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Update FAR vs PD

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Ksyer
2024-07-16 15:56:53 +08:00
parent 9556bdf832
commit 5ac5ef1787
4 changed files with 133 additions and 39 deletions
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FAR vs PD/FAR_simu.m
+90 -30
View File
@@ -1,4 +1,4 @@
function P_fa = FAR_simu(threshold)
function threshold = FAR_simu(P_fa_FAR)
global N M epi trail_times
% Define measurement matrix
@@ -9,64 +9,124 @@ function P_fa = FAR_simu(threshold)
Lambda_C = setdiff(1:N*M, Lambda);
% Try "trail_times" times
NN = N;
results = zeros(trail_times, N * M);
results_0 = zeros(trail_times, N * M);
results_1 = zeros(trail_times, N * M);
thresholds_0 = [];
thresholds_1 = [];
if exist("FAR_recovery_1_LASSO_5.mat")
load("FAR_recovery_0_debiasedLASSO_500.mat", "results");
noise_sigma = 0.01;
noise_sigma_2 = noise_sigma ^ 2;
if exist("520BP.mat")
load("50.mat", "results_0", "results_1");
else
% 0 假设
for T = 1: trail_times
% y = Ax + n
n = randn(NN, 1) * 0.1;
n = randn(N, 1) * noise_sigma;
y_noise = n;
[x_hat, threshold] = debiased_LASSO(A, y_noise, P_fa_FAR, noise_sigma_2);
results_0(T, :) = x_hat;
thresholds_0 = [thresholds_0 threshold];
end
% 1 假设
for T = 1: trail_times
% y = Ax + n
n = randn(N, 1) * noise_sigma;
y_noise = A * x + n;
% x_hat = CS(A, y)
x_hat = recovery(A, y_noise);
results(T, :) = x_hat;
[x_hat, threshold] = debiased_LASSO(A, y_noise, P_fa_FAR, noise_sigma_2);
results_1(T, :) = x_hat;
thresholds_1 = [thresholds_1 threshold];
end
end
% Distribute of H_0 and H_1
H_0_distribute = zeros(1, length(Lambda_C));
H_1_distribute = zeros(1, length(Lambda));
H_00_distribute = zeros(1, length(Lambda_C));
H_01_distribute = zeros(1, length(Lambda));
H_10_distribute = zeros(1, length(Lambda_C));
H_11_distribute = zeros(1, length(Lambda));
i1 = 1;
i2 = 1;
Ts = [];
T_00 = [];
T_01 = [];
T_10 = [];
T_11 = [];
for threshold = 1: trail_times
x_0_hat = results_0(threshold, :);
x_1_hat = results_1(threshold, :);
t_00 = 0;
t_01 = 0;
t_10 = 0;
t_11 = 0;
for t = 1: trail_times
x_hat = results(t, :);
T = 0;
for i = 1: length(x)
if ismember(i, Lambda_C)
H_0_distribute(i1) = x_hat(i);
t_00 = t_00 + abs(x_0_hat(i));
t_10 = t_10 + abs(x_1_hat(i));
H_00_distribute(i1) = x_0_hat(i);
H_10_distribute(i1) = x_1_hat(i);
i1 = i1 + 1;
elseif ismember(i, Lambda)
T = T + abs(x_hat(i));
H_1_distribute(i2) = x_hat(i);
t_01 = t_01 + abs(x_0_hat(i));
t_11 = t_11 + abs(x_1_hat(i));
H_01_distribute(i2) = x_0_hat(i);
H_11_distribute(i2) = x_1_hat(i);
i2 = i2 + 1;
end
end
Ts = [Ts T];
T_00 = [T_00 t_00];
T_01 = [T_01 t_01];
T_10 = [T_10 t_10];
T_11 = [T_11 t_11];
end
% Draw
figure(1)
subplot(2, 1, 1);
subplot(2, 2, 1);
title("Freq histogram of H_0");
histfit(real(H_0_distribute));
histfit(real(H_00_distribute));
subplot(2, 1, 2);
subplot(2, 2, 2);
title("Freq histogram of H_1");
histfit(real(H_1_distribute));
histfit(real(H_01_distribute));
H_0_mean = mean(H_0_distribute);
H_0_std = std(H_0_distribute);
H_1_mean = mean(H_1_distribute);
H_1_std = std(H_1_distribute);
subplot(2, 2, 3);
title("Freq histogram of H_0");
histfit(real(H_10_distribute));
subplot(2, 2, 4);
title("Freq histogram of H_1");
histfit(real(H_11_distribute));
H_00_mean = mean(H_00_distribute);
H_00_std = std(H_00_distribute);
H_01_mean = mean(H_01_distribute);
H_01_std = std(H_01_distribute);
H_10_mean = mean(H_10_distribute);
H_10_std = std(H_10_distribute);
H_11_mean = mean(H_11_distribute);
H_11_std = std(H_11_distribute);
fprintf("H_00: mu = %f, std = %f\n", H_00_mean, H_00_std);
fprintf("H_01: mu = %f, std = %f\n", H_01_mean, H_01_std);
fprintf("H_10: mu = %f, std = %f\n", H_10_mean, H_10_std);
fprintf("H_11: mu = %f, std = %f\n", H_11_mean, H_11_std);
figure(2);
subplot(2, 2, 1);
histfit(real(T_00));
subplot(2, 2, 2);
histfit(real(T_01));
subplot(2, 2, 3);
histfit(real(T_10));
subplot(2, 2, 4);
histfit(real(T_11));
fprintf("H_0: mu = %f, std = %f\n", H_0_mean, H_0_std);
fprintf("H_1: mu = %f, std = %f\n", H_1_mean, H_1_std);
% P_fa = normcdf(threshold, H_0_mean, H_0_std);
end
FAR vs PD/Main.m
+8 -7
View File
@@ -7,19 +7,20 @@ N = 64;
M = 4;
K = 10;
lambda = zeros(M * N, 1);
lambda(:) = 0.3;
tau = 1e-4;
iter_max = 500;
% method = "debiased_LASSO";
lambda(:) = 0.8;
tau = 1e-6;
iter_max = 50;
method = "debiased_LASSO";
% method = "LASSO";
method = "BP";
% method = "BP";
% method = "VAMP";
trail_times = 1e2;
trail_times = 1000;
epi = 0;
extend_target = 1;
%% FAR
P_fa_FAR = FAR_simu(3);
P_fa_FAR = 1e-5;
threshold_FAR = FAR_simu(P_fa_FAR);
% fprintf("FAR: %f\n", P_fa_FAR);
%% PD
FAR vs PD/check_orth.m
Executable
+25
View File
@@ -0,0 +1,25 @@
clc; clear;
N = 16;
M = 4;
epi = 0;
d_n = floor(rand(N, 1)*M) / M;
A = get_Psi(N, M, d_n, epi);
B = get_Psi_2(N, M, d_n, epi);
C = A - B;
real_C = real(C);
imag_C = imag(C);
% subplot(121)
% heatmap(real_C)
%
% subplot(122)
% heatmap(imag_C)
r = zeros(N);
for i = 1: N
for j = 1: N
r(i, j) = A(i, :) * (A(j, :)');
end
end
heatmap(abs(r));
FAR vs PD/recovery.m
+9 -1
View File
@@ -25,6 +25,14 @@ function x_hat = recovery(A, y_noise)
x_d_CROD = x_LASSO + A'*(y_noise - A*x_LASSO)/Q_hat;
x_hat = x_d_CROD;
RSS = 1/sz(2) * norm(y_noise - A * x_LASSO, 2)^2;
noise_sigma_2 = 1e-4;
P_fa = normcdf(1, 0, 1);
sigma_w_2 = (gamma * (1-gamma)) / ((gamma - Rho)^2) * RSS + noise_sigma_2;
k_d = -sigma_w_2 * log(P_fa);
fprintf("%f %f %f\n", gamma, sigma_w_2, k_d);
elseif method == "LASSO"
sz = size(A);
N = sz(2);
@@ -47,7 +55,7 @@ function x_hat = recovery(A, y_noise)
cvx_end
else
global lambda tau iter_max;
[x_hat, z_hat_d] = cVAMPro(y_noise, A, lambda, tau, iter_max);
[x_hat, x_hat_d] = cVAMPro(y_noise, A, lambda, tau, iter_max);
end
end