CS229作业之过拟合

一、使用循环：

1.1原始版逻辑回归：

　　　　

 function g = sigmoid(z)
 g = zeros(size(z));
 g =  ./ ( + exp(-z));
 end

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

 % Initialize some useful values
 m = length(y); % number of training examples

 J = ;
 grad = zeros(size(theta));

 n = size(theta);
 gradtemp = ;

 %compute costfunction
 for i = :m
   temp1 = y(i) * log(sigmoid(X(i,:) * theta)) + ( - y(i)) * log( - sigmoid(X(i,:) * theta));
   J = J + temp1;
 endfor

 J = -(J / m);

 %compute grade
 for j = :n
   for i = :m
     temp2 = (sigmoid(X(i,:) * theta) - y(i)) * X(i,j);
     gradtemp = gradtemp + temp2;
   endfor
   gradtemp = gradtemp / m;
   grad(j) = gradtemp;
   gradtemp = ;
 endfor

 end

 function p = predict(theta, X)

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

 p = zeros(m, );

 for i =:m
   h = sigmoid(X(i,:) * theta);
   if h >= 0.5
     y = ;
   else
     y = ;
   endif
   p(i) = y;
 endfor

 end

1.2正则化版逻辑回归：

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

 % Initialize some useful values
 m = length(y); % number of training examples

 J = ;
 grad = zeros(size(theta));

 n = length(theta)
 temp1 = ;
 temp2 = ;
 temp3 = ;
 result1 = ;
 result2 = ;
 %compute costfunction
 for i = :m
   h = sigmoid(X(i,:) * theta)
   temp1 = y(i) * log(h) + ( - y(i)) * log(-h);
   result1 = result1 + temp1;
 endfor
 for j = :n
   temp2 = theta(j) * theta(j);
   result2 = result2 + temp2;
 endfor

 J = (- / m) * result1 + lambda / ( * m) * result2;

 temp3 =
 temp4 =
 result3 =
 for i = :m
     h = (sigmoid(X(i,:) * theta))
     temp3 = (h - y(i)) * X(i,);
     result3 = result3 + temp3;
 endfor
 grad() = ( / m) * result3

 %compute grade
 for j = :n
   result4 = ;
   for i = :m
     h = (sigmoid(X(i,:) * theta))
     temp4 = (h - y(i)) * X(i,j);
     result4 = result4 + temp4;
   endfor
   grad(j) = ( / m) * result4 + (lambda / m) * theta(j)
 endfor

 end

二、矩阵向量方式整体运算：

2.1原始版逻辑回归：

 function g = sigmoid(z)

 g = zeros(size(z));

 g =  ./ ( + exp(-z));

 end

 function [J, grad] = costFunction(theta, X, y)
 % Initialize some useful values
 m = length(y); % number of training examples

 J = ;
 grad = zeros(size(theta));

 h = sigmoid(X * theta);

 J = sum(- y .* log(h) - ( - y) .* log( - h)) / m;

 grad = (/m * sum((h - y).* X))';

 end

 function p = predict(theta, X)

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

 p = zeros(m, );

 h = sigmoid(X * theta);

 p(find(h >= 0.5)) = ;

 end

2.2正则化版逻辑回归：

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

 % Initialize some useful values
 m = length(y); % number of training examples

 J = ;
 grad = zeros(size(theta));

 n = size(theta,);

 h = sigmoid(X * theta);

 J = sum(- y .* log(h) - ( - y) .* log( - h)) / m + lambda / ( * m) * sum(theta(:n) .^ );

 grad = (/m * sum((h - y).* X))';

 grad(:n) = grad(:n) + lambda / m * theta(:n);

 end