From 93da019cd349db721de52ef85dd5efc2dfe99e1c Mon Sep 17 00:00:00 2001 From: agjycxysow <104630041+agjycxysow@users.noreply.github.com> Date: Mon, 18 Jul 2022 17:20:01 +0800 Subject: [PATCH] Add files via upload --- ex2/costFunction.m | 32 ++++++++ ex2/costFunctionReg.m | 33 ++++++++ ex2/ex2.m | 151 +++++++++++++++++++++++++++++++++++++ ex2/ex2.pdf | Bin 0 -> 261449 bytes ex2/ex2_reg.m | 136 +++++++++++++++++++++++++++++++++ ex2/ex2data1.txt | 100 ++++++++++++++++++++++++ ex2/ex2data2.txt | 118 +++++++++++++++++++++++++++++ ex2/mapFeature.m | 21 ++++++ ex2/plotData.m | 36 +++++++++ ex2/plotDecisionBoundary.m | 48 ++++++++++++ ex2/predict.m | 33 ++++++++ ex2/sigmoid.m | 18 +++++ ex2/submit.m | 62 +++++++++++++++ ex2/token.mat | Bin 0 -> 263 bytes 14 files changed, 788 insertions(+) create mode 100644 ex2/costFunction.m create mode 100644 ex2/costFunctionReg.m create mode 100644 ex2/ex2.m create mode 100644 ex2/ex2.pdf create mode 100644 ex2/ex2_reg.m create mode 100644 ex2/ex2data1.txt create mode 100644 ex2/ex2data2.txt create mode 100644 ex2/mapFeature.m create mode 100644 ex2/plotData.m create mode 100644 ex2/plotDecisionBoundary.m create mode 100644 ex2/predict.m create mode 100644 ex2/sigmoid.m create mode 100644 ex2/submit.m create mode 100644 ex2/token.mat diff --git a/ex2/costFunction.m b/ex2/costFunction.m new file mode 100644 index 0000000..aff6b22 --- /dev/null +++ b/ex2/costFunction.m @@ -0,0 +1,32 @@ +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 +% +h = sigmoid(((theta') * X')'); +J = (1/m) * sum(-y .* log(h) - (1 - y) .* log(1 - h)); + + +grad = (1/m) * (h - y)' * X; +grad = grad'; + + +% ============================================================= + +end diff --git a/ex2/costFunctionReg.m b/ex2/costFunctionReg.m new file mode 100644 index 0000000..0b6c675 --- /dev/null +++ b/ex2/costFunctionReg.m @@ -0,0 +1,33 @@ +function [J, grad] = costFunctionReg(theta, X, y, lambda) +%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization +% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using +% theta as the parameter for regularized 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 + +h = sigmoid(((theta') * X')'); + +theta1 = theta; +theta1(1) = 0; + +J = (1/m) * sum(-y .* log(h) - (1 - y) .* log(1 - h)) + lambda/(2*m) * theta1' * theta1; + + +grad = (1/m) * (h - y)' * X + lambda/m * theta1'; +grad = grad'; + +% ============================================================= + +end diff --git a/ex2/ex2.m b/ex2/ex2.m new file mode 100644 index 0000000..103fe11 --- /dev/null +++ b/ex2/ex2.m @@ -0,0 +1,151 @@ +%% Machine Learning Online Class - Exercise 2: Logistic Regression +% +% Instructions +% ------------ +% +% This file contains code that helps you get started on the logistic +% regression exercise. You will need to complete the following functions +% in this exericse: +% +% sigmoid.m +% costFunction.m +% predict.m +% costFunctionReg.m +% +% For this exercise, you will not need to change any code in this file, +% or any other files other than those mentioned above. +% + +%% Initialization +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]); y = data(:, 3); + +%% ==================== 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); + +% 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); + +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; + + +%% ============= Part 3: Optimizing using fminunc ============= +% In this exercise, you will use a built-in function (fminunc) to find the +% optimal parameters theta. + +% 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('Expected cost (approx): 0.203\n'); +fprintf('theta: \n'); +fprintf(' %f \n', theta); +fprintf('Expected theta (approx):\n'); +fprintf(' -25.161\n 0.206\n 0.201\n'); + +% 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; + +fprintf('\nProgram paused. Press enter to continue.\n'); +pause; + +%% ============== 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 + +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'); + + diff --git a/ex2/ex2.pdf b/ex2/ex2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a49d8261477667ddb98b3ad89004bf9d1e469c04 GIT binary patch literal 261449 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0 HcmV?d00001 diff --git a/ex2/ex2_reg.m b/ex2/ex2_reg.m new file mode 100644 index 0000000..f363318 --- /dev/null +++ b/ex2/ex2_reg.m @@ -0,0 +1,136 @@ +%% Machine Learning Online Class - Exercise 2: Logistic Regression +% +% Instructions +% ------------ +% +% This file contains code that helps you get started on the second part +% of the exercise which covers regularization with logistic regression. +% +% You will need to complete the following functions in this exericse: +% +% sigmoid.m +% costFunction.m +% predict.m +% costFunctionReg.m +% +% For this exercise, you will not need to change any code in this file, +% or any other files other than those mentioned above. +% + +%% Initialization +clear ; close all; clc + +%% Load Data +% The first two columns contains the X values and the third column +% contains the label (y). + +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; + + +%% =========== Part 1: Regularized Logistic Regression ============ +% In this part, you are given a dataset with data points that are not +% linearly separable. However, you would still like to use logistic +% regression to classify the data points. +% +% To do so, you introduce more features to use -- in particular, you add +% polynomial features to our data matrix (similar to polynomial +% regression). +% + +% Add Polynomial Features + +% 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('Expected cost (approx): 0.693\n'); +fprintf('Gradient at initial theta (zeros) - first five values only:\n'); +fprintf(' %f \n', grad(1:5)); +fprintf('Expected gradients (approx) - first five values only:\n'); +fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n'); + +fprintf('\nProgram paused. Press enter to continue.\n'); +pause; + +% Compute and display cost and gradient +% with all-ones theta and lambda = 10 +test_theta = ones(size(X,2),1); +[cost, grad] = costFunctionReg(test_theta, X, y, 10); + +fprintf('\nCost at test theta (with lambda = 10): %f\n', cost); +fprintf('Expected cost (approx): 3.16\n'); +fprintf('Gradient at test theta - first five values only:\n'); +fprintf(' %f \n', grad(1:5)); +fprintf('Expected gradients (approx) - first five values only:\n'); +fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n'); + +fprintf('\nProgram paused. Press enter to continue.\n'); +pause; + +%% ============= Part 2: Regularization and Accuracies ============= +% Optional Exercise: +% In this part, you will get to try different values of lambda and +% see how regularization affects the decision coundart +% +% Try the following values of lambda (0, 1, 10, 100). +% +% How does the decision boundary change when you vary lambda? How does +% the training set accuracy vary? +% + +% 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'); + diff --git a/ex2/ex2data1.txt b/ex2/ex2data1.txt new file mode 100644 index 0000000..3a5f952 --- /dev/null +++ b/ex2/ex2data1.txt @@ -0,0 +1,100 @@ 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b/ex2/ex2data2.txt new file mode 100644 index 0000000..a888992 --- /dev/null +++ b/ex2/ex2data2.txt @@ -0,0 +1,118 @@ +0.051267,0.69956,1 +-0.092742,0.68494,1 +-0.21371,0.69225,1 +-0.375,0.50219,1 +-0.51325,0.46564,1 +-0.52477,0.2098,1 +-0.39804,0.034357,1 +-0.30588,-0.19225,1 +0.016705,-0.40424,1 +0.13191,-0.51389,1 +0.38537,-0.56506,1 +0.52938,-0.5212,1 +0.63882,-0.24342,1 +0.73675,-0.18494,1 +0.54666,0.48757,1 +0.322,0.5826,1 +0.16647,0.53874,1 +-0.046659,0.81652,1 +-0.17339,0.69956,1 +-0.47869,0.63377,1 +-0.60541,0.59722,1 +-0.62846,0.33406,1 +-0.59389,0.005117,1 +-0.42108,-0.27266,1 +-0.11578,-0.39693,1 +0.20104,-0.60161,1 +0.46601,-0.53582,1 +0.67339,-0.53582,1 +-0.13882,0.54605,1 +-0.29435,0.77997,1 +-0.26555,0.96272,1 +-0.16187,0.8019,1 +-0.17339,0.64839,1 +-0.28283,0.47295,1 +-0.36348,0.31213,1 +-0.30012,0.027047,1 +-0.23675,-0.21418,1 +-0.06394,-0.18494,1 +0.062788,-0.16301,1 +0.22984,-0.41155,1 +0.2932,-0.2288,1 +0.48329,-0.18494,1 +0.64459,-0.14108,1 +0.46025,0.012427,1 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size +% + +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 \ No newline at end of file diff --git a/ex2/plotData.m b/ex2/plotData.m new file mode 100644 index 0000000..d950cfa --- /dev/null +++ b/ex2/plotData.m @@ -0,0 +1,36 @@ +function plotData(X, y) +%PLOTDATA Plots the data points X and y into a new figure +% PLOTDATA(x,y) plots the data points with + for the positive examples +% and o for the negative examples. X is assumed to be a Mx2 matrix. + +% Create New Figure +figure; hold on; + +% ====================== YOUR CODE HERE ====================== +% Instructions: Plot the positive and negative examples on a +% 2D plot, using the option 'k+' for the positive +% examples and 'ko' for the negative examples. +% + + +% Find Indices of Positive and Negative Examples +pos = find(y==1); neg = find(y == 0); +% Plot Examples +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 diff --git a/ex2/plotDecisionBoundary.m b/ex2/plotDecisionBoundary.m new file mode 100644 index 0000000..cd36314 --- /dev/null +++ b/ex2/plotDecisionBoundary.m @@ -0,0 +1,48 @@ +function plotDecisionBoundary(theta, X, y) +%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with +%the decision boundary defined by theta +% PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the +% positive examples and o for the negative examples. X is assumed to be +% a either +% 1) Mx3 matrix, where the first column is an all-ones column for the +% intercept. +% 2) MxN, N>3 matrix, where the first column is all-ones + +% 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 diff --git a/ex2/predict.m b/ex2/predict.m new file mode 100644 index 0000000..2b11311 --- /dev/null +++ b/ex2/predict.m @@ -0,0 +1,33 @@ +function p = predict(theta, X) +%PREDICT Predict whether the label is 0 or 1 using learned logistic +%regression parameters theta +% p = PREDICT(theta, X) computes the predictions for X using a +% threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1) + +m = size(X, 1); % Number of training examples + +% You need to return the following variables correctly +p = zeros(m, 1); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Complete the following code to make predictions using +% your learned logistic regression parameters. +% You should set p to a vector of 0's and 1's +% + +p = sigmoid(X * theta); +for i = 1:m + if p(i) >= 0.5 + p(i) = 1; + else + p(i) = 0; + end +end + + + + +% ========================================================================= + + +end diff --git a/ex2/sigmoid.m b/ex2/sigmoid.m new file mode 100644 index 0000000..393c5d3 --- /dev/null +++ b/ex2/sigmoid.m @@ -0,0 +1,18 @@ +function g = sigmoid(z) +%SIGMOID Compute sigmoid function +% g = SIGMOID(z) computes the sigmoid of z. + +% You need to return the following variables correctly +g = zeros(size(z)); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Compute the sigmoid of each value of z (z can be a matrix, +% vector or scalar). + +g = 1 ./ (1 + exp(-z)); + + + +% ============================================================= + +end diff --git a/ex2/submit.m b/ex2/submit.m new file mode 100644 index 0000000..d8a775c --- /dev/null +++ b/ex2/submit.m @@ -0,0 +1,62 @@ +function submit() + addpath('./lib'); + + conf.assignmentKey = 'JvOPouj-S-ys8KjYcPYqrg'; + conf.itemName = 'Logistic Regression'; + conf.partArrays = { ... + { ... + 'sFxIn', ... + { 'sigmoid.m' }, ... + 'Sigmoid Function', ... + }, ... + { ... + 'yvXBE', ... + { 'costFunction.m' }, ... + 'Logistic Regression Cost', ... + }, ... + { ... + 'HerlY', ... + { 'costFunction.m' }, ... + 'Logistic Regression Gradient', ... + }, ... + { ... + '9fxV6', ... + { 'predict.m' }, ... + 'Predict', ... + }, ... + { ... + 'OddeL', ... + { 'costFunctionReg.m' }, ... + 'Regularized Logistic Regression Cost', ... + }, ... + { ... + 'aUo3H', ... + { 'costFunctionReg.m' }, ... + 'Regularized Logistic Regression Gradient', ... + }, ... + }; + conf.output = @output; + + submitWithConfiguration(conf); +end + +function out = output(partId, auxstring) + % Random Test Cases + X = [ones(20,1) (exp(1) * sin(1:1:20))' (exp(0.5) * cos(1:1:20))']; + y = sin(X(:,1) + X(:,2)) > 0; + if partId == 'sFxIn' + out = sprintf('%0.5f ', sigmoid(X)); + elseif partId == 'yvXBE' + out = sprintf('%0.5f ', costFunction([0.25 0.5 -0.5]', X, y)); + elseif partId == 'HerlY' + [cost, grad] = costFunction([0.25 0.5 -0.5]', X, y); + out = sprintf('%0.5f ', grad); + elseif partId == '9fxV6' + out = sprintf('%0.5f ', predict([0.25 0.5 -0.5]', X)); + elseif partId == 'OddeL' + out = sprintf('%0.5f ', costFunctionReg([0.25 0.5 -0.5]', X, y, 0.1)); + elseif partId == 'aUo3H' + [cost, grad] = costFunctionReg([0.25 0.5 -0.5]', X, y, 0.1); + out = sprintf('%0.5f ', grad); + end +end diff --git a/ex2/token.mat b/ex2/token.mat new file mode 100644 index 0000000000000000000000000000000000000000..db8a3f9b7074101e5191999e703a58d2e4c4ad24 GIT binary patch literal 263 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQV4Jk_w+L}(NS}aZCnRt%B$+8Z zV@MKX<49=zB-t3j;?;a4s94yzxM2%Jh|R?#2M%4jbl}d3D~hrzOQ+A7&wYuX;p}ma xogh;z;ih~*H-!Ocir1&j!Jii-DZF_qG3iz6jECtH(w-%~%a&qcn83sy2LM7%PiO!D literal 0 HcmV?d00001