197 lines
6.9 KiB
Matlab
197 lines
6.9 KiB
Matlab
%% Initial
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clc; clear; close all;
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trail_times = 250;
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method = "cVAMPro";
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Ns = [64, 128, 256, 512, 1024];
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Ms = [4, 8, 16, 32];
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sigma = 0.01;
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tau = 1e-6;
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iter_max = 100;
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epi = 0;
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lg_lambdas = -5: 0.05: -1;
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lambdas = 10 .^ lg_lambdas;
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H0_REE_means = zeros(length(Ns), length(Ms));
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H0_REE_maxs = zeros(length(Ns), length(Ms));
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H1_REE_means = zeros(length(Ns), length(Ms));
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H1_REE_maxs = zeros(length(Ns), length(Ms));
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figure;
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for N_idx = 1: length(Ns)
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for M_idx = 1: length(Ms)
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subplot(length(Ns), length(Ms), (N_idx - 1) * length(Ms) + M_idx);
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FAR_N = Ns(N_idx);
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FAR_M = Ms(M_idx);
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fprintf("Simluating: N = %d, M = %d\n\n", FAR_N, FAR_M);
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MN = FAR_N * FAR_M;
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betas_wide = zeros(FAR_M * FAR_N, 1) + 1;
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[Lambda, Lambda_C, x] = get_sparse_vector(FAR_N, FAR_M, betas_wide, true);
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% get lambda
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signal_model_filename = "./Signal_Model/Signal_Model_" + string(FAR_N) + "_" + string(FAR_M) + ".mat";
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if exist(signal_model_filename, "file")
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load(signal_model_filename, "A", "C_n", "ref_lambda");
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else
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curr_metric = FAR_N;
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for TT = 1: 20
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[C_n, A] = get_Psi(FAR_N, FAR_M, epi);
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noise = get_noise(sigma, FAR_N, 1);
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y_noise = A * x + noise;
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MSEs = zeros(length(lambdas), 1);
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all_x_hat = zeros(length(x), length(lambdas));
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for lambda_idx = 1: length(lambdas)
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lambda = lambdas(lambda_idx);
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[x_LASSO, x_hat_d] = cVAMPro(y_noise, A, lambda, tau, iter_max);
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MSEs(lambda_idx) = sum(real(x_LASSO - x));
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all_x_hat(:, lambda_idx) = x_LASSO;
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end
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[metric, idx] = min(abs(MSEs));
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if curr_metric > metric
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ref_lambda = lambdas(idx);
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save(signal_model_filename, "A", "C_n", "ref_lambda");
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curr_metric = metric;
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end
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end
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end
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fprintf("get lambda: lambda = %.15f. \n", ref_lambda);
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fprintf("Signal Model filename: " + signal_model_filename + "\n\n");
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% train
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LASSO_lambda = ref_lambda;
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simulate_results_filename = ...
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"./data5/" + ...
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"FAR" + "_" + ...
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string(FAR_N) + "_" + ...
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string(FAR_M)+ "_" + ...
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method + "_" + ...
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string(sigma) + "_" + ...
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trail_times + ...
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".mat";
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if exist(simulate_results_filename, "file")
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load( ...
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simulate_results_filename, ...
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"recovery_results", "sigma_w2", "thresholds",...
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"C_n", "A", "Lambda", "Lambda_C", "x" ...
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);
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else
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% Mento Carlo Recovery
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[recovery_results, sigma_w2, thresholds] = All_Recovery2(A, x, LASSO_lambda, sigma, trail_times, LASSO_lambda, tau);
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save( ...
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simulate_results_filename, ...
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"recovery_results", "sigma_w2", "thresholds",...
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"C_n", "A", "Lambda", "Lambda_C", "x" ...
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);
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end
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fprintf("Simulate results filename: " + simulate_results_filename + "\n\n");
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% test
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i1 = 1; i2 = 1;
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Lambda_distributes = zeros(2, length(Lambda) * trail_times);
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Lambda_C_distributes = zeros(2, length(Lambda_C) * trail_times);
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for t = 1:trail_times
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x_0_hat = squeeze(recovery_results(1, t, :));
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x_1_hat = squeeze(recovery_results(2, t, :)) - x;
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if anynan(x_1_hat)
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continue;
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end
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for i = 1: length(Lambda) + length(Lambda_C)
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if ismember(i, Lambda_C)
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Lambda_C_distributes(1, i1) = x_0_hat(i);
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Lambda_C_distributes(2, i1) = x_1_hat(i);
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i1 = i1 + 1;
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elseif ismember(i, Lambda)
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Lambda_distributes(1, i2) = x_0_hat(i);
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Lambda_distributes(2, i2) = x_1_hat(i);
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i2 = i2 + 1;
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end
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end
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end
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real_H00 = real(Lambda_C_distributes(1, 1:i1-1));
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real_H01 = real(Lambda_distributes(1, 1:i2-1));
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real_H10 = real(Lambda_C_distributes(2, 1:i1-1));
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real_H11 = real(Lambda_distributes(2, 1:i2-1));
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% figure;
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% subplot(2, 2, 1); histfit(real_H00); xlabel("x\_hat"); ylabel("times"); title("H_0 (not in support set)")
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% subplot(2, 2, 2); histfit(real_H01); xlabel("x\_hat"); ylabel("times"); title("H_0 (in support set)")
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% subplot(2, 2, 3); histfit(real_H10); xlabel("x\_hat"); ylabel("times"); title("H_1 (not in support set)")
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% subplot(2, 2, 4); histfit(real_H11); xlabel("x\_hat"); ylabel("times"); title("H_1 (in support set)")
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% sgtitle("N = " + string(FAR_N) + ", M = " + string(FAR_M));
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histfit(real_H11); xlabel("x\_hat"); ylabel("times"); title("N = " + string(FAR_N) + ", M = " + string(FAR_M));
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means = [ ...
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mean(Lambda_C_distributes(1, 1:i1-1)), ...
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mean(Lambda_distributes(1, i2-1)), ...
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mean(Lambda_C_distributes(2, 1:i1-1)), ...
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mean(Lambda_distributes(2, i2-1)), ...
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mean([Lambda_distributes(1, i2-1) Lambda_C_distributes(1, 1:i1-1)]) ...
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];
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stds = [ ...
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std(Lambda_C_distributes(1, 1:i1-1)), ...
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std(Lambda_distributes(1, i2-1)), ...
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std(Lambda_C_distributes(2, 1:i1-1)), ...
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std(Lambda_distributes(2, i2-1)), ...
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std([Lambda_distributes(1, i2-1) Lambda_C_distributes(1, 1:i1-1)]) ...
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];
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fprintf("H_00: mu = %.15f, std = %.15f\n", means(1), stds(1));
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fprintf("H_01: mu = %.15f, std = %.15f\n", means(2), stds(2));
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fprintf("H_10: mu = %.15f, std = %.15f\n", means(3), stds(3));
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fprintf("H_11: mu = %.15f, std = %.15f\n", means(4), stds(4));
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fprintf("H_0: mu = %.15f, std = %.15f\n", means(5), stds(5));
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[ss, vs, H0_mean, H0_max, H1_mean, H1_max] = get_sigma_var(recovery_results, sigma_w2, x);
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H0_REE_means(N_idx, M_idx) = H0_mean;
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H0_REE_maxs(N_idx, M_idx) = H0_max;
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H1_REE_means(N_idx, M_idx) = H1_mean;
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H1_REE_maxs(N_idx, M_idx) = H1_max;
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fprintf("Test Complete \n\n");
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end
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end
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sgtitle("H_1 (in support set)");
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figure;
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subplot(221);
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h = heatmap(Ns, Ms, H0_REE_means');
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h.XLabel = "N";
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h.YLabel = "M";
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h.Title = "H_0, mean(REE)";
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subplot(222);
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h = heatmap(Ns, Ms, H0_REE_maxs');
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h.XLabel = "N";
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h.YLabel = "M";
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h.Title = "H_0, max(REE)";
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subplot(223);
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h = heatmap(Ns, Ms, H1_REE_means');
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h.XLabel = "N";
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h.YLabel = "M";
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h.Title = "H_1, mean(REE)";
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subplot(224);
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h = heatmap(Ns, Ms, H1_REE_maxs');
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h.XLabel = "N";
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h.YLabel = "M";
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h.Title = "H_1, max(REE)";
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