吴恩达 MachineLearning Week6
第六周知识点总结
- 应将数据分割为训练集(training set)/交叉验证集(cross validation set)/测试集(test set)三个部分。
训练集用于训练数据，验证集用于确定模型选定的参数维度，是否过拟合等，测试集用来最终测验模型效果。 - 模型的参数维度越小，越容易过拟合，体现在交叉验证集误差（cross validation error)会很大但可能会造成过拟合。
一般随着参数维度的逐渐增加，训练集误差(train error)会越来越大，但泛化效果会越好，交叉验证即误差会减小。最终两个误差值会越来越接近并收敛。 - 对于过拟合或者高误差的解决方法一般有如下几种
- 更多的训练集 —— 解决过拟合
- 更少的参数维度 —— 解决过拟合
- 更多的参数维度 —— 解决高误差
- 增大lambda —— 解决过拟合
- 减小lambda —— 解决高误差
- 有些时候可能会有偏斜数据问题(Skewed data)。如癌症发病率为 0.5% 如果预测模型对所有病人都预测未得癌症则该模型也能有99.5的正确率。这显然是不合适的。于是引入了如下几个量
- Precision = true positive / (true positive + false positive)
- Recall = true positive / (true positive + false negatvie)
- Fscore = 2 * ( P * R ) / (P + R)
其中 true positive 表示当实际得病，预测得病。False positive 表示实际未得病，预测值得病。
false negative 表示实际得病，预测未得病。True negative 表示实际未得病，预测未得病。
Precision 越高说明预测精度越高，预测得病的得病概率很高，但这样会导致低 Recall 值，即可能会漏诊。
把得病的预测未得病的。最后用一个 Fscore 值来评价预测模型值越高越好。
课后作业代码
linearRegCostFunction.m
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 values
m = 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.
%
theta_without1 = theta(2:end , :);
J = sum((X * theta - y) .^ 2) / ( 2 * m) + sum(lambda * theta_without1 .^ 2 /( 2 * m)) ;
theta_without1 = theta;
theta_without1(1) = 0;
grad = X' * (X * theta - y) / m + lambda * theta_without1 / m;
% =========================================================================
grad = grad(:);
end
learningCurve.m
function [error_train, error_val] = ...
learningCurve(X, y, Xval, yval, lambda)
%LEARNINGCURVE Generates the train and cross validation set errors needed
%to plot a learning curve
% [error_train, error_val] = ...
% LEARNINGCURVE(X, y, Xval, yval, lambda) returns the train and
% cross validation set errors for a learning curve. In particular,
% it returns two vectors of the same length - error_train and
% error_val. Then, error_train(i) contains the training error for
% i examples (and similarly for error_val(i)).
%
% In this function, you will compute the train and test errors for
% dataset sizes from 1 up to m. In practice, when working with larger
% datasets, you might want to do this in larger intervals.
%
% Number of training examples
m = size(X, 1);
% You need to return these values correctly
error_train = zeros(m, 1);
error_val = zeros(m, 1);
% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return training errors in
% error_train and the cross validation errors in error_val.
% i.e., error_train(i) and
% error_val(i) should give you the errors
% obtained after training on i examples.
%
for i = 1:m
theta = trainLinearReg(X(1:i , :) , y(1:i) , lambda);
error_train(i) = linearRegCostFunction(X(1:i , :) , y(1:i) , theta , 0);
error_val(i) = linearRegCostFunction(Xval , yval , theta , 0);
end
% -------------------------------------------------------------
% =========================================================================
end
polyFeatures.m
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;
end
end
% =========================================================================
end
validationCurve.m
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)
%
for i = 1:length(lambda_vec)
lambda = lambda_vec(i);
theta = trainLinearReg(X, y, lambda);
error_train(i) = linearRegCostFunction(X , y , theta , 0);
error_val(i) = linearRegCostFunction(Xval , yval , theta , 0);
end
% =========================================================================
end