斯坦福大学深度学习练习题代码

% Exercise 2 Linear Regression % Data is roughly based on 2000 CDC growth figures % for boys % % x refers to a boy's age % y is a boy's height in meters % clear all; close all; clc x = load('ex2x.dat'); y = load('ex2y.dat'); m = length(y); % number of training examples % Plot the training data figure; % open a new figure window plot(x, y, 'o'); ylabel('Height in meters') xlabel('Age in years') % Gradient descent x = [ones(m, 1) x]; % Add a column of ones to x theta = zeros(size(x(1,:)))'; % initialize fitting parameters MAX_ITR = 1500; alpha = 0.07; for num_iterations = 1:MAX_ITR % This is a vectorized version of the % gradient descent update formula % It's also fine to use the summation formula from the videos % Here is the gradient grad = (1/m).* x' * ((x * theta) - y); % Here is the actual update theta = theta - alpha .* grad; % Sequential update: The wrong way to do gradient descent % grad1 = (1/m).* x(:,1)' * ((x * theta) - y); % theta(1) = theta(1) + alpha*grad1; % grad2 = (1/m).* x(:,2)' * ((x * theta) - y); % theta(2) = theta(2) + alpha*grad2; end % print theta to screen theta % Plot the linear fit hold on; % keep previous plot visible plot(x(:,2), x*theta, '-') legend('Training data', 'Linear regression') hold off % don't overlay any more plots on this figure % Closed form solution for reference % You will learn about this method in future videos exact_theta = (x' * x)\x' * y % Predict values for age 3.5 and 7 predict1 = [1, 3.5] *theta predict2 = [1, 7] * theta % Calculate J matrix % Grid over which we will calculate J theta0_vals = linspace(-3, 3, 100); theta1_vals = linspace(-1, 1, 100); % initialize J_vals to a matrix of 0's J_vals = zeros(length(theta0_vals), length(theta1_vals)); for i = 1:length(theta0_vals) for j = 1:length(theta1_vals) t = [theta0_vals(i); theta1_vals(j)]; J_vals(i,j) = (0.5/m) .* (x * t - y)' * (x * t - y); end end % Because of the way meshgrids work in the surf command, we need to % transpose J_vals before calling surf, or else the axes will be flipped J_vals = J_vals'; % Surface plot figure; surf(theta0_vals, theta1_vals, J_vals) xlabel('\theta_0'); ylabel('\theta_1'); % Contour plot figure; % Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100 contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 2, 15)) xlabel('\theta_0'); ylabel('\theta_1');