of 5
8/3/2019 Mlpr Exam at Home 2011
1/5
(X 1 , Y 1), (X 2 , Y 2) . . . (X P , Y P ), P [1, 1000] X i
Y i
500
H k = log(1 + exp( Ak )) H k k Ak
LA k
= something goes here L
H k
W X W X
Q
Qy P (Y |X ) Q = softmax( A) A Ak = W k X, k = 1 ..4 W k y
Qy =exp( Ay )
4k =1 exp( Ak )
LA i =
something goes here L
Q j
(X i , Y i ) L log = log QY i QY i W X i
L(W,X i , Y i ) = logexp( W Y i X i
4k =1 exp( W k X i )
W k k = Y i k = Y i
8/3/2019 Mlpr Exam at Home 2011
2/5
L1 pq |W pq |
L1
L1
K (K 1)/ 2 K
C
minW,b,
|| W || 2 + C n
i =1i , subject to Y i (W X i + b) 1 i i, and i 0
C K (X, X i ) = exp( s || X X i || 2)
s s
1000 50 X X i i
3 50 P Y i = P X i
8/3/2019 Mlpr Exam at Home 2011
3/5
X i
(X ) K
K (X, Z ) = ( X ) (Z )
|| P hi (X ) P hi (Z )||
Y f y (X ) f y (X ) P (X |Y ) Y
P (Y |X ) Y X P (Y |X ) f y (X )
P (X ) = y P (X, Y )
P (Y |X ) f y (X ) f y (X ) =
1Z y i s. t .Y i = Y R(X, X
i ) R(X, X i ) X Z y P (X |Y )
X Y
P (Y |X )
8/3/2019 Mlpr Exam at Home 2011
4/5
AX
A
X i C i X i
L(A) =i j C i
exp( || AX i AX j || 2
k = i exp( || AX i AX k || 2 )
X i
L (A )A
A
D ij i j
i j i C i
i { j C i } D ij
X i i D ij
X i { j C i }
Y = W X + b W X b
L(W ) = 1P pi =1
12 || Y
i (W X i + b)|| 2
(X, Y ) ([ 2 1], 1), ([+2 + 1] , +1) W (k+1) = W (k) L (W (k ))W
W 1 W 2 W
8/3/2019 Mlpr Exam at Home 2011
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W 1 W 2
W 1 eta W 2
W 1 W 2 (X, Y ) ([0 2], 1)
([0 0], 1) ([2 0], 1) ([2 2], 1) L(W ) = 12 W HW +
G W + C H H
H