machine-learning第六周 上机作业

本周不复杂，但还是很关键，且要注意一些细节点。

1、如何评估算法好坏：高偏差与高方差的问题；

2、当某个集合中，一个类别远小于另一个类别的时候（如患癌），如何评估在面对偏斜类(Skewed classes)的算法好坏：查准率和召回率；

3、如何选择一个好的阀值：F1 = 2 * (P*R / (P+R))；

4、如何选择一个好的算法：头脑风暴，快速试错（好熟悉的赶脚），足够的属性值（消除偏差）加足够的数据量（消除方差）。

有意思吧，上代码了~~

function [J, grad] = linearRegCostFunction(X, y, theta, lambda)%LINEARREGCOSTFUNCTION Compute cost and gradient for regularized linear %regression with multiple variables%   [J, grad] = LINEARREGCOSTFUNCTION(X, y, theta, lambda) computes the %   cost of using theta as the parameter for linear regression to fit the %   data points in X and y. Returns the cost in J and the gradient in grad% Initialize some useful valuesm = length(y); % number of training examples% You need to return the following variables correctly J = 0;grad = zeros(size(theta));% ====================== 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.%theta1 = [0;theta(2:end)];J = 1/(2 * m) * sum(( X * theta - y ).^2) + lambda / (2 * m) * sum(theta1.^2);regularized = lambda / m * theta1 ;grad = 1 / m * (X * theta - y)' *X ;grad = grad +  regularized';% =========================================================================grad = grad(:);end

function [X_poly] = polyFeatures(X, p)%POLYFEATURES Maps X (1D vector) into the p-th power%   [X_poly] = POLYFEATURES(X, p) takes a data matrix X (size m x 1) and%   maps each example into its polynomial features where%   X_poly(i, :) = [X(i) X(i).^2 X(i).^3 ...  X(i).^p];%% You need to return the following variables correctly.X_poly = zeros(numel(X), p);% ====================== 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.%% m = numel(X);X1 = X(:);disp(X1);for i = 1:p  for j = 1:m        X_poly(j,i) = X1(j)^i;  % =========================================================================  endend

function [lambda_vec, error_train, error_val] = ...    validationCurve(X, y, Xval, yval)%VALIDATIONCURVE Generate the train and validation errors needed to%plot a validation curve that we can use to select lambda%   [lambda_vec, error_train, error_val] = ...%       VALIDATIONCURVE(X, y, Xval, yval) returns the train%       and validation errors (in error_train, error_val)%       for different values of lambda. You are given the training set (X,%       y) and validation set (Xval, yval).%% Selected values of lambda (you should not change this)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 ======================% Instructions: Fill in this function to return training errors in %               error_train and the validation errors in error_val. The %               vector lambda_vec contains the different lambda parameters %               to use for each calculation of the errors, i.e, %               error_train(i), and error_val(i) should give %               you the errors obtained after training with %               lambda = lambda_vec(i)%% Note: You can loop over lambda_vec with the following:%%       for i = 1:length(lambda_vec)%           lambda = lambda_vec(i);%           % Compute train / val errors when training linear %           % regression with regularization parameter lambda%           % You should store the result in error_train(i)%           % and error_val(i)%           ....%           %       end%%for i = 1:length(lambda_vec)  lambda = lambda_vec(i);  theta = trainLinearReg(X, y, lambda);    J1 = linearRegCostFunction(X, y, theta, 0);   % pay attention , this lambda is zero.%  J2 = linearRegCostFunction(Xval, yval, theta, 0);    error_train(i) = J1;  error_val(i) = J2;end% =========================================================================end