Fast Support Vector Machines for Structural Kernels
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1 ECML PK 2011 Fst Support ector Mchines for Structurl Kernels Aliksei Severyn nd Alessndro Moschi: University of Trento, Itly September 7,
2 Structured t Much of rel dt is structured: Sequences Trees Grphs Embedding in rel vector spce requires extensive pre- processing nd feture engineering A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 2
3 Ex: Predicte- Argument IdenRficRon gives JJ NN nice tlk A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 3
4 Ex: Predicte- Argument IdenRficRon JJ NN JJ NN gives JJ nice NN gives JJ nice NN tlk nice tlk gives JJ NN nice tlk gives JJ NN gives JJ NN gives JJ NN gives tlk A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 4
5 Explicit feture vector representron gives JJ NN nice tlk φ(t x )=x =(0,..,1,..,0,..1,..,0,..1,..0,..1,..0) JJ NN gives gives JJ NN nice tlk gives nice A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 5
6 Stte of the rt in mny tsks Nturl Lnguge processing RelRon ExtrcRon, Co- reference ResoluRon, SemnRc Role Lbeling, Textul Entilment RecogniRon, QuesRon ClssificRon InformRon Retrievl nd dt mining: QuesRon ClssificRon BioinformRcs NA clssificron, Protein- Protein IntercRon A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 6
7 Trining SMs with Structurl Kernels Kernel methods require lerning in dul spces ConvenRonl methods (SM- Light) or SMO scle qudr?clly in the number of exmples This prohibits trining of SMs with structurl kernels on lrge dt A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 7
8 Key ides in the pper 3 importnt enhncements of the pproximte cunng plne lgorithm (CPA) for SMs with structurl kernels: 1. Compct yet exct representron of cunng plne models using directed cyclic grphs to speed up trining nd clssificron 2. Prlleliz?on to mke the trining scle linerly with the number of CPUs 3. Altern?ve smpling strtegy for clss- imblnced problem A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 8
9 CPA in nutshell Introduced in the context of Structurl SMs (Tsochntridis et.l.,2004) Gives liner trining?me with liner kernels A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 9
10 CPA in nutshell Originl SM Problem Exponen?l constrints Most re dominted by smll set of importnt constrints * courtesy of Thorsten Jochims CPA SM Approch Repetedly finds the next most violted constrint un?l set of constrints is good pproxim?on. A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 10
11 CPA in nutshell Originl SM Problem Exponen?l constrints Most re dominted by smll set of importnt constrints CPA SM Approch Repetedly finds the next most violted constrint un?l set of constrints is good pproxim?on. A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 11
12 CPA in nutshell Originl SM Problem Exponen?l constrints Most re dominted by smll set of importnt constrints CPA SM Approch Repetedly finds the next most violted constrint un?l set of constrints is good pproxim?on. A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 12
13 CPA in nutshell Originl SM Problem Exponen?l constrints Most re dominted by smll set of importnt constrints CPA SM Approch Repetedly finds the next most violted constrint un?l set of constrints is good pproxim?on. A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 13
14 Compu?ng most violted constrint (MC) w φ(x i )= t j=1 α j g (j) φ(x i ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 14
15 Compu?ng most violted constrint (MC) w φ(x i )= t j=1 α j g (j) φ(x i ) g (j) = 1 n n k=1 c (j) k y kφ(x k ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 15
16 Compu?ng most violted constrint (MC) w φ(x i )= t j=1 α j g (j) φ(x i ) w φ(x i )= g (j) = 1 n t j=1 α j n k=1 n k=1 c (j) k y kφ(x k ) 1 n c(j) k y k K(x i,x k ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 16
17 ComputRonl bogleneck Min borleneck to pply kernels comes from the inner product: w φ(x i )= t j=1 α j n k=1 1 n c(j) k y k K(x i,x k ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 17
18 ComputRonl bogleneck Min borleneck to pply kernels comes from the inner product: w φ(x i )= Use smpling to pproximte exct cunng plne models (Yu & Jochims, 2009) w φ(x i )= t j=1 t j=1 α j α j n k=1 r k=1 1 n c(j) k y k 1 r c(j) k y k K(x i,x k ) K(x i,x k ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 18
19 Approximte CPA + Structurl Kernels (Severyn & MoschiN, ECML 2010) pplied this ide to SM lerning with structurl kernels, e.g. tree kernels, on lrge dt (millions of exmples) chieving speed up fctors up to 10 over convenronl SMs (SM- light- TK) 7.5 dys - > 0.5 dys A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 19
20 Compct model representron using AGs For structured dt, e.g. sequences, trees, grphs, mny exmples shre common sub- structures Key ide to reduce the number of kernel evlurons - void computrons over repe?ng sub- structures Use AGs to compct collecron of trees Gives exct kernel evluron (proof in the pper) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 20
21 Three syntcrc trees nd the resulrng AG,1,1,2,2,1 buy JJ N N buy N buy,2,3 JJ,1 N,3 red cr cr cr,3 red,1 cr,3 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 21
22 Three syntcrc trees nd the resulrng AG,1,1,2,2,1 buy JJ N N buy N buy,2,3 JJ,1 N,3 red cr cr cr,3 red,1 cr,3 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 22
23 Three syntcrc trees nd the resulrng AG,1,1,2,2,1 buy JJ N N buy N buy,2,3 JJ,1 N,3 red cr cr cr,3 red,1 cr,3 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 23
24 Three syntcrc trees nd the resulrng AG,1,1,2,2,1 buy JJ N N buy N buy,2,3 JJ,1 N,3 red cr cr cr,3 red,1 cr,3 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 24
25 ComputRonl bogleneck Min borleneck to pply kernels comes from the inner product: w φ(x i )= t j=1 α j n k=1 1 n c(j) k y k K(x i,x k ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 25
26 SAG Compcts ech CPA model into single AG w φ(x i )= t j=1 α j r k=1 1 r c(j) k y k K(x i,x k ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 26
27 SAG Compcts ech CPA model into single AG w φ(x i )= t j=1 α j r k=1 1 r c(j) k y k K(x i,x k ) w φ(x i )= t j=1 α j K dg ( dg (j),x i ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 27
28 SAG+ Compcts ll CPA models in the working set into single AG w φ(x i )= t j=1 α j r k=1 1 r c(j) k y k K(x i,x k ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 28
29 SAG+ Compcts ll CPA models in the working set into single AG w φ(x i )= t j=1 α j r k=1 1 r c(j) k y k K(x i,x k ) w φ(x i )=K dg ( dg(t),x i ) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 29
30 Exmple: compurng K dg ( dg, x) x sell NN cr dg,1,1,2,2,1 buy JJ N N buy N buy,2,3 JJ,1 N,3 red cr cr cr,3 red,1 cr,3 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 30
31 Exmple: compurng K dg ( dg, x) x sell NN cr dg,1,1,2,2,1 buy JJ N N buy N buy,2,3 JJ,1 N,3 red cr cr cr,3 red,1 cr,3 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 31
32 Exmple: compurng K dg ( dg, x) x sell NN cr dg,1,1,2,2,1 buy JJ N N buy N buy,2,3 JJ,1 N,3 red cr cr cr,3 red,1 cr,3 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 32
33 Experimentl setup tsets 1. Predicte- Argument IdenRficRon (SemnRc Role Lbeling) 2. Yhoo! Answers (QuesRon/Answer ClssificRon) 3. QuesRon ClssificRon from TREC- 10 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 33
34 SemnRc Role Lbeling (SRL) dtset " Tsk: identifiction of rgument boundries Exmple of SRL nnottion: Pul gives tlk in Rome [ B Pul] [ trget gives ] [ B tlk] [ B in Rome] " Consists of PropBnk, PennTree bnk nd Chrnik prse trees s provided by CoNLL 2005 " Trining set: 100,000 " Two Test sets: " Sections 23 nd 24 (234,416 nd 149,140 instnces)
35 Speedups during trining on SRL dtset (100k) 20 Speedup usm SAG SAG Smple size A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 35
36 ClssificRon speedups on SRL dtset (100k) Speedup usm SAG SAG k 25k 50k 75k 100k Trining size A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 36
37 PrllelizRon 95% of?me is spent compurng cunng plne model t ech iterron CPA llows for stright- forwrd prlleliz?on to bring down complexity from O(r 2 ) to O(r 2 /p) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 37
38 Speedups due to prllelizron on 50k YA dtset smple size = 100 smple size = 250 smple size = 500 smple size = 1000 speedup number of CPUs A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 38
39 Hndling clss- imblnce problem 1- slck OP mkes it difficult to include penlres for exmples from different clsses The ide of smpling to build pproximte cunng plne t ech iterron suggests stright- forwrd solu?on Use importnce smpling Preserves theoreticl convergence bounds A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 39
40 Results on QA clssificron: TREC nd Yhoo! Answers Our empiricl findings revel: 1. Outperforms pproximte CPA when tuning is needed [Yu & Jochims, NIPS 08] 2. As fst s pproximte CPAs [Severyn & MoschiN, ECML 10] 3. Gives more flexible control over Precision/ Recll thn SM- light A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 40
41 Conclusions 1. Two lerning lgorithms SAG nd SAG+ tht compct CPA models using AGs to give much fster trining nd clssific?on Rmes 2. Prlleliz?on 3. Altern?ve smpling to beger hndle clss- imblnced dt t lrge- scle 4. Solu?on for lerning with structurl kernels on lrge scle Softwre will be vilble t 41
42 Future work Extend the AG pproch to more generl kernels, e.g. PT kernel [MoschiN, ECML 2006] Explore other Structurl Kernels, e.g. grph kernels Other tsks, e.g. from NLP (relron extrcron, co- reference resoluron) Try lternrve trining lgorithms, e.g. SG, Pegsos A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 42
43 Thnk you! A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 43
44 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 44
45 usm vs SAG/SAG+ on SRL dtset Trining smple usm SAG SAG (7.0) 283 (7.8) (7.3) 752 (11.0) (7.2) 1275 (14.3) (7.2) 1802 (17.2) (7.6) 2497 (20.0) Clssifiction t #Ss usm SAG SAG+ 10k (1.1) 1 (24.0) 25k (1.6) 1 (33.2) 50k (2.1) 3 (28.3) 75k (2.0) 5 (20.5) 100k (2.2) 7 (19.5) A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 45
46 Hndling clss- imblnce on TREC- 10 nd YA dtsets Trec 10 t Rtio usm usm+j SM F-1 P/R F-1 P/R F-1 P/R ABBR 1: / / /88.9 ESC 1: / / /92.0 ENTY 1: / / /78.7 HUM 1: / / /86.2 LOC 1: / / /79.0 NUM 1: / / /82.3 Yhoo Answers 10k 1: / / / k 1: / / / k 1: / / / k 1: / / k 1: / / BOW 1: / / /93.5 A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 46
47 Bckground: Structurl Kernels Given prse tree of sentence, they generte exponen?lly mny fetures Help to void mnul feture engineering for poorly understood linguisrc phenomen Achieve stte- of- the- rt results in mny NLP tsks, e.g. quesron nswering, semnrc role lbeling, etc. Mny levels of grnulrity to generte sub- trees, e.g. ST, SSK, PT A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 47
48 Some of the fetures generted by PT kernel AuRsm is disese N Autism S BZ is N disese S S BZ BZ BZ BZ is N N is N is N N disese disese disese Autism N N disese disese BZ BZ BZ N N N N Autism BZ Autism is N disese BZ... is N is is disese disese Autism disese A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 48
49 QuesRons A. Severyn & A. MoschiN. Fst Support ector Lerning for Structurl Kernels 49
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