Add Example

0 - example/nsq - 恢复算法/cal_debiased_LASSO.m

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