient =============
%  You should now implement the gradient for regularized linear 
%  regression.
%

theta = [1 ; 1];
[J, grad] = linearRegCostFunction([ones(m, 1) X], y, theta, 1);

fprintf(['Gradient at theta = [1 ; 1]:  [%f; %f] '...
         '\n(this value should be about [-15.303016; 598.250744])\n'], ...
         grad(1), grad(2));

fprintf('Program paused. Press enter to continue.\n');
pause;


%% =========== Part 4: Train Linear Regression =============
%  Once you have implemented the cost and gradient correctly, the
%  trainLinearReg function will use your cost function to train 
%  regularized linear regression.

%  Write Up Note: The data is non-linear, so this will not give a great 
%                 fit.
%

%  Train linear regression with lambda = 0
lambda = 0;
[theta] = trainLinearReg([ones(m, 1) X], y, lambda);

%  Plot fit over the data
plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5);
xlabel('Change in water level (x)');
ylabel('Water flowing out of the dam (y)');
hold on;
plot(X, [ones(m, 1) X]*theta, '--', 'LineWidth', 2)
hold off;

fprintf('Program paused. Press enter to continue.\n');
pause;


%% =========== Part 5: Learning Curve for Linear Regression =============
%  Next, you should implement the learningCurve function. 
%
%  Write Up Note: Since the model is underfitting the data, we expect to
%                 see a graph with "high bias" -- Figure 3 in ex5.pdf 
%

lambda = 0;
[error_train, error_val] = ...
    learningCurve([ones(m, 1) X], y, ...
                  [ones(size(Xval, 1), 1) Xval], yval, ...
                  lambda);

plot(1:m, error_train, 1:m, error_val);
title('Learning curve for linear regression')
legend('Train', 'Cross Validation')
xlabel('Number of training examples')
ylabel('Error')
axis([0 13 0 150])

fprintf('# Training Examples\tTrain Error\tCross Validation Error\n');
for i = 1:m
    fprintf('  \t%d\t\t%f\t%f\n', i, error_train(i), error_val(i));
end

作者:我爱Matlab编程原文地址:https://blog.csdn.net/m0_73907476/article/details/128671768

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