首先我们先说一下ex2.m不使用高级算法的代码详解，也就是梯度下降的过程。
clear ; close all; clc
%% Load Data
% The first two columns contains the exam scores and the third column
% contains the label.
data = load('ex2data1.txt');
X = data(:, [1, 2]); %考试成绩
y = data(:, 3); %录取与否
%% ==================== Part 1: Plotting ====================
% We start the exercise by first plotting the data to understand the
% the problem we are working with.
fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
'indicating (y = 0) examples.\n']);
plotData(X, y);
% Put some labels
hold on;
% Labels and Legend
xlabel('Exam 1 score')
ylabel('Exam 2 score')
% Specified in plot order
legend('Admitted', 'Not admitted')
hold off;
fprintf('\nProgram paused. Press enter to continue.\n');
pause;
%% ============ Part 2: Compute Cost and Gradient ============
% In this part of the exercise, you will implement the cost and gradient
% for logistic regression. You neeed to complete the code in
% costFunction.m
% Setup the data matrix appropriately, and add ones for the intercept term
[m, n] = size(X); %存储X矩阵的行数m，列数n
% Add intercept term to x and X_test
X = [ones(m, 1) X]; %添加一列为1的
% Initialize fitting parameters
initial_theta = zeros(n + 1, 1);
% Compute and display initial cost and gradient
[cost, grad] = costFunction(initial_theta, X, y);
fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf('Expected cost (approx): 0.693\n');
fprintf('Gradient at initial theta (zeros): \n');
fprintf(' %f \n', grad);
fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
% Compute and display cost and gradient with non-zero theta
test_theta = [-24; 0.2; 0.2];
[cost, grad] = costFunction(test_theta, X, y);
fprintf('\nCost at test theta: %f\n', cost);
fprintf('Expected cost (approx): 0.218\n');
fprintf('Gradient at test theta: \n');
fprintf(' %f \n', grad);
fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
fprintf('\nProgram paused. Press enter to continue.\n');
pause;
从part2开始，
part2 计算代价和theta值
function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
% J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
% parameter for logistic regression and the gradient of the cost
% w.r.t. to the parameters.
% 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 of a particular choice of theta.
% You should set J to the cost.
% Compute the partial derivatives and set grad to the partial
% derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%
J = (-y' * log(sigmoid(X * theta)) - (1 - y)' * log(1 - sigmoid(X * theta))) / m;
grad = X' * (sigmoid(X * theta) - y) / m;
% =============================================================
end
输出part2的内容 当值是
Program paused. Press enter to continue.
Cost at initial theta (zeros): 0.693147
Expected cost (approx): 0.693
Gradient at initial theta (zeros):
-0.100000
-12.009217
-11.262842
Expected gradients (approx):
-0.1000
-12.0092
-11.2628
Cost at test theta: 0.218330
Expected cost (approx): 0.218
Gradient at test theta:
0.042903
2.566234
2.646797
Expected gradients (approx):
0.043
2.566
2.647
%% ============== Part 4: Predict and Accuracies ==============
% After learning the parameters, you'll like to use it to predict the outcomes
% on unseen data. In this part, you will use the logistic regression model
% to predict the probability that a student with score 45 on exam 1 and
% score 85 on exam 2 will be admitted.
%
% Furthermore, you will compute the training and test set accuracies of
% our model.
%
% Your task is to complete the code in predict.m
% Predict probability for a student with score 45 on exam 1
% and score 85 on exam 2
fprintf('thera的值为 :%f \n', theta);
fprintf('[1 45 85] * theta的值为：%f\n',[1 45 85] * theta)
prob = sigmoid([1 45 85] * theta);
fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
'probability of %f\n'], prob);
fprintf('Expected value: 0.775 +/- 0.002\n\n');
% Compute accuracy on our training set
p = predict(theta, X);
fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
fprintf('Expected accuracy (approx): 89.0\n');
fprintf('\n');
将拟合的theta值与原数据集进行计算得出p(hθ(x))然后使用mean函数进行比较 。
mean(double(p==y)*100):将预测结果向量p与真实值向量y逐一对比，相同则置为1，不同则置为0，然后通过mean()函数计算一下均值，精确度就计算出来了。double(p~=y) 向量p与真实值向量y逐一对比，相同则置为0，不同则置为1。与上述对比正好相反。
