機械学習

Coursera-機械学習（線形回帰）week2プログラミングの宿題の回答



Coursera Machine Learning Week2 Programming Homework Answers



1. warmUpExercise.m：5 * 5単位行列を出力します

function A = warmUpExercise() %WARMUPEXERCISE Example function in octave % A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix A = [] % ============= YOUR CODE HERE ============== % Instructions: Return the 5x5 identity matrix % In octave, we return values by defining which variables % represent the return values (at the top of the file) % and then set them accordingly. A=eye(5) % =========================================== end

Octaveに次のようにコマンドを入力します。
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2、plotData.m：散布図を描画します



function plotData(x, y) %PLOTDATA Plots the data points x and y into a new figure % PLOTDATA(x,y) plots the data points and gives the figure axes labels of % population and profit. figure %Open a new image window % ====================== YOUR CODE HERE ====================== % Instructions: Plot the training data into a figure using the % 'figure' and 'plot' commands. Set the axes labels using % the 'xlabel' and 'ylabel' commands. Assume the % population and revenue data have been passed in % as the x and y arguments of this function. % % Hint: You can use the 'rx' option with plot to have the markers % appear as red crosses. Furthermore, you can make the % markers larger by using plot(..., 'rx', 'MarkerSize', 10) plot(x,y,'rx','MarkerSize',10) ylabel('Profit in $10,000s') xlabel('Population of City in 10,000s') % ============================================================ end

Octaveのコマンドは次のとおりです。
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3. computeCost.m：単一の変数の下でコスト関数J（θ）を計算します
computeCostMulti.m：複数の変数の下でコスト関数J（θ）を計算します
どちらの場合もコードは同じです。
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function J = computeCost(X, y, theta) %COMPUTECOST Compute cost for linear regression % J = COMPUTECOST(X, y, theta) computes the cost of using theta as the % parameter for linear regression to fit the data points in X and y % Initialize some useful values m = length(y)% number of training set samples % You need to return the following variables correctly J = 0 % ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta % You should set J to the cost. J=1/(2*m)*sum((X*theta-y).^2) % ========================================================================= end

Octaveでのコマンドは次のとおりです。Xは1列とm行増加し、値は1、初期化θは2行と1列、値は0
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4.gradientDescent.m / gradientDescentMulti.m：θの最適解のための勾配降下アルゴリズム



function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters) %GRADIENTDESCENT Performs gradient descent to learn theta % theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by % taking num_iters gradient steps with learning rate alpha % Initialize some useful values m = length(y) % number of training examples J_history = zeros(num_iters, 1) for iter = 1:num_iters % ====================== YOUR CODE HERE ====================== % Instructions: Perform a single gradient step on the parameter vector % theta. % % Hint: While debugging, it can be useful to print out the values % of the cost function (computeCost) and gradient here. % theta=theta-alpha*(1/m)*(X'*(X*theta-y)) % ============================================================ % Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta) end end

オクターブの下のコマンドは次のとおりです。
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5. featureNormalize.m：スケーリング後の機能の値

function [X_norm, mu, sigma] = featureNormalize(X) %FEATURENORMALIZE Normalizes the features in X % FEATURENORMALIZE(X) returns a normalized version of X where % the mean value of each feature is 0 and the standard deviation % is 1. This is often a good preprocessing step to do when % working with learning algorithms. % You need to set these values correctly X_norm = X mu = zeros(1, size(X, 2)) sigma = zeros(1, size(X, 2)) % ====================== YOUR CODE HERE ====================== % Instructions: First, for each feature dimension, compute the mean % of the feature and subtract it from the dataset, % storing the mean value in mu. Next, compute the % standard deviation of each feature and divide % each feature by it's standard deviation, storing % the standard deviation in sigma. % % Note that X is a matrix where each column is a % feature and each row is an example. You need % to perform the normalization separately for % each feature. % % Hint: You might find the 'mean' and 'std' functions useful. % for i=1:size(X,2) mu(i)=mean(X(:,i))% average value of all elements in column i sigma(i)=std(X(:,i)) end X_norm=(X_norm - mu) ./ sigma % ============================================================ end

Octaveのコマンドは次のとおりです。
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6、normalEqn.m：正規方程式はθの最適解を直接見つけることができます
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function [theta] = normalEqn(X, y) %NORMALEQN Computes the closed-form solution to linear regression % NORMALEQN(X,y) computes the closed-form solution to linear % regression using the normal equations. theta = zeros(size(X, 2), 1) % ====================== YOUR CODE HERE ====================== % Instructions: Complete the code to compute the closed form solution % to linear regression and put the result in theta. % % ---------------------- Sample Solution ---------------------- theta=pinv(X'*X)*X'*y % ------------------------------------------------------------- % ============================================================ end

Octaveのコマンドは次のとおりです。
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最後に提出し、
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