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fun_statistical_tests_ultimate.m
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function fun_statistical_tests_ultimate(example, rs, N, calc_score_6)
if nargin < 3
N = 500;
end
if nargin < 4
calc_score_6 = 1;
end
N_rs = 1;
alpha6 = [];
% N = 1600;
switch example
case 0
z_marginal = 'uniform';
z_marginal = 'normal';
fileName = ['Gaussian_1D_',num2str(rs),'_out.txt'];
case 2
z_marginal = 'beta';
fileName = ['Skew_1D_',num2str(rs),'_out.txt'];
case 6
z_marginal = 'uniform';
fileName = ['Bimodal_',num2str(rs),'_out.txt'];
case 10
z_marginal = 'categorical2';
fileName = ['Cat2_',num2str(rs),'_out.txt'];
case 11
z_marginal = 'categorical';
fileName = ['Cat_',num2str(rs),'_out.txt'];
case 12
z_marginal = 'uniform';
fileName = ['Smooth1_',num2str(rs),'_out.txt'];
case 13
z_marginal = 'uniform';
fileName = ['Smooth2_',num2str(rs),'_out.txt'];
case 14
z_marginal = 'uniform';
fileName = ['Tent_',num2str(rs),'_out.txt'];
end
a = 2.5;
viz = false;
weight = 0;
fileID = fopen(fileName,'a');
zstar = [];
nums_to_do = [1,2,3,4,5,6,7];%,6];
nums_to_do = [6];
center_x = true;
hdists_rs = zeros(nums_to_do(end),N_rs);
score_rs = zeros(nums_to_do(end),N_rs);
score_loo_rs = zeros(nums_to_do(end),N_rs);
score_cv_rs = zeros(nums_to_do(end),N_rs);
alphas_rs = zeros(1,N_rs);
k7 = zeros(1,N_rs);
rs
%if strcmp(z_marginal,'categorical2')
% [x,z, xstar, fstar_true, z_type, range_star] = generate_data_1D(example, N, z_marginal, viz, zstar, rs, a);
% [x_cv,z_cv] = generate_data_1D(example, 200, z_marginal, viz, zstar, rs,a);
%else
[x,z, xstar, fstar_true, z_type, range_star] = generate_data_1D(example, N+200, z_marginal, viz, zstar, rs, a);
x_cv = x(N+1:end);
z_cv = z(N+1:end);
x = x(1:N);
z = z(1:N);
%end
G = @(x,h,m) 1./(sqrt(2*pi*h.^2)).*exp( -1/2*( x - m').^2./h./h);
L = size(z,1);
hz = cell(1,nums_to_do(end));
hx = cell(1,nums_to_do(end));
lklhdval = zeros(1,nums_to_do(end));
if sum(1 == nums_to_do)
% Proposal 1: benchmark: both rule-of-thumb
[hx{1},hz{1},output1, lklhdval(1), KCDE_fun{1}, KCDE_fun_loo{1}] = find_both_h2(x,z,z_type,'none','constant',center_x);
end
if sum(2 == nums_to_do)
% Proposal 2: rule-of-thumb hz, variable hx
[hx{2},hz{2},output2, lklhdval(2), KCDE_fun{2}, KCDE_fun_loo{2}] = find_both_h2(x,z,z_type,'none','variable',center_x);
end
if sum(3 == nums_to_do)
% Proposal 3: variable hx as a function of hz; hz constant chosen via LOO-CV
[hx{3},hz{3},output3, lklhdval(3), KCDE_fun{3}, KCDE_fun_loo{3}] = find_both_h2(x,z,z_type,'z','variable',center_x);
end
if sum(4 == nums_to_do)
% Proposal 4: Solve for hz and then hx4 separately
[hx{4},hz{4},output4, lklhdval(4), KCDE_fun{4}, KCDE_fun_loo{4}] = find_both_h2(x,z,z_type,'both','constant',center_x);
end
if sum(5 == nums_to_do)
% Proposal 6: Solve an optimization problem for two variables at once
[hx{5}, hz{5},output5, lklhdval(5), KCDE_fun{5}, KCDE_fun_loo{5}] = find_both_h2(x,z,z_type,'both','variable',center_x);
alphas_rs(rs) = output5(1);
if z_type == 'd'
a_params_rs(rs) = 1/2+1/2*cos(2*pi*output5(2)).^2 ;
end
end
if sum(7 == nums_to_do)
% Proposal 6: Solve an optimization problem for two variables at once
[hx{7}, hz{7},output7, lklhdval(7), KCDE_fun{7}, KCDE_fun_loo{7}] = find_both_h2(x,z,z_type,'both-oracle','oracle',center_x);
alphas_rs(rs) = output7(1);
if z_type == 'd'
a_params_rs(rs) = 1/2+1/2*cos(2*pi*output7(2)).^2 ;
end
k7(rs) = output7(end);
end
% score_true = sum( log(fstar_true(x,z)))/N;
% linestyles = {'--','-.',':'};
%%
for i = 1:size(hz,2)
if ismember(i,nums_to_do)
% fstar{i} = KCDE_fun{i}(xgrid, zstarl);
score(i) = 0;
score_loo(i) = 0;
score_cv(i) = 0;
if i ~= 6
score_cv(i) = sum( diag( log( KCDE_fun{i}(x_cv, z_cv) )))/size(z_cv,2);
if score_cv(i) == -Inf
score_cv
stop
end
% for j = 1:size(z_cv,2)
% score_cv(i) = score_cv(i) + log( KCDE_fun{i}(x_cv(j), z_cv(j)) );
%
% if score_cv(i) == -Inf
% stop
% end
%
% end
score_loo_temp = zeros(1,N);
for j = 1:N
%score(i) = score(i) + log( KCDE_fun{i}(x(j), z(j)));
score_loo_temp(j) = log( KCDE_fun_loo{i}(x(j), z(j), j));
%score_loo(i) = score_loo(i) + log( KCDE_fun_loo{i}(x(j), z(j), j));
%score_loo_temp
%stop
end
score_loo(i) = mean(score_loo_temp);
score(i) = sum(diag( log( KCDE_fun{i}(x, z))))/N;
else
score_loo_temp = zeros(1,N);
score_temp = zeros(1,N);
if calc_score_6
for j = 1:N
fileID = fopen(fileName,'a');
fprintf(fileID,['Approach 6 Run ',num2str(rs), ', in-sample: ',num2str(j/N),'\n']);
[~, ~,~, ~, KCDE_fun6, KCDE_fun_loo6] = find_both_h2_ultimate(x,z,z_type,'both','variable',center_x, z(j),weight);
% score(i) = score(i) + log( KCDE_fun6(x(j), z(j)));
% score_loo(i) = score_loo(i) + log( KCDE_fun_loo6(x(j), z(j), j));
score_temp(j) = log( KCDE_fun6(x(j), z(j)));
score_loo_temp(j) = log( KCDE_fun_loo6(x(j), z(j), j));
end
score_loo(i) = mean(score_loo_temp);
score(i) = mean(score_temp);
end
score_cv_temp = zeros(1,size(z_cv,2));
for j = 1:size(z_cv,2)
fileID = fopen(fileName,'a');
fprintf(fileID,['Approach 6 Run ',num2str(rs), ', out-of-sample: ',num2str(j/size(z_cv,2)),'\n']);
[~, ~,~, ~, KCDE_fun6, KCDE_fun_loo6] = find_both_h2_ultimate(x,z,z_type,'both','variable',center_x, z_cv(j),weight);
score_cv_temp(j) = log( KCDE_fun6(x_cv(j), z_cv(j)));
end
%else
% score_cv_temp = [0,0];
% score_loo(i) = 0; score(i) = 0;
%end
score_cv(i) = mean(score_cv_temp);
end
% score(i) = score(i)/N;
% score_loo(i) = score_loo(i)/N;
% score_cv(i) = score_cv(i)/size(z_cv,2);
% plot(xgrid,fstar{i},linestyles{mod(i,3)+1},'linewidth',2), hold on,
end
end
%%
zgrid = sort(z);
switch z_type
case 'c'
zgrid = linspace(0,1,50);
case 'd'
zgrid = unique(z);
end
Hdist = zeros( size(hz,2), length(zgrid));
% ISEdist = zeros( size(hz,2), length(zgrid));
for i = 1:size(hz,2)
if ismember(i,nums_to_do)
for j = 1:length(zgrid)
if i == 6
fprintf(fileID,['Approach 6 Run ',num2str(rs), ', calculate H^2: ',num2str(j/length(zgrid)),'\n']);
[~, ~, output6, ~, KCDE_fun6, KCDE_fun_loo6] = find_both_h2_ultimate(x,z,z_type,'both','variable',center_x, zgrid(j),weight);
hz6(j) = abs(output6(2));
alpha6(j) = abs(output6(1));
f_est = @(xi) KCDE_fun6(xi, zgrid(j));
else
f_est = @(xi) KCDE_fun{i}(xi, zgrid(j));
end
f_true = @(xi) fstar_true(xi,zgrid(j));
Hdist(i, j) = pqdistances(f_est, f_true, 1,'Hellinger', range_star(zgrid(j)));
ISEdist(i, j) = pqdistances(f_est, f_true, 1,'ISE', range_star(zgrid(j)));
TVdist(i,j) = pqdistances(f_est, f_true, 1, 'TV', range_star(zgrid(j)));
% Hdist(i, j) = sqrt(Hdist(i, j) );
end
end
end
%%
% figure;
% for i = 1:size(hz,2)
% if size(hz{i},1)>0
%
% plot( zgrid, Hdist(i,:),'linewidth',2), hold on
% end
% end
% legs{1} = ['rule-of-thumb hz & hx (',num2str(mean(Hdist(1,:)),'%.2f'),')'];
% legs{2} = ['rule-of-thumb hz, variable hx (',num2str(mean(Hdist(2,:)),'%.2f'),')'];
% legs{3} = ['ML constant hz, variable hx (',num2str(mean(Hdist(3,:)),'%.2f'),')'];
% legs{4} = ['ML constant hz, constant hx, both optimized (',num2str(mean(Hdist(4,:)),'%.2f'),')'];
% legs{5} = ['ML constant hz, variable hx (\alpha), both optimized (',num2str(mean(Hdist(5,:)),'%.2f'),')'];
% legs_used = cell(1,length(nums_to_do));
% counter = 1;
% for i = 1:5
% if sum(i == nums_to_do)
% legs_used{counter} = legs{i};
% counter = counter + 1;
% end
% end
% leg = legend(legs_used);
%
% set(leg,'location','southoutside','fontsize',14)
% xlabel('$z$','interpreter','latex')
% title('squared Hellinger distance vs $z$','interpreter','latex')
% set(gca,'fontsize',16)
%%
% if strcmp(z_marginal, 'categorical')
%
%
%
% hx_vals = zeros( size(hz,2), length(zgrid));
%
% for i = 1:size(hz,2)
% if size(hz{i},1)>0
% for j = 1:length(zgrid)
% hx_vals(i,j) = hx{i}(zgrid(j));
% end
%
% end
% end
%
%
%
% end
% figure;
% for i = 1:size(hz,2)
% if size(hz{i},1)>0
%
% plot( zgrid, hx_vals(i,:),'linewidth',2), hold on
% end
% end
% legs{1} = ['rule-of-thumb hz & hx (',num2str(mean(hx_vals(1,:)),'%.2f'),')'];
% legs{2} = ['rule-of-thumb hz, variable hx (',num2str(mean(hx_vals(2,:)),'%.2f'),')'];
% legs{3} = ['ML constant hz, variable hx (',num2str(mean(hx_vals(3,:)),'%.2f'),')'];
% legs{4} = ['ML constant hz, constant hx, both optimized (',num2str(mean(hx_vals(4,:)),'%.2f'),')'];
% legs{5} = ['ML constant hz, variable hx (\alpha), both optimized (',num2str(mean(hx_vals(5,:)),'%.2f'),')'];
%
% legs_used = cell(1,length(nums_to_do));
% counter = 1;
% for i = 1:5
% if sum(i == nums_to_do)
% legs_used{counter} = legs{i};
% counter = counter + 1;
% end
% end
% leg = legend(legs_used);
%
% set(leg,'location','southoutside','fontsize',14)
% xlabel('$z$','interpreter','latex')
% title('$hx(z)$ vs $z$','interpreter','latex')
% set(gca,'fontsize',16)
hdists_sq_rs(:,rs) = mean(sqrt(Hdist'));
ise_rs(:,rs) = mean(ISEdist');
ise_sq_rs = mean(sqrt(ISEdist'));
hdists_rs(:,rs) = mean(Hdist');
TVdists_rs(:,rs) = mean(TVdist');
score_rs(:,rs) = score;
score_loo_rs(:,rs) = score_loo;
score_cv_rs(:,rs) = score_cv;
fclose(fileID);
cd results
save([fileName(1:end-4),'_',num2str(N),'_6.mat'],'hdists_sq_rs','ise_rs','ise_sq_rs','hdists_rs','TVdists_rs','score_rs','score_loo_rs','score_cv_rs','alpha6','k7','alphas_rs')
if z_type == 'd'
%a_params_rs
save([fileName(1:end-4),'.mat'],'hdists_sq_rs','ise_rs','ise_sq_rs','hdists_rs','score_rs','score_loo_rs','TVdists_rs','score_cv_rs','alpha6','alphas_rs','k7','a_params_rs')
end