ex5 MACHINE LEARNING COURSERA

☆1绘制learning curve时需要注意

在绘制error_train 与 error_cv随着样本数目的增加而变化的learning curve

需要根据当前循环内的样本数目i来求解对应的训练出的theta值，再供以求解J_train与J_cv。同时需要注意的是，J_train处的求解m对应的是i，是样本集的子集，而每一次的J_cv的求解对应的都是整个数据集。

意思也就是，当随着样本数量不断增加，训练得到的theta值将不断变化，而cv验证集需要去验证当前样本个数下的theta值的效果如何，当然需要整个验证数据集一起求得误差val_error。其中，train_error也就是当前使用的样本数目下的误差。  

☆2计算error时需注意

λ=0

上代码

function [J, grad] = linearRegCostFunction(X, y, theta, lambda)

m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));  %n*1

% ====================== YOUR CODE HERE ======================

h=X*theta;  %theta=n*1,X=m*n h=m*1
J= 1/2/m*sum( (h-y).^2 ) + lambda/2/m*sum(theta(2:end,:).^2);

grad(2:end)=1/m * (X'*(h-y))(2:end) + lambda/m*theta(2:end);
grad(1)=1/m * (X'*(h-y))(1);


% =========================================================================

grad = grad(:);

end

 function [error_train, error_val] = ...
    learningCurve(X, y, Xval, yval, lambda)

m = size(X, 1);

% You need to return these values correctly
error_train = zeros(m, 1);
error_val   = zeros(m, 1);

% ====================== YOUR CODE HERE ======================


for i=1:m
  
  sample_x=X(1:i, :);
  sample_y=y(1:i);
  
  [theta] = trainLinearReg(sample_x, sample_y, lambda);
  
  [J, grad] = linearRegCostFunction(sample_x, sample_y, theta, 0);
  error_train(i)=J;
  
  [J, grad] = linearRegCostFunction(Xval, yval, theta, 0) ;
  error_val(i)=J;

end

function [X_poly] = polyFeatures(X, p)

X_poly = zeros(numel(X), p);

% ====================== YOUR CODE HERE ======================

for i=1:p
  X_poly(:,i)=X.^i;
end
% =========================================================================


end

 function [lambda_vec, error_train, error_val] = ...
    validationCurve(X, y, Xval, yval)

lambda_vec = [0 0.001 0.003 0.01 0.03 0.1 0.3 1 3 10]';

% You need to return these variables correctly.
error_train = zeros(length(lambda_vec), 1);
error_val = zeros(length(lambda_vec), 1);

% ====================== YOUR CODE HERE ======================


for i = 1:length(lambda_vec)
  lambda = lambda_vec(i);
  
  theta=trainLinearReg(X, y, lambda);
  
  [error_train(i),grad]=linearRegCostFunction(X, y,theta, 0);
  
  [error_val(i),grad]=linearRegCostFunction( Xval, yval , theta, 0);



end