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reproduce_fig1_fig4_fig5.m
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clear all
close all
clc
% Paths to access functions from other folders
function_paths = [genpath('tpls/'), genpath('util/'), ...
genpath('predictive_error/'), genpath('baselines/')];
% Add the paths
addpath(function_paths)
% Main Script ==========================================================
% Settings
var_y = 1; % Observation noise Variance
ps = 5; % Number of 0s in theta
K = 12; % Number of available features
var_features = 1; % Range of input data H
var_theta = 1; % Variance of theta
T = 200; % Number of data points
p = K - ps; % True model dimension
% SYNTHETIC DATA =================================================================
%Create data
[y, H, theta] = generate_data(T, K, var_features, var_theta, ps, var_y);
% Indices of true features
idx_h = find(theta ~= 0)';
% Pad original true indices for comparison later
idx_h_padded = [idx_h zeros(1, K - length(idx_h))];
% OLASSO params
epsilon = 1e-7;
% Initial batch of data
t0 = K+1;
k_init = 3;
% rjMCMC params
n = round(0.2*T);
Ns = 700;
Nb = 50;
%% CALL METHODS
% TPLS =================================================================
[theta_tpls, idx_tpls, J, plot_stats] = tpls(y, H, k_init, t0, idx_h);
% Results for plotting
[tpls_correct, tpls_incorrect] = plot_stats{:};
J_tpls = J;
% OlinLASSO =================================================================
[theta_olin, idx_olin, J, plot_stats, idx_olin_store] = olasso(y, H, t0, epsilon, idx_h);
% Results for plotting
[olin_correct, olin_incorrect] = plot_stats{:};
J_olin = J;
% OCCD =================================================================
[theta_occd, idx_occd, J, plot_stats, idx_occd_store] = occd(y, H, t0, var_y, idx_h);
% Results for plotting
[occd_correct, occd_incorrect] = plot_stats{:};
J_occd = J;
% RJ MCMC =================================================================
% Data partition and Number of sweeps
[idx_mcmc, theta_RJ, plot_stats, J] = rj_mcmc(y, H, n, Ns, Nb, idx_h, var_y, t0);
% Results for plotting
[mcmc_correct, mcmc_incorrect] = plot_stats{:};
J_mcmc = J;
%% GROUND TRUTHS ===========================================================
% GENIE
[J_true, ~] = true_PE(y, H, t0, T, idx_h, var_y);
% SUPER GENIE
e_super = y(t0+1:end) - H(t0+1:end,:)*theta;
J_super = cumsum(e_super.^2);
% SINGLE EXPECTATIONS =====================================================
[E_add, E_rmv] = expectations(y, H, t0, T, idx_h, var_y, theta);
% BARS (for statistical performance)
tpls_features = [tpls_correct; tpls_incorrect];
olin_features = [olin_correct; olin_incorrect];
occd_features = [occd_correct; occd_incorrect];
mcmc_features = [mcmc_correct; mcmc_incorrect];
%% FIGURE 1: TPLS vs OLinLASSO vs RJMCMC barplots
% Specific run with feature bar plots
% Colors, FontSizes, Linewidths
load plot_settings.mat
fszl= 10;
% Time range to plot
time_plot = t0+1:T;
x_str = 'Arrival of n^{th} data point';
% BAR PLOTS SPECIFIC RUN =========================================
figure('Renderer', 'painters', 'Position', [900 100 1000 900])
% TPLS
subplot(3,2,1)
formats = {fsz, fszl, fsz_title, lwdt, c_tpls, c_inc, c_true, 'TPLS', x_str};
bar_plots(tpls_features, t0+1, T, p, K, formats)
% OLinLASSO
subplot(3,2,2)
formats = {fsz, fszl, fsz_title, lwdt, c_olin, c_inc, c_true, 'OLinLASSO', x_str};
bar_plots(olin_features, t0+1, T, p, K, formats)
% OCCD
subplot(3,2,3)
formats = {fsz, fszl, fsz_title, lwdt, c_occd, c_inc, c_true, 'OCCD-TWL', x_str};
bar_plots(occd_features, t0+1, T, p, K, formats)
% RJMCMC
subplot(3,2,4)
formats = {fsz, fszl, fsz_title, lwdt, c_mcmc, c_inc, c_true, 'RJMCMC', 'Iteration'};
bar_plots(mcmc_features, 1, Ns, p, K, formats)
% PREDICTIVE ERRORs ===============================================
% Difference
subplot(3,2,6)
hold on
plot(time_plot, J_occd - J_true, 'Color', c_occd, 'LineWidth', lwd)
plot(time_plot, J_olin - J_true, 'Color', c_olin, 'LineWidth', lwd)
plot(time_plot, J_mcmc - J_true, 'Color', c_mcmc, 'LineWidth', lwd)
plot(time_plot, J_tpls - J_true, 'Color', c_tpls, 'LineWidth', lwd)
yline(0, 'Color',c_true, 'linewidth', 2)
hold off
xlim([t0+1, T])
set(gca, 'FontSize', 15)
title('Relative', 'FontSize', fsz_title)
legend('\Delta J_{OCCD}','\Delta J_{OLin}', '\Delta J_{RJMCMC}', '\Delta J_{TPLS}', 'FontSize', fszl-2)
xlabel(x_str, 'FontSize', fsz)
ylabel('Predictive Error Difference', 'FontSize', fsz)
grid on
box on
% Raw
subplot(3,2,5)
hold on
plot(time_plot, J_occd, 'Color', c_occd, 'LineWidth', lwd)
plot(time_plot, J_olin, 'Color', c_olin, 'LineWidth', lwd)
plot(time_plot, J_mcmc, 'Color', c_mcmc, 'LineWidth', lwd)
plot(time_plot, J_tpls, 'Color', c_tpls, 'LineWidth', lwd)
plot(time_plot, J_true, 'Color', c_true, 'LineWidth', lwd)
plot(time_plot, J_super, 'Color', c_true, 'LineWidth', lwd, 'LineStyle','--')
hold off
xlim([t0+1, T])
set(gca, 'FontSize', 15)
legend('J_{OCCD}','J_{OLin}', 'J_{RJMCMC}', 'J_{TPLS}', 'J_{GENIE}', 'J_{TRUTH}', 'FontSize', fszl-2)
title('Predictive Error', 'FontSize', fsz_title)
ylabel('Predictive Error ', 'FontSize', fsz)
xlabel(x_str, 'FontSize', fsz)
grid on
box on
lwd = lwd+0.5;
%% FIGURES 4 and 5: PLOT EXPECTATIONS
% Import colors
load colors.mat
col{7} = [0,0.5,0];
title_str = 'INSTANT';
y_str = '\Delta_n';
time_plot = time_plot(1:100);
% ADD A FEATURE =======================================================
figure('Renderer', 'painters', 'Position', [0 100 450 900])
subplot(4,1,1)
formats = {fsz, lwd, col, 'Extra Feature', '\Delta^{+m}_n', ''};
expectation_plots(E_add(time_plot,:), time_plot, K-p, formats)
subplot(4,1,2)
formats = {fsz, lwd, col, '', '\Sigma \Delta^{+m}_n', ''};
expectation_plots(cumsum(E_add(time_plot,:)), time_plot, K-p, formats)
% REMOVING A FEATURE ==================================================
%col{7} = [0,0,0];
subplot(4,1,3)
formats = {fsz, lwd, col, 'Removed Feature', '\Delta^{-m}_n', ''};
expectation_plots(E_rmv(time_plot,:), time_plot, p, formats)
subplot(4,1,4)
formats = {fsz, lwd, col, '', '\Sigma \Delta^{-m}_n', x_str};
expectation_plots(cumsum(E_rmv(time_plot,:)), time_plot, p, formats)