37 lines
809 B
Matlab
37 lines
809 B
Matlab
function [x_d, hat_Q1, sigma_d] = cal_debiased_LASSO(x, A, y, lambda, sigma)
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[M, N] = size(A);
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gamma = M/N;
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hat_Q1 = gamma;
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[~, D] = eig(A'*A);
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d = diag(D);
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diff = 1;
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T = 1000;
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t = 0;
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while (t < T) && (diff > 1e-6)
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Q1_pre = hat_Q1;
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rho = mean((2 - lambda./(hat_Q1*abs(x) + lambda)).*(abs(x) > 1e-4))/2;
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hat_Q1 = rho/mean(1./(d + (1-rho)*hat_Q1/rho));
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diff = abs(Q1_pre - hat_Q1);
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t = t+1;
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end
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x_d = x + 1/hat_Q1*A'*(y - A*x);
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chi = rho/hat_Q1;
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hat_Q2 = 1/chi - hat_Q1;
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t = -hat_Q2;
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t_prime = -1/mean((1./(d+hat_Q2)).^2);
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G_prime = t + 1/chi;
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G_wprime = t_prime + 1/chi/chi;
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RSS = sum(abs(y - A*x).^2)/M;
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hat_chi = gamma*G_wprime/(2*G_prime-2*chi*G_wprime)*RSS +...
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(-G_wprime*gamma+G_prime*G_prime)/(2*G_prime-2*chi*G_wprime)*sigma^2;
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sigma_d = sqrt(2*hat_chi)/hat_Q1;
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end |