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This commit is contained in:
Michael Zhang 2023-11-12 11:42:19 -06:00
parent 9eee507d73
commit 9da52cfbfa
5 changed files with 143 additions and 136 deletions
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2
assignments/hwk03/EMG.m
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@ -24,6 +24,7 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: Initialise cluster means using k-means % TODO: Initialise cluster means using k-means
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
means = kmeans(x, k);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: Determine the b values for all data points % TODO: Determine the b values for all data points
@ -59,6 +60,7 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: Store the value of the complete log-likelihood function % TODO: Store the value of the complete log-likelihood function
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
end end

1
assignments/hwk03/E_step.m
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@ -17,5 +17,6 @@ function [Q, h] = E_step(x, Q, h, pi, m, S, k)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: perform E-step of EM algorithm % TODO: perform E-step of EM algorithm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
z = 1 + 1
end end

6
assignments/hwk03/hw3_sol.typ
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@ -47,7 +47,7 @@ Updates:
= Problem 1b = Problem 1b
- $E(ww,vv|XX) = - sum_t r^t log y^t + (1 - r^t) log (1 - y^t)$ - $E(ww,vv|XX) = - sum_t r^t log y^t + (1 - r^t) log (1 - y^t)$
- $y^t = "sigmoid"(v_2 z_2 + v_1 z_1 + v_0)$ - $y^t = "sigmoid"(v_2 z^t_2 + v_1 z^t_1 + v_0)$
- $z^t_1 = "ReLU"(w_2 x^t_2 + w_1 x^t_1 + w_0)$ - $z^t_1 = "ReLU"(w_2 x^t_2 + w_1 x^t_1 + w_0)$
- $z^t_2 = tanh(w_2 x^t_2 + w_1 x^t_1 + w_0)$ - $z^t_2 = tanh(w_2 x^t_2 + w_1 x^t_1 + w_0)$
@ -62,4 +62,8 @@ Updates:
&= - sum_t frac(diff E, diff y^t) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \ &= - sum_t frac(diff E, diff y^t) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \
&= - sum_t (frac(r^t, y^t) - frac(1-r^t, 1-y^t)) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \ &= - sum_t (frac(r^t, y^t) - frac(1-r^t, 1-y^t)) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \
&= - sum_t (frac(r^t-y^t, y^t (1-y^t))) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \ &= - sum_t (frac(r^t-y^t, y^t (1-y^t))) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \
&= - sum_t (frac(r^t-y^t, y^t (1-y^t))) (y^t (1-y^t) v_1 frac(diff z^t_1, diff w_j) + y^t (1-y^t) v_2 frac(diff z^t_2, diff w_j)) \
&= - sum_t (r^t-y^t) (v_1 frac(diff z^t_1, diff w_j) + v_2 frac(diff z^t_2, diff w_j)) \
&= - 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))) \
$ $