4_05_maximum-entropy_markov_model

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1、NeuralnetworksTrainingCRFs-maximum-entropyMarkovmodel•(y,X)=(y)=expbHugoLarochelleK(L+1)Khugo.larochelle@usherbrooke.caf•f(•y,Xff)=(•y,kXff)=(•(yy,kX)=expff)=((yy,kcX)=expf)=(yb⇣ck)=expfk(=1yb⇣kc)=exp1ykk=1=b⇣cc1ykk=1=b⇣cc1ykkUniversit=1=c⇣1ykk=1=ced

2、eSherbrooke´1⌘yk=c⌘⌘2⌘HugoLarochelleD(Lepartementd’informatique´+1,+1)(L+1P,+1)K(L+11P,K+1)1PK(L+11P,+1)PK1•(•y,X)=(•y,X)=((yy,,xX)=(•y,x)=exp((yy,,xX)=exp)=⇣W)=exp⇣(yW,x⇣W)=exp⇣hugo.larochelle@usherbrooke.cax(L⇣+1Wx,1+1)⌘x1K1⌘1September26,2012⌘x

3、⌘ffff•kDfkepartementd’informatique(´+1yk,,iXff)=k+1k,ifk(+1yk,i,xc,i(fUniversitLk+1+1k,,ic,i()=expL1)k+1+1PedeSherbrooke´,,iKk(c,i1)=1L+1PW,Kkk(c,i1)=1L+1+1P,i,Kk(kyc,i1)L+1=1k+1=P,ic,Kkky1)+1=1k=P,icxkky+1=1k=,ic1ky+1k=,ic•(•y,X)=(•y,LINEARCHAINCRF

4、X)=(•(yy,X,x)=(•(yy,X,x)=exp)=((yy,X,x)=exp)=(yW,x)=exp(yW,x)=expW)=expWxWx1x1x1Kx11ffffkffkUniversitk1,iffkkedeSherbrooke´1,if⇣kk1hugo.larochelle@usherbrooke.ca,ifc,ik⇣Pk1,ic,ik⇣1,ikc,i=2⇣kkc,i=2⇣1,iSeptember26,2012kkc,iy⌘=2k1=,ickky⌘=2k1=,i

5、ckky⌘=2k1=,icky⌘k1=,icyhugo.larochelle@usherbrooke.caK1PK1PK1PK1PK1•f(•y,Xf)=(•y,Xff)=((•yyk,,yXf)=k(•+1yk,)=exp,yXffk)=((+1yyk,)=exp,yX⇣f)=k(V+1yc,ck)=exp,y⇣0fk(V+1ySeptember26,2012c,ckk)=expP,y=1⇣0kV+11c,cyP)=expk⇣0=cV11c,cyyk⇣k=0+1c=V1⌘cc,c

6、yP0k+1=0c=1⌘1cyyk0k=1=+1c=⌘11cyy0k=c=⌘1cy0k+1Abstract=⌘cTopics:Markovnetwork(L+1,0)(L+1K,0)(kL=1+1K,0)(LkP+1=1K,0)(Lk+1=1K,0)PkKk+1•f(•y,Xf)=(•y,Xff)=(•(yy,kX,xff)=(•k,i(yy,kSeptember26,2012)=expX,xff)=(k,i(yy,k)=expX,xf)=k,i(Wyk)=expc,i,xfk,iW(ykc,i

7、)=exp=observed,xk,iWkMathformyslides“TrainingCRFs”.=1)=expc,ixWk,ik=1c,i1yxkWk,i=k=1cc,i1yxkk,i=k=1cAbstract1yxkk,i=k=1c1yxkk,i=c1yk=c•Illustrationfor•f(•yKk,y=5fk(+2y•k),yfk(+2y•fk(),yykfk,y(+2yf•kk(+1)y,ykf,y,yk(+2yfkkMathformyslides“TrainingCRF

8、s”.k(+2+1)y,yk),yk,y+2⇣fkk(+2+1)yk),y,y⇣fkk(+2+1yk),y,y⇣kPk+2+1),y⇣(LPk+1+2,0))⇣PP⌘(L+1⌘,1)⌘⌘(L+1•,+1)a(uL(y+1kAbstract)=,+1)K(La+11,+1)K(L(x+11k),y+1)Kk(+1L+11k>,+1)K1a1PK(1xk1)yk+1••xf(••xy,xXxf)=(•yx•,xx