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star.m
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close all;
clear all;
setSeed(0);
rng(0, 'twister');
%method='cvi_hess'
%method='iBayesLRule_hess'
method='iBayesLRule_first_order'
%method='bbvi_first_order'
d=2;
init_P = eye(d); %initial precision should be small to avoid stuck in one mode
init_m = zeros(d,1);
p_nrComponents = 5;
p_mixMeans = cell(p_nrComponents,1);
p_mixPrecs = cell(p_nrComponents,1);
p_logMixWeights = ones(1,p_nrComponents)*(-log(p_nrComponents));
offset = 10;
max_mean = -2*offset;
min_mean = 2*offset;
assert(d==2)
theta = 2*pi/p_nrComponents;
U =[ cos(theta), sin(theta);
-sin(theta), cos(theta) ];
for c=1:p_nrComponents
if c==1
p_mixMeans{c} =[1.5;0.0];
p_mixPrecs{c} = diag([1,100]);
else
p_mixMeans{c} =U*p_mixMeans{c-1};
p_mixPrecs{c} =U*p_mixPrecs{c-1}*U';
end
max_mean = max(p_mixMeans{c}, max_mean);
min_mean = min(p_mixMeans{c}, min_mean);
end
true_dist.mixWeights = exp(p_logMixWeights);
true_dist.mixMeans = p_mixMeans;
true_dist.mixPrecs = p_mixPrecs;
if d==2
Range = 4;
Step=0.05;
max_x = max_mean(1) + Range;
min_x = min_mean(1) - Range;
max_y = max_mean(2) + Range;
min_y = min_mean(2) - Range;
axis_x= [min_x, max_x];
axis_y= [min_y, max_y];
[w1,w2]=meshgrid(min_x:Step:max_x,min_y:Step:max_y);
[n1,n2]=size(w1);
W=[reshape(w1,n1*n2,1) reshape(w2,n1*n2,1)];
W_tr = W';
[~,~,logMarPrb] = Get_Conditional_Log_Prbs(W_tr,p_logMixWeights,p_mixMeans,p_mixPrecs);
post = exp(logMarPrb)';
callback= @(iter,post_dist)plotFun2(iter,true_dist,post_dist,w1,w2,W_tr,n1,n2,post,axis_x,axis_y);
else
callback= @(iter,post_dist)plotFun(iter,true_dist,post_dist);
end
likelihood =@(xSampled,iter)Log_Mix_Gauss(xSampled,p_logMixWeights,p_mixMeans,p_mixPrecs);
q_nrComponents=10;
nrSteps = 1e4;
preIt=floor(nrSteps/50); %plot every preIt iterations
stepSize = 0.01;%bbvi
decay_mix = 0.05;%update for mixing weight
nrSamples = 50; %MC samples
dataset_name = sprintf('toy-%d',d);
disp('running')
switch method
case {'cvi_hess'}
option='hess'
[q_mixWeights,q_mixMeans,q_mixPrecs] = mix_gauss_cvi_new(option,likelihood,q_nrComponents,nrSteps,init_m,init_P,preIt, nrSamples, stepSize, decay_mix, dataset_name,callback);
case {'bbvi_hess'}
option='hess'
[q_mixWeights,q_mixMeans,q_mixPrecs] = mix_gauss_bbvi(option,likelihood,q_nrComponents,nrSteps,init_m,init_P,preIt, nrSamples, stepSize, decay_mix, dataset_name,callback);
case {'bbvi_first_order'}
option='first'
[q_mixWeights,q_mixMeans,q_mixPrecs] = mix_gauss_bbvi(option,likelihood,q_nrComponents,nrSteps,init_m,init_P,preIt, nrSamples, stepSize, decay_mix, dataset_name,callback);
case {'iBayesLRule_hess'}
option='hess'
[q_mixWeights,q_mixMeans,q_mixPrecs] = mix_gauss_iBayesLRule(option,likelihood,q_nrComponents,nrSteps,init_m,init_P,preIt, nrSamples, stepSize, decay_mix, dataset_name,callback);
case {'iBayesLRule_first_order'}
option='first'
[q_mixWeights,q_mixMeans,q_mixPrecs] = mix_gauss_iBayesLRule(option,likelihood,q_nrComponents,nrSteps,init_m,init_P,preIt, nrSamples, stepSize, decay_mix, dataset_name,callback);
otherwise
error('no such method')
end
method_name = sprintf('%s_star_GMM%d',method, q_nrComponents);
ww = 15;
hh = 12;
set(gcf, 'PaperPosition', [0 0 ww hh]); %Position plot at left hand corner with width 5 and height 5.
set(gcf, 'PaperSize', [ww hh]); %Set the paper to have width 5 and height 5.
export_fig(method_name, '-pdf')
%saveas(gca, method_name, 'pdf')
function dummy=plotFun(iter,true_dist,post_dist)
figure(1);
nrComponents = size(post_dist.mixMeans,1);
d =length(post_dist.mixMeans{1});
[true_uni_mean_info, true_uni_prec_info, true_uni_max_x, true_uni_min_x] = get_uni_infos(true_dist.mixWeights,true_dist.mixMeans,true_dist.mixPrecs);
[uni_mean_info, uni_prec_info, uni_max_x, uni_min_x] = get_uni_infos(post_dist.mixWeights,post_dist.mixMeans,post_dist.mixPrecs);
for k=1:d
xSamples = linspace(true_uni_min_x{k}, true_uni_max_x{k}, 10000);
[~, ~, uni_logMarPrb] = Get_Conditional_Log_Prbs(xSamples, log(post_dist.mixWeights), uni_mean_info{k}, uni_prec_info{k});
figure(k);
plot(xSamples, exp(uni_logMarPrb), 'color', 'r');
hold on;
[~, ~, true_uni_logMarPrb] = Get_Conditional_Log_Prbs(xSamples, log(true_dist.mixWeights), true_uni_mean_info{k}, true_uni_prec_info{k});
plot(xSamples, exp(true_uni_logMarPrb), 'color', 'b');
legend({'approx', 'true'})
title(sprintf('Dim %d',k))
hold off;
end
drawnow
dummy = 0;
end
function dummy=plotFun2(iter,true_dist,post_dist,w1,w2,W_tr,n1,n2,post,axis_x,axis_y)
figure(1);
nrComponents = size(post_dist.mixMeans,1);
subplot(3,2,1)
% exact post
contourf(w1,w2,reshape(post,[n1,n2]),10); colorbar;
title('exact')
%figure(2);
subplot(3,2,2)
[~,~,logMarPrb] = Get_Conditional_Log_Prbs(W_tr,log(post_dist.mixWeights),post_dist.mixMeans,post_dist.mixPrecs);
post = exp(logMarPrb)';
Z = reshape(post,[n1,n2]);
contour(w1,w2,Z,10); colorbar;
hold on
grid on
axis([axis_x(1) axis_x(2) axis_y(1) axis_y(2)]);
hold off;
title('approx')
subplot(3,2,3)
contourf(w1,w2,reshape(post,[n1,n2]),10); colorbar;
lwt = cell(nrComponents+1,1);
lwt{1} = sprintf('iter-%d',iter);
ii = (1:nrComponents)';
colors=num2cell(jet(length(ii)));
for c=1:nrComponents
hold on
h2 = plot_gaussian_ellipsoid(post_dist.mixMeans{c}, inv( post_dist.mixPrecs{c}));
set(h2, 'color', [colors{nrComponents-c+1,:}], 'linewidth', 3);
lwt{c+1} = sprintf('%.5f',post_dist.mixWeights(c));
end
%legend(lwt)
grid on
axis([axis_x(1) axis_x(2) axis_y(1) axis_y(2)]);
hold off;
tl = sprintf('fitted using %d components', nrComponents);
title(tl)
subplot(3,2,4)
pie(post_dist.mixWeights)
title('mixing weights')
d =length(post_dist.mixMeans{1});
[true_uni_mean_info, true_uni_prec_info, true_uni_max_x, true_uni_min_x] = get_uni_infos(true_dist.mixWeights,true_dist.mixMeans,true_dist.mixPrecs);
[uni_mean_info, uni_prec_info, uni_max_x, uni_min_x] = get_uni_infos(post_dist.mixWeights,post_dist.mixMeans,post_dist.mixPrecs);
for k=1:d
xSamples = linspace(true_uni_min_x{k}, true_uni_max_x{k}, 10000);
[~, ~, uni_logMarPrb] = Get_Conditional_Log_Prbs(xSamples, log(post_dist.mixWeights), uni_mean_info{k}, uni_prec_info{k});
%figure(2+k);
subplot(3,2,4+k)
plot(xSamples, exp(uni_logMarPrb), 'color', 'r');
hold on;
[~, ~, true_uni_logMarPrb] = Get_Conditional_Log_Prbs(xSamples, log(true_dist.mixWeights), true_uni_mean_info{k}, true_uni_prec_info{k});
plot(xSamples, exp(true_uni_logMarPrb), 'color', 'b');
legend({'approx', 'true'})
title(sprintf('Dim %d',k))
hold off;
end
drawnow
dummy = 0;
end