10.1.1.50.8099

10.1.1.50.8099 - c M ITM ed iaLabP e rcep tua lCom pu t...

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Unformatted text preview: c M ITM ed iaLabP e rcep tua lCom pu t ing/Lea rn ingandComm onSenseT echn ica lR epo rt nov,rev isedjun C oup ledh iddenM arkovm ode lsform ode ling in teract ingp rocesses M atthewB rand b rand@m ed ia .m it.edu T heM ed iaLab ,M IT h ttp ://www .m ed ia .m it.edu/~b rand Am esS tree t C am br idge ,MA USA A b stract W ep resen tm ethod sforcoup lingh iddenM arkovm ode ls( hmm s)tom ode l sy stem so fm u lt ip lein teract ingp rocesses . T heresu lt ingm ode lshavem u lt ip le statevar iab lesthataretem pora llycoup ledv iam atr iceso fcond it iona lp robab il- it ies .W ein troduceadeterm in ist ic O ( T ( CN ))app rox im at ionform ax im um a poster ior (MAP )stateest im at ionw h ichenab lesfastc lass icat ionandparam eter est im at ionv iaexpectat ionm ax im izat ion .A n/N-head s"dynam icp rogramm ing a lgor ithm sam p lesfrom theh ighestp robab ilitypath sth roughacom pactstate tre llis ,m in im iz inganupperboundonthecrossen tropyw iththefu ll(com b i- nator ic)dynam icp rogramm ingp rob lem . T hecom p lex ity is O ( T ( CN ))for C cha in so f N statesap ieceob serv ing T datapo in ts ,com paredw ith O ( TN C )for na ive(C artes ianp roduct) ,exact(statec lu ster ing) ,andstochast ic(M on teC ar lo) m ethod sapp liedtothesam ein ferencep rob lem .Insevera lexper im en tsexam in ing tra in ingt im e ,m ode llike lihood s ,c lass icat ionaccu racy ,androbu stnessto in it ia l cond it ion s ,coup led hmm scom pared favorab lyw ithconven t iona l hmm sandw ith energy-basedapp roachestocoup led in ferencecha in s .W edem on strateandcom pare thesea lgor ithm sonsyn thet icandrea ldata ,inc lud ing in terp retat iono fv ideo . .In troduct ion H iddenM arkovm ode ls( hmm s)areapopu larp robab ilist icfram ew ork form ode ling p rocessesthathavestructu reint im e .Theyhaveac learB ayes iansem an t ics ,ec ient a lgor ithm sforstateandparam eterest im at ion ,andtheyau tom at ica llyperform dy- nam ict im ew arp ingfors igna lsthatareloca llysquashedandstretched .A n hmm is essen t ia llyaquan t izat iono fasy stem 'scongu rat ionspacein toasm a llnum bero f d iscretestates ,togetherw ithp robab ilit iesfortran s it ion sbetw eenstates .A s ing le n ited iscretevar iab leindexesthecu rren tstateo fthesy stem .A ny in form at ion abou ttheh istoryo fthep rocessneeded forfu tu rein ferencesm u stbere ected inthe cu rren tva lueo fth isstatevar iab le .H ow ever ,m any in terest ingsy stem sarecom posed o fm u lt ip lein teract ingp rocesses ,andthu sm er itacom pos it iona lrep resen tat iono f tw oorm orevar iab les .Th isistyp ica llythecaseforsy stem sthathavestructu reboth D ra ftunde rrev iew . Brand int im eandspace .W ithas ing lestatevar iab le ,M arkovm ode lsareill-su itedtothese p rob lem s . W ep resen tm ethod sforcoup lingh iddenM arkovm ode lstocap tu rethesein- teract ion s .Cha in sarecoup ledv iam atr iceso fcond it iona lp robab ilit iesm ode ling cau sa l(tem pora l)in uencesbetw eenthe irh iddenstatevar iab les .C oup led hmm sare...
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10.1.1.50.8099 - c M ITM ed iaLabP e rcep tua lCom pu t...

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