102009129*

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() () 4 C. D. Manning & Hinrich Schtze FOUNDATIONS OF STATISTICAL NATURAL LANGUAGE PROCESSING MIT Press, 1999Christopher M. Bishop PATTERN RECOGNITION AND MACHINE LEARNING Springer, 2006*

EM() 1/3: : x: y: X={x1, x2, , xn}: log p(X)*

EM() 2/3: : x: y: X={x1, x2, , xn}: log p(X)*!

EM() 3/3E

M*Lp(X) L KLQ

POS TAGGING(SEQUENTIAL LABELING) ( )*

*I have a pen.Ihaveapen.Ihaveapen.POS

(1/3)*IheMary (transition) (emission)Ihaveapen.

(2/3)*IheMary (transition) (emission)Ihaveapen.0.50.10.30.430.010.30.250.010.30.01

(3/3)Q: : q0: a(i, j): ijjQ a(i, j)=1a(q0, i): ib(i, o): ioo b(i,o) = 1*

*()()O(|Q|n )()

: (1/4)*1o1o2ono3234(t, q): t(ot)q

maxq Q (n, q)123n

: (2/4)*o1o2onot-1 qot12

: (3/4)*o1o2onon-2 3on-212 4

: (4/4)[1,q] := a(q0, q) (for all q)for t =2 to n for q Q [t, q] := maxqQ {[t-1, q]a(q,q)b(q, ot)} bp[t,q] := argmaxqQ {[t-1, q]a(q,q)b(q, ot)}*

*

(1/3)*1o1o2ono3234(t, q): o1 otot(t)q

q Q (n, q)123n

(2/3)*o1o2onot-1 qot12

[1,q] := a(q0, q) (for all q)for t =2 to n for q Q [t, q] := qQ {[t-1, q]a(q,q)b(q, ot)}* (3/3)

(1/2)(t, q) :tqot+1on

*

(2/2)[n,q] := 1 (for all q)for t := n-1 to 1 for q Q [t, q] := qQ {a(q, q)b(q, ot+1)[t+1, q]}*

EM*

q, r, s3 () o1o2o3*qr: 0.02+0.02+0.001+0.03+0.085+0.07=0.226

qqqqqrqqsqrqqrrqrsqsqqsrqss0.030.020.0080.020.0010.030.020.080.07

rqqrqrrqsrrqrrrrrsrsqrsrrss0.0820.0850.0240.0110.0090.0980.0530.0550.001

sqqsqrsqssrqsrrsrsssqssrsss0.0030.070.0080.0020.020.0050.0030.0180.008

(1/2)a,b()()

(t,q,r): o1ontqra,b*

(2/2)(t,q,r): o1ontqr*o1o2onot qot+1 r

INSIDE OUTSIDE ALGORITHM*

PCFGEM(0) := [E] (i)s

[M] (i+1)

2. *

PCFGEM[E]s(i)sp(t|s)[M] s1s2s3...parseparseparse......p(t|s1)=p(t)/Z1 = 0.1 0.3 0.6p(t|s2)=p(t)/Z 2= 1.0p(t|s3)=p(t)/Z3 = 0.21 0.16 0.51 0.05 0.07C(r;t) = 0.6C(r; t)*

PCFGEM()sparsep(t)/Z = 0.21 0.06 0.001 0.05 0.07...*

EMCKYCKY*

(i,j,A)Awi+1,...,wj(=wi+1,...,wj()A)w1,...,wiwj+1,...,wnwi+1, ..................,wjA*

Si,jmaxsumSi,j: (X: , p: )Si,jfor k = i+1 to j-1 forall Si,k forall Sk,j forall A G(B, C) if( exists in Si,j ) p := p + pXpYZX Y else Si,j := Si,j

summax*

(i,j,B)S()w1...wiBwj+1...wnw1,...,wiwj+1,...,wnwi+1, ..................,wjBS*

2AC(i,j,B)AB C: ACAB CAC B :ACAC Bw1..wiwk+1..wnwi+1 ..wjBSCAwj+1 ..wkw1..wkwj+1..wnwi+1 ..wjBSCAwk+1 ..wi

(i,j,B)*

(i,j,X)S0,1S1,2S2,3S3,4S0,2S1,3S2,4S0,3S1,4S0,4S4,5S5,6S3,5S4,6S2,5S3,6S1,5S2,6S0,5S1,6S0,6w1w2w3w4w5w60123456*

for all 0 i < j n, XVN (i,j,X) := 0(0,n,S) := 1.0for l = n 1 to 1 for i = 0 to n l j := i + l forall Ai,j Bi,k Ck,j in Si,j (i, k, B):=(i, k, B)+(i,j,A)(k,j,C)A B C (k, j, C):=(k, j, C)+(i,j,A)(i,k,B)AB CAi,j Bi,k Ck,j in Si,jSi,jAAB CBSi,kCSk,j*

Ai,jBi,k Ck,j= Ai,jBi,k Ck,j sparsep(t)/Z = 0.21 0.16 0.07...Ai,jBi,kCk,jAi,jBi,kCk,jAi,jBi,kCk,j*

Ai,jBi,k Ck,j =1/Z(Ai,jBi,k Ck,j ) =1/Z(Bi,kCk,jAB CAi,j)w1..wiwj+1..wnwi+1 ..wkBSCAwk+1 ..wj*

*

(0) := [E] (i)[M] (i+1)

2. *

() () ()12/16() 16:30 HPSG (HPSG)http://www.r.dl.itc.u-tokyo.ac.jp/~ninomi/mistH21w/cl/

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