45. e- E
KL
q
q 1
KL[q||p] =
Z X
Z
q(X, Z) ln
q(X, Z)
p(X, Z|✓)
dX
q(X, Z) =
NY
n=1
(X Xn)q(Z)
X
Z
q(Z) = 1
{Xn}N
n=1
EM
KL
45
46. e- E
KL
q
q 1
KL[q||p] =
Z X
Z
q(X, Z) ln
q(X, Z)
p(X, Z|✓)
dX
q(X, Z) =
NY
n=1
(X Xn)q(Z)
X
Z
q(Z) = 1
{Xn}N
n=1
EM
KL
X 1
46
47. e- E
KL[q||p] =
Z X
Z
q(X, Z) ln
q(X, Z)
p(X, Z|✓)
dX
=
X
Z
q(Z){ln q(Z) ln p({Xn}, Z|✓)}
Lagrangeq(Z)
q(Z) = e ( +1)
p({Xn}, Z|✓)
λ
47
=
Z X
Z
NY
n=1
(X Xn)q(Z) ln
P
Z
QN
n=1 (X Xn)q(Z)
p(X, Z|✓)
dX
48. e- E
1 =
X
Z
q(Z) = e ( +1)
X
Z
p(Z|{Xn}, ✓)p({Xn}|✓)
= e ( +1)
p({Xn}|✓)
q(Z) =
p({Xn}, Z|✓)
p({Xn}|✓)
= p(Z|{Xn}, ✓)
EM E
48
49. m- M
KL[q||p] =
X
Z
q(Z){ln q(Z) ln p({Xn}, Z|✓)} =
X
Z
q(Z) ln
q(Z)
p({Xn}, Z|✓)
KL p
L[q, ✓] =
Z
q(Z) ln
p(X, Z|✓)
q(Z)
EM
KL[q||p] = L[q, ✓]
(M ) KL
(m- )
49