working kinda?

This commit is contained in:
Michael Zhang 2023-11-16 20:23:38 -06:00
parent bc30320eef
commit 97dc43c792
6 changed files with 54 additions and 21 deletions

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assignments/hwk03/2a.png Normal file

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@ -65,13 +65,8 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: Store the value of the complete log-likelihood function
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
L = 0;
% for i = 1:num_data
% for j = 1:k
% prior = mvnpdf(x, m(j, :), S(:, :, j));
% L = L + h(i, j) * (log(pi(i)) + log(prior(i)));
% end
% end
Q(2*n - 1) = Q_step(x, m, S, k, pi, h);
%%%%%%%%%%%%%%%%
% M-step
@ -82,6 +77,7 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: Store the value of the complete log-likelihood function
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q(2*n) = Q_step(x, m, S, k, pi, h);
end

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@ -20,18 +20,25 @@ function [S, m, pi] = M_step(x, h, S, k, flag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% update mixing coefficients
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pi = zeros(k, 1);
N_i = zeros(k, 1);
m = zeros(k, dim);
for i = 1:k
N_i(i) = sum(h(:, i));
for j = 1:num_data
m(i, :) = m(i, :) + h(j, i) * x(j, :);
end
end
pi = N_i / num_data;
for i = 1:k
m(i, :) = m(i, :) ./ N_i(i);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% update cluster means
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = zeros(k, dim);
m = h' * x ./ N_i;
% m = zeros(k, dim);
% m = h' * x ./ N_i;
% for i = 1:k
% m(i, :) = sum(h(:, i) .* x(i, :)) / N_i(i);
% end
@ -40,19 +47,24 @@ function [S, m, pi] = M_step(x, h, S, k, flag)
% Calculate the covariance matrix estimate
% further modifications will need to be made when doing 2(d)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
S = zeros(dim, dim, k);
S = zeros(dim, dim, k) + eps;
for i = 1:k
% for j = 1:num_data
% S(:, :, i) = S(:, :, i) + h(j, i) * (x(j, :) - m(i, :)) * (x(j, :) - m(i, :))';
% end
s = (x - m(i, :))' * ((x - m(i, :)) .* h(:, i)) / N_i(i);
s = zeros(dim, dim);
for j = 1:num_data
s = s + h(j, i) * (x(j, :) - m(i, :))' * (x(j, :) - m(i, :));
end
s = s / N_i(i);
% s = (x - m(i, :))' * ((x - m(i, :)) .* h(:, i)) / N_i(i);
% % MAKE IT SYMMETRIC https://stackoverflow.com/a/38730499
% S(:, :, i) = (s + s') / 2;
% https://www.mathworks.com/matlabcentral/answers/366140-eig-gives-a-negative-eigenvalue-for-a-positive-semi-definite-matrix#answer_290270
s = (s + s') / 2;
% https://www.mathworks.com/matlabcentral/answers/57411-matlab-sometimes-produce-a-covariance-matrix-error-with-non-postive-semidefinite#answer_69524
[V, D] = eig(s);
S(:, :, i) = V * max(D,eps) / V;
s = V * max(D, eps) / V;
S(:, :, i) = s;
end
end

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@ -45,6 +45,7 @@ function [] = Problem2()
c = repmat([1 0 0; 0 1 0], length(x)/2, 1);
scatter(x,Q,20,c);
index = index + 1;
pause;
end
shg
@ -69,6 +70,7 @@ function [] = Problem2()
% TODO: plot goldy image after using clusters from k-means
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% begin code here
[~, ~, ~, D] = kmeans(goldy_x, k);
% end code here
shg

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@ -0,0 +1,11 @@
function [LL] = Q_step(x, m, S, k, pi, h)
[num_data, ~] = size(x);
LL = 0;
for i = 1:k
N = mvnpdf(x, m(i, :), S(:, :, i));
for j = 1:num_data
LL = LL + h(j, i) * (log(pi(i) + eps) + log(N(j) + eps));
end
end
end

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@ -67,3 +67,15 @@ Updates:
&= - sum_t (r^t-y^t) (x^t_j v_1 cases(0 "if" ww dot xx < 0, 1 "otherwise") + x^t_j v_2 (1 - tanh^2 (ww dot xx))) \
&= - sum_t (r^t-y^t) x^t_j (v_1 cases(0 "if" ww dot xx < 0, 1 "otherwise") + v_2 (1 - tanh^2 (ww dot xx))) \
$
#pagebreak()
= Problem 2a + 2b
#image("2a.png")
= Problem 2c
= Problem 2d
MLE of $Sigma_i$