题目太长啦！文档下载【传送门】
第1题
简述：实现逻辑回归。
第1步：加载数据文件：
data = load('ex2data1.txt');
X = data(:, [1, 2]); y = data(:, 3);
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;
第2步：plotData函数实现训练样本的可视化：
function plotData(X, y)
% Create New Figure
figure;
hold on; pos = find(y==1);
neg = find(y==0);
plot(X(pos,1),X(pos,2),'k+','LineWidth',2,'MarkerSize',7);
plot(X(neg,1),X(neg,2),'ko','MarkerFaceColor','y','MarkerSize',7); hold off;
end
第3步：计算代价函数和梯度：
% Setup the data matrix appropriately, and add ones for the intercept term
[m, n] = size(X); % Add intercept term to x and X_test
X = [ones(m, 1) X]; % Initialize fitting parameters
initial_theta = zeros(n + 1, 1); % Compute and display initial cost and gradient
[cost, grad] = costFunction(initial_theta, X, y);
第4步：实现costFunction函数：
function [J, grad] = costFunction(theta, X, y) m = length(y); % number of training examples
J = 0;
grad = zeros(size(theta)); h = sigmoid(X*theta);
J = 1/m*(-y'*log(h)-(1-y')*log(1-h));
grad = 1/m*(X'*(h-y)); end
第5步：实现sigmoid函数：
function g = sigmoid(z)
g = zeros(size(z));
g = 1./(1+exp(-z));
end
第6步：使用fminunc函数求θ和Cost：
% Set options for fminunc
options = optimset('GradObj', 'on', 'MaxIter', 400); % Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options); % Print theta to screen
fprintf('Cost at theta found by fminunc: %f\n', cost);
fprintf('theta: \n');
fprintf(' %f \n', theta); % Plot Boundary
plotDecisionBoundary(theta, 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;
第7步：实现plotDecisionBoundary函数：
function plotDecisionBoundary(theta, X, y) % Plot Data
plotData(X(:,2:3), y);
hold on if size(X, 2) <= 3
% Only need 2 points to define a line, so choose two endpoints
plot_x = [min(X(:,2))-2, max(X(:,2))+2]; % Calculate the decision boundary line
plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1)); % Plot, and adjust axes for better viewing
plot(plot_x, plot_y) % Legend, specific for the exercise
legend('Admitted', 'Not admitted', 'Decision Boundary')
axis([30, 100, 30, 100])
else
% Here is the grid range
u = linspace(-1, 1.5, 50);
v = linspace(-1, 1.5, 50); z = zeros(length(u), length(v));
% Evaluate z = theta*x over the grid
for i = 1:length(u)
for j = 1:length(v)
z(i,j) = mapFeature(u(i), v(j))*theta;
end
end
z = z'; % important to transpose z before calling contour % Plot z = 0
% Notice you need to specify the range [0, 0]
contour(u, v, z, [0, 0], 'LineWidth', 2)
end
hold off end
运行结果：
第8步：预测[45 85]成绩的学生，并计算准确率：
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');
第9步：实现predict预测函数：
function p = predict(theta, X)
m = size(X, 1); % Number of training examples
p = zeros(m, 1);
p = round(sigmoid(X*theta));
end
运行结果：
第2题
简述：通过正规化实现逻辑回归。
第1步：加载数据文件：
data = load('ex2data2.txt');
X = data(:, [1, 2]); y = data(:, 3);
plotData(X, y);
% Put some labels
hold on;
% Labels and Legend
xlabel('Microchip Test 1')
ylabel('Microchip Test 2')
% Specified in plot order
legend('y = 1', 'y = 0')
hold off;
第2步：正规化逻辑回归：
% Note that mapFeature also adds a column of ones for us, so the intercept
% term is handled
X = mapFeature(X(:,1), X(:,2)); % Initialize fitting parameters
initial_theta = zeros(size(X, 2), 1); % Set regularization parameter lambda to 1
lambda = 1; % Compute and display initial cost and gradient for regularized logistic
% regression
[cost, grad] = costFunctionReg(initial_theta, X, y, lambda); fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf('Gradient at initial theta (zeros) - first five values only:\n');
fprintf(' %f \n', grad(1:5));
第3步：mapFeature函数实现特征设置：
function out = mapFeature(X1, X2) degree = 6;
out = ones(size(X1(:,1)));
for i = 1:degree
for j = 0:i
out(:, end+1) = (X1.^(i-j)).*(X2.^j);
end
end end
其设置的特征值为：
第4步：实现costFunctionReg函数：
function [J, grad] = costFunctionReg(theta, X, y, lambda) % 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)); theta2 = theta(2:end,1);
h = sigmoid(X*theta);
J = 1/m*(-y'*log(h)-(1-y')*log(1-h)) + lambda/(2*m)*sum(theta2.^2);
theta(1,1) = 0;
grad = 1/m*(X'*(h-y)) + lambda/m*theta; end
第5步：使用fminunc函数求θ和Cost，并预测准确率：
% Initialize fitting parameters
initial_theta = zeros(size(X, 2), 1); % Set regularization parameter lambda to 1 (you should vary this)
lambda = 1; % Set Options
options = optimset('GradObj', 'on', 'MaxIter', 400); % Optimize
[theta, J, exit_flag] = ...
fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options); % Plot Boundary
plotDecisionBoundary(theta, X, y);
hold on;
title(sprintf('lambda = %g', lambda)) % Labels and Legend
xlabel('Microchip Test 1')
ylabel('Microchip Test 2') legend('y = 1', 'y = 0', 'Decision boundary')
hold off; % Compute accuracy on our training set
p = predict(theta, X); fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
运行结果：