wehub-resource-sync
38 lines
818 B
Matlab
Executable File
38 lines
818 B
Matlab
Executable File
function model = linReg(X, t, lambda)
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% Fit linear regression model y=w'x+w0
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% Input:
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% X: d x n data
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% t: 1 x n response
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% lambda: regularization parameter
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% Output:
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% model: trained model structure
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% Written by Mo Chen (sth4nth@gmail.com).
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if nargin < 3
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lambda = 0;
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end
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d = size(X,1);
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idx = (1:d)';
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dg = sub2ind([d,d],idx,idx);
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xbar = mean(X,2);
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tbar = mean(t,2);
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X = bsxfun(@minus,X,xbar);
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t = bsxfun(@minus,t,tbar);
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XX = X*X';
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XX(dg) = XX(dg)+lambda; % 3.54 XX=inv(S)/beta
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% w = XX\(X*t');
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U = chol(XX);
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w = U\(U'\(X*t')); % 3.15 & 3.28
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w0 = tbar-dot(w,xbar); % 3.19
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model.w = w;
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model.w0 = w0;
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model.xbar = xbar;
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%% for probability prediction
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beta = 1/mean((t-w'*X).^2); % 3.21
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% alpha = lambda*beta; % lambda=a/b P.153 3.55
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% model.alpha = alpha;
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model.beta = beta;
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model.U = U;
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