?? linear_regression.m
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function [muY, SigmaY, weightsY] = linear_regression(X, Y, varargin)% LINEAR_REGRESSION Fit params for P(Y|X) = N(Y; W X + mu, Sigma) %% X(:, t) is the t'th input example% Y(:, t) is the t'th output example%% Kevin Murphy, August 2003%% This is a special case of cwr_em with 1 cluster.% You can also think of it as a front end to clg_Mstep.[cov_typeY, clamp_weights, muY, SigmaY, weightsY,... cov_priorY, regress, clamp_covY] = process_options(... varargin, ... 'cov_typeY', 'full', 'clamp_weights', 0, ... 'muY', [], 'SigmaY', [], 'weightsY', [], ... 'cov_priorY', [], 'regress', 1, 'clamp_covY', 0); [nx N] = size(X);[ny N2] = size(Y);if N ~= N2 error(sprintf('nsamples X (%d) ~= nsamples Y (%d)', N, N2));endw = 1/N;WYbig = Y*w;WYY = WYbig * Y'; WY = sum(WYbig, 2);WYTY = sum(diag(WYbig' * Y));if ~regress % This is just fitting an unconditional Gaussian weightsY = []; [muY, SigmaY] = ... mixgauss_Mstep(1, WY, WYY, WYTY, ... 'cov_type', cov_typeY, 'cov_prior', cov_priorY); % There is a much easier way... assert(approxeq(muY, mean(Y'))) assert(approxeq(SigmaY, cov(Y') + 0.01*eye(ny)))else % This is just linear regression WXbig = X*w; WXX = WXbig * X'; WX = sum(WXbig, 2); WXTX = sum(diag(WXbig' * X)); WXY = WXbig * Y'; [muY, SigmaY, weightsY] = ... clg_Mstep(1, WY, WYY, WYTY, WX, WXX, WXY, ... 'cov_type', cov_typeY, 'cov_prior', cov_priorY);endif clamp_covY, SigmaY = SigmaY; endif clamp_weights, weightsY = weightsY; endif nx==1 & ny==1 & regress P = polyfit(X,Y); % Y = P(1) X^1 + P(2) X^0 = ax + b assert(approxeq(muY, P(2))) assert(approxeq(weightsY, P(1)))end%%%%%%%% Testif 0 c1 = randn(2,100); c2 = randn(2,100); y = c2(1,:); X = [ones(size(c1,2),1) c1']; b = regress(y(:), X); % stats toolbox [m,s,w] = linear_regression(c1, y); assert(approxeq(b(1),m)) assert(approxeq(b(2), w(1))) assert(approxeq(b(3), w(2)))end?? 快捷鍵說明
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