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

5/5

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