Ng機器學習 Week6

Advice for Applying Machine Learning

linearRegCostFunction.m

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost and gradient of regularized linear 
%               regression for a particular choice of theta.
%
%               You should set J to the cost and grad to the gradient.
%

h = X * theta;

theta2 = [0 ; theta(2:size(theta), :)];

J = 1 / (2 * m) * sum((h - y) .^ 2) + lambda / (2 * m) * sum(theta2 .^ 2);

grad =  ( X' * (h - y) + lambda * theta2 ) / m;

learningCurve.m

for i=1:m
   % train parameter: theta 
   theta=trainLinearReg(X(1:i,:),y(1:i), lambda);
   % Compute train errors using training examples
   [error_train(i),grad]=linearRegCostFunction(X(1:i,:), y(1:i), theta, 0); 
   % cross-validation error
   [error_val(i),  grad]=linearRegCostFunction(Xval, yval, theta, 0);
end

polyFeatures.m

% ====================== YOUR CODE HERE ======================
% Instructions: Given a vector X, return a matrix X_poly where the p-th 
%               column of X contains the values of X to the p-th power.
%
% 

for i =1:p

   X_poly(:,i) = X(:,1).^i;

end 

validationCurve.m

for i=1:length(lambda_vec)
    lambda = lambda_vec(i);
    theta = trainLinearReg(X,y, lambda);
    % Compute train / val errors when training linear
    [error_train(i), grad] = linearRegCostFunction(X, y, theta, 0); 
    [error_val(i), grad] = linearRegCostFunction(Xval, yval, theta, 0); 
end

（轉載）machine learning week6 確診機器學習算法的性能 各種學習曲線 來判斷學習算法是過擬合或欠擬合

%%-------------------------------------------------------------------------
%%Optional (ungraded) exercise: Computing test set
lambda=3;
theta=trainLinearReg(X_poly,y, lambda);
[error_test,grad]=linearRegCostFunction(X_poly_test, ytest, theta, 0); 
fprintf(' %f\n',error_test);
%%-------------------------------------------------------------------------
%%Optional (ungraded) exercise: Plotting learning curves with randomly selected examples
% m=size(X_poly,1);
% X_poly_y=[X_poly,y];
% X_poly_val_y=[X_poly_val,yval];
% lambda=0.01;
% error_train = zeros(m, 1);
% error_val   = zeros(m, 1);
% for i=1:m
%    error_train_sum=0;
%    error_val_sum  =0;
%    for k=1:20                           %50次迭代
%         rand_seq=round(rand(1,i)*(m-1))+1;%生成i個隨機序列 0~m
%         rand_X_poly_y=X_poly_y(rand_seq,:);
%         rand_X_poly_val_y=X_poly_val_y(rand_seq,:);
%         X=rand_X_poly_y(:,1:end-1);
%         y=rand_X_poly_y(:,end);
%         Xval=rand_X_poly_val_y(:,1:end-1);
%         yval=rand_X_poly_val_y(:,end);
%         theta=trainLinearReg(X,y,lambda);
%         [error_train_val,grad]=linearRegCostFunction(X, y, theta, 0);
%         [error_val_val,  grad]=linearRegCostFunction(Xval, yval, theta, 0);
%         error_train_sum=error_train_sum+error_train_val;
%         error_val_sum=error_val_sum+error_val_val;
%    end
%    error_train(i)=error_train_sum/20;
%    error_val(i)=error_val_sum/20;
% end
% plot(1:m, error_train, 1:m, error_val);
% title(sprintf('Polynomial Regression Learning Curve (lambda = %f)', lambda));
% xlabel('Number of training examples')
% ylabel('Error')
% axis([0 13 0 100])
% legend('Train', 'Cross Validation')
% fprintf('Polynomial Regression (lambda = %f)\n\n', lambda);
% fprintf('# Training Examples\tTrain Error\tCross Validation Error\n');
%%-------------------------------------------------------------------------

Machine Learning System Design

1. precision = ture positive / #predicted positive
   recall = true positive / # actual positive
2. • Suppose we want to predict y=1 (cancer) only if very confident
     Threshold: higher value
     Higher precision, lower recall
   • avoid missing too many cases of cancer (avoid false negtives)
     Threshold: lower value
     Higher recall, lower precision

3. F1 Score: 2PR/(P+R)
   Measure presicion (P) and recall(R) on the cross validation set and choose the value of threshold which maximizes 2PR/(P+R)

4. Large data rationale:
   Use a learning algorithm with many parameters: low bias
   => Jtrain(theta) will be small
   Use a very large training set(unlikely to overfit): low variance
   =>Jtrain(theta) ≈Jtest(theta)
   So Jtest(theta) will be small

Q3錯了。。。