本文共 4924 字,大约阅读时间需要 16 分钟。
Andrew Ng的UFLDL在2014年9月底更新了!
对于开始研究Deep Learning的童鞋们来说这真的是极大的好消息!
新的Tutorial相比旧的Tutorial增加了Convolutional Neural Network的内容,了解的童鞋都知道CNN在Computer Vision的重大影响。并且从新编排了内容及exercises。
新的UFLDL网址为:
http://ufldl.stanford.edu/tutorial/
对于线性回归Linear Regression,恐怕大部分童鞋都了解,简单的说
线性回归问题就是一个目标值y取决于一组输入值x,我们要寻找一个最合适的假设Hypothesis来描述这个y与x的关系,然后利用这个Hypothesis来预测新的输入x对应的y。
这是个简单的最优化问题,我们需要一个代价函数cost function来描述在training set样本中的y与通过h函数预测的y之间的差距,从而利用这个cost function通过Gradient Decent梯度下降法来计算h的最优参数从而得到最优的h。
因为是通过样本让计算机“学习”合适的参数theta,因此这是一个最基本的机器学习算法。
cost function:
J(θ)=12∑i(hθ(x(i))−y(i))2=12∑i(θ⊤x(i)−y(i))2
对theta做偏导:
Differentiating the cost function J(θ) as given above with respect to a particular parameter θj gives us:
%%This exercise uses a data from the UCI repository:% Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository% http://archive.ics.uci.edu/ml% Irvine, CA: University of California, School of Information and Computer Science.%%Data created by:% Harrison, D. and Rubinfeld, D.L.% ''Hedonic prices and the demand for clean air''% J. Environ. Economics & Management, vol.5, 81-102, 1978.%addpath ../commonaddpath ../common/minFunc_2012/minFuncaddpath ../common/minFunc_2012/minFunc/compiled% Load housing data from file.data = load('housing.data'); % housing data 506x14 data=data'; % put examples in columns 14x506 一般这里将每一个样本放在每一列% Include a row of 1s as an additional intercept feature.data = [ ones(1,size(data,2)); data ]; % 15x506 增加intercept term % Shuffle examples. 乱序 目的在于之后能够随机选取training set和test setsdata = data(:, randperm(size(data,2))); %randperm(n)用于随机生成1到n的排列% Split into train and test sets% The last row of 'data' is the median home price.train.X = data(1:end-1,1:400); %选择前400个样本来训练,后面的样本来做测试train.y = data(end,1:400);test.X = data(1:end-1,401:end);test.y = data(end,401:end);m=size(train.X,2); %训练样本数量n=size(train.X,1); %每个样本的变量个数% Initialize the coefficient vector theta to random values.theta = rand(n,1); %随机生成初始theta 每个值在(0,1)之间% Run the minFunc optimizer with linear_regression.m as the objective.%% TODO: Implement the linear regression objective and gradient computations% in linear_regression.m%tic; %Start a stopwatch timer. 开始计时options = struct('MaxIter', 200);theta = minFunc(@linear_regression, theta, options, train.X, train.y);fprintf('Optimization took %f seconds.\n', toc); %toc Read the stopwatch timer% Run minFunc with linear_regression_vec.m as the objective.%% TODO: Implement linear regression in linear_regression_vec.m% using MATLAB's vectorization features to speed up your code.% Compare the running time for your linear_regression.m and% linear_regression_vec.m implementations.%% Uncomment the lines below to run your vectorized code.%Re-initialize parameters%theta = rand(n,1);%tic;%theta = minFunc(@linear_regression_vec, theta, options, train.X, train.y);%fprintf('Optimization took %f seconds.\n', toc);% Plot predicted prices and actual prices from training set.actual_prices = train.y;predicted_prices = theta'*train.X;% Print out root-mean-squared (RMS) training error.平方根误差train_rms=sqrt(mean((predicted_prices - actual_prices).^2));fprintf('RMS training error: %f\n', train_rms);% Print out test RMS erroractual_prices = test.y;predicted_prices = theta'*test.X;test_rms=sqrt(mean((predicted_prices - actual_prices).^2));fprintf('RMS testing error: %f\n', test_rms);% Plot predictions on test data.plot_prices=true;if (plot_prices) [actual_prices,I] = sort(actual_prices); %从小到大排序价格,I为index predicted_prices=predicted_prices(I); plot(actual_prices, 'rx'); hold on; plot(predicted_prices,'bx'); legend('Actual Price', 'Predicted Price'); xlabel('House #'); ylabel('House price ($1000s)');end
function [f,g] = linear_regression(theta, X,y) % % Arguments: % theta - A vector containing the parameter values to optimize. % X - The examples stored in a matrix. % X(i,j) is the i'th coordinate of the j'th example. % y - The target value for each example. y(j) is the target for example j. % m=size(X,2); n=size(X,1); f=0; g=zeros(size(theta)); % % TODO: Compute the linear regression objective by looping over the examples in X. % Store the objective function value in 'f'. % % TODO: Compute the gradient of the objective with respect to theta by looping over % the examples in X and adding up the gradient for each example. Store the % computed gradient in 'g'. %%% YOUR CODE HERE %%%% Step 1 : Compute f cost functionfor i = 1:m f = f + (theta' * X(:,i) - y(i))^2;endf = 1/2*f;% Step 2: Compute gradient for j = 1:n for i = 1:m g(j) = g(j) + X(j,i)*(theta' * X(:,i) - y(i)); end end
【本文为原创文章,转载请注明出处:blog.csdn.net/songrotek】