Gusesengura Ibimenyetso Byiza hamwe na Binary-ibisubizo Ubushakashatsi Mubice bibiri na@bayesianinference
Gusesengura Ibimenyetso Byiza hamwe na Binary-ibisubizo Ubushakashatsi Mubice bibiri
Birebire cyane; Gusoma
Iki gice gisuzuma ibimenyetso byiza mubyiciro bibiri byo kwemeza Bayesian hamwe no kohereza igeragezwa ryicyiciro-I hamwe no kugerageza icyiciro cya II, harimo nudukoryo duto. Lemma 1 yerekana ko ubushakashatsi bworoheje icyiciro-II butanga ingamba zisa nigeragezwa ryicyiciro kimwe.
Abanditsi:
(1) Shih-Tang Su, Kaminuza ya Michigan, Ann Arbor ([email protected]);
(2) Vijay G. Subramanian, kaminuza ya Michigan, Ann Arbor na ([email protected]);
(3) Tanga Schoenebeck, Kaminuza ya Michigan, Ann Arbor ([email protected]).
Imbonerahamwe
2.1 Icyitegererezo cyibigeragezo-Ibisubizo mubigeragezo bibiri
3.2 Ibitekerezo n'ingamba zatewe
3.3 Inzitizi zitangwa nubushakashatsi bwa II
3.4 Ikigereranyo cyo kwemeza nuburyo bwiza bwo gutangaza ibimenyetso
3.5 Gereranya ningamba za kera zo muri Bayesiya
4.2 Byemejwe nubushakashatsi bwateguwe
4.3 Icyiciro cyinshi nicyitegererezo cya Bayesian kwemeza hamwe na References
3 Binary-ibisubizo Ubushakashatsi mubyiciro bibiri
Muri iki gice ikibazo cyo kohereza cyoherejwe cyatanzwe muri (2) Igice cya 2.1, gikemurwa guhera ku rubanza rworoshye rudafite akamaro. Hano hari ibyiciro bibiri gusa mubigeragezo byize hano, kandi duhereye kuri ibi tuzatezimbere kurushaho kumenya uburyo ubwoko butandukanye bwubushakashatsi (bwagenwe nubushakashatsi bwakozwe) bugira ingaruka nziza muburyo bwo kohereza ibimenyetso. Kugirango turusheho gusobanuka, tuzasesengura uburyo ubushakashatsi bubiri bwiyemeje (mugice cya II) hamwe nubushakashatsi bwateguwe bwoherejwe (mugice cya I) bizagira ingaruka kubikorwa byiza byoherejwe. Mbere yo kwerekana ikibazo rusange, turaganira kumurongo wibyiciro bibiri byikigereranyo bisa nicyiciro kimwe. Muri iki cyiciro cyibigeragezo byibyiciro bibiri, murimwe mubigeragezo byicyiciro cya II, byitwa igeragezwa rito, kugabana ibisubizo ntabwo bigenga leta yukuri. Ubushakashatsi budafite akamaro [2], nabwo bwitwa (Blackwell) ubushakashatsi butamenyesha amakuru mubuvanganzo bumwe na bumwe, bukoreshwa kenshi nkibipimo byo kugereranya impinduka ziteganijwe kubakozi muri gahunda zerekana ibimenyetso, urugero, [22,20,21]. Ubu buryo bw'ibyiciro bibiri hamwe nubushakashatsi bworoheje bugerageza gukemura ibibazo nyabyo byisi hamwe nubushakashatsi bumwe (kandi buhenze), urugero, ibizamini byamavuriro, ishoramari ry’ishoramari, cyangwa ubutumwa bwo mu kirere. Kubera ko igeragezwa rihenze, uburyo bwo gusuzuma butangwa kugirango hamenyekane niba bikwiye gukora ubushakashatsi. Hanyuma tuzasesengura ingamba nziza zerekana ibimenyetso muburyo rusange, aho ubushakashatsi bwombi mugice cya II butari buke.
3.1 Ubushakashatsi hamwe no kwerekana
Dutangira dusesenguye ingamba nziza zohereje (imiterere yerekana ibimenyetso) muburyo bworoshye aho hariho igeragezwa rimwe ridafite akamaro ryakozwe mugice cya II. Ububasha bwohereje guhitamo ibishoboka (p1, p2) bigenzura inzira yo gusuzuma. Kugira ngo twirinde ibidasobanutse neza, tubanze dusobanure icyo igerageza rito.
Iyo hakozwe igeragezwa rito (mu cyiciro cya II), imyizerere yinyuma ya leta igumaho nkuko imyizerere mfatakibanza ikomoka (1). Iyo habaye igeragezwa rito muburyo bubiri bwo kugerageza-icyiciro cya kabiri, noneho Lemma 1 ivuga ko uwayohereje hamwe nuwakiriye ibyo akeneye byateganijwe muburyo bwiza bwo gutangaza ibimenyetso ni kimwe no mubibazo (icyiciro kimwe) cya kera cyo kwemeza Bayesian.
Lemma 1. Iyo umwanya wa leta ari binary, abohereza hamwe nuwakiriye ibikorwa byateganijwe ni bimwe muri gahunda ebyiri zikurikira zo kwemeza Bayesian muri buri gahunda yuburyo bwiza bwo kwerekana ibimenyetso:
Kwemeza kwa Bayesian mu rubanza rumwe,
Kwemeza kwa Bayesian mubigeragezo byibyiciro bibiri hamwe nuwagerageje kohereza icyiciro-I hamwe nubushakashatsi bworoheje mugice cya II.
Mu rubanza rumwe rwo mu rwego rwo kwemeza Bayesian, ingamba nziza zo gutangaza ibimenyetso zivanga gusa ibihugu byombi bishoboka mu gisubizo kimwe (urugero, iyo umushinjacyaha avuga ko ukekwaho icyaha). Ku bindi bisubizo, uwayohereje agaragaza imiterere nyayo ishobora kuba imwe (urugero, iyo umushinjacyaha avuga ko ukekwaho icyaha ari umwere). Mugihe habaye igeragezwa rito mugice cya II, ubundi igeragezwa (ukeka ko rizakorwa mubisubizo ωB) rizahinduka nkuwohereje guhitamo ubushakashatsi mugice cya I. Iki kintu kibaho kuko uwagitumye ashobora guhitamo guhitamo guhishura imiterere nyayo mugihe igeragezwa ridafite akamaro rigomba gukorwa, ni ukuvuga mugushiraho P (θ1 | EB) = 1 cyangwa P (θ2 | EB) = 1; n'ingamba za kera zo kwemeza Bayesian zirashobora kwigana. Mubyukuri, kugira igeragezwa rito mubigeragezo-II ntibibuza uwayohereje.
Uru rupapuro ruraboneka kuri arxiv munsi ya CC 4.0.
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