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1.
2.
3.
4.
2
(a) 0 2 2 0 2
5.
2
(b) 0 2 2 0 2
6.
2
(b) 0 2 2 0 2
7.
2
(c) (b) 0 2 2 0 2
8.
2
(c) (d) (b) 0 2 2 0 2
9.
2
(c) (e) (d) (b) 0 2 2 0 2
10.
2
(f) (c) (e) (d) (b) 0 2 2 0 2
11.
2
(g) (f) (c) (e) (d) (b) 0 2 2 0 2
12.
2
(h) (g) (f) (c) (e) (d) (b) 0 2 2 0 2
13.
2
(i) (h) (g) (f) (c) (e) (d) (b) 0 2 2 0 2
14.
1000 J 500
0 1 2 3 4
15.
16.
17.
18.
19.
20.
21.
22.
…
…
23.
24.
25.
26.
2 0 2
2 0 (a) 2
27.
2 0 2
2 0 (b) (a) 2
28.
2
L=1 0 2 2 0 (b) (a) (c) 2
29.
2
1 L=2 0 2 2 0 (d) (b) (a) (c) 2
30.
2
1 L=2 5 0 2 2 0 (e) (d) (b) (a) (c) 2
31.
2
1 L = 20 5 2 0 2 2 0 (e) (d) (b) (a) (c) (f) 2
32.
33.
ln p(X|θ) =
ln p(X, Z|θ) z
34.
35.
Q(θ, θold )
= p(Z|X, θold )p(X, Z|θ) Z θnew = argmaxθ Q(θ, θold )
36.
Q(θ, θold )
znk p(X, Z|µ, Σ, π) = πk N (xn |µk , Σk )znk i k ln p(X, Z|µ, Σ, π) = znk {ln πk + ln N (xn |µk , Σk )} i,k Z =
37.
p(zk = 1)p(x|zk
= 1) γ(zk ) ≡ p(zk = 1|x) = K j=1 p(zj = 1)p(x|zj = 1) πk N (x|µk , Σk ) = K j πj N (x|µj , Σj ) N N 1 µk = γ(zik )xi Nk = γ(zik ) Nk i=1 i=1 N 1 Σk = γ(zik )(xi − µk )(xi − µk )T Nk i=1
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