Iimvavanyo ezongezelelweyo zamanani kwi-K-SIF kunye ne-SIF: Ubunzulu, ingxolo, kunye namandla ocalucalulo

Itheyibhile yoQhagamshelwano

Isishwankathelo kunye 1. Intshayelelo

2. Imvelaphi kunye nezandulela

2.1. Ihlathi eliSebenzayo lokuzahlula

2.2. Indlela yoMtyikityo

3. Utyikityo lweNdlela yokuzahlula kwehlathi

4. Iimvavanyo zamanani

4.1. IiParameters Uhlalutyo lobuthathaka

4.2. Izinto eziluncedo ze-(K-)SIF ngaphezulu kwe-FIF

4.3. Idatha yokwenyani yokuFumana iBenchmark

5. Ingxoxo kunye nesiphelo, iiNkcazelo zeMpembelelo, kunye neeReferensi

Isihlomelo

A. Ulwazi olongezelelweyo malunga noMsayino

B. K-SIF kunye SIF Algorithms

C. Iimvavanyo zamanani ezongezelelweyo

C. Iimvavanyo zamanani ezongezelelweyo

Kweli candelo, sibonisa imifuniselo yamanani eyongezelelweyo ekuxhaseni i-algorithms ecetywayo kunye neengxabano eziphuhliswe kumzimba oyintloko wephepha. Okokuqala, Sichaza indima yobunzulu botyikityo kwii-algorithms kwaye sichaze ukuba le parameter ibachaphazela njani. Sibonelela ngeebhokisi zeeseti ezimbini zedatha eyenziweyo kwaye sixoxa ngokubaluleka kobunzulu beparameter kulo mxholo. Emva koko, sinika imifuniselo eyongezelelweyo ukomelela kwinzuzo yengxolo ye (K) -SIF ngaphezulu kwe-FIF, enxulumene neCandelo 4.2 lomzimba oyintloko wephepha. Umhlathi wesithathu ubhekiselele kwidatha eyenziweyo yovavanyo 'lweziganeko zokutshintshana' kwicandelo 4.2 lomzimba ophambili wephepha libonisiwe. Sinikezela ngoMfanekiso wokubonwa kunye nokuqonda okungcono. Siphinda siphawule ngendlela esakhe ngayo idatha. Icandelwana lesine ke libonisa ixesha lokubala le-algorithms ecetywayo ngokuthelekisa ngokuthe ngqo kwi-FIF. Emva koko, uvavanyo olongezelelweyo olubonisa ubungqina obongezelelweyo bamandla ocalucalulo malunga nomsebenzi we-AD we-(K) -SIF phezu kwe-FIF uyaboniswa. Ekugqibeleni, icandelwana lokugqibela libonisa iThebhile echaza ulwazi malunga nobukhulu beesethi zedatha ezinxulumene nebenchmark kwiCandelo 4.3.

C.1. Indima yobunzulu boMsayino

Kolu vavanyo, siphanda impembelelo yale parameter kwi-K-SIF ngeendidi ezimbini ezahlukeneyo zeenkqubo zestochastic. Intshukumo ye-Brownian ene-dimensional-dimensional (ene µ = 0 kunye ne-σ = 0.1), ephawulwe ngamaxesha ayo amabini okuqala, kunye nenkqubo ye-dimensional Merton-jump diffusion process, inkqubo yomsila onzima esetyenziswa ngokubanzi ukulinganisa i-stock market. Kwimeko enjalo

Algorithms

Indlela, sithelekisa udidi lwangaphambili lwemodeli yestochastic ukuya kokugqibela, leyo, endaweni yoko, ayinakubonakaliswa yimizuzu emibini yokuqala kwaye ibone ukusebenza kwe (K) -SIF kulo mba.

Sibale i-K-SIF ngezichazi-magama ezithathu ezinamanqanaba okunqunyulwa ahluka kwi- {2, 3, 4} kuzo zombini iiseti zedatha ezifanisiweyo. Sibeka inani leefestile eziqhekezayo ukuya kwi-10, ngokwecandelo langaphambili, kunye nenani lemithi ukuya kwi-1000. Emva koko, sibala ulungelelwaniso lwe-Kendall lwenqanaba elibuyiswe yile mifuziselo kwizicwangciso ezintathu zokubini: inqanaba 2 vs kwinqanaba 3 , inqanaba 2 vs kwinqanaba 4, kunye nenqanaba lesi-3 vs kwinqanaba lesi-4.

Siphindaphinda lo mvavanyo ngamaxesha e-100 kwaye sichaza iibhokisi zebhokisi ezihambelanayo kwi-Figure 5 ye-Brownian motion kunye ne-Figure 6 ye-Merton-jump diffusion process. Qaphela ukuba izicwangciso ekhohlo nasekunene zibhekisa kwi parameters ezahlulo ezahlukeneyo zefestile ezikhethiweyo kwi K-SIF, ehambelana ne ω = 3 yeendawo zolawulo zasekhohlo, ngelixa, kwabalungileyo, sikhethe ω = 5. Ezi bhokisi zebhokisi zibonisa unxulumano lwe Kendall tau. phakathi kwamanqaku abuyiswe yenye ye-algorithms esetyenziswa ngobunzulu obuthile kunye ne-algorithm efanayo enobunzulu obahlukileyo. Iziphumo ze-K-SIF ezinezichazi-magama ezithathu zimelwe ngombala oblowu, orenji, noluhlaza kwiBrownian, Cosine kunye namaza amaza eGaussian aluhlaza, ngokulandelelanayo. Iibhokisi ze-SIF endaweni yoko zimfusa. I-y-axis ibhekisa kumaxabiso olungelelwaniso lwe-Kendall kunye ne-x-axis kwizicwangciso zamaxabiso obunzulu ngokubhekiselele ekunxibelelaneni kwayo.

Ulungelelwaniso oluphezulu lubonisa irenki elinganayo ebuyiswa yi-algorithm eneparameters zobunzulu obahlukeneyo. Ngoko ke, ukuba ulungelelwaniso luphezulu, oku kubonisa ukuba le parameter ayichaphazeli iziphumo ze-algorithm ecatshangelwayo, kwaye ubunzulu obuphantsi kufuneka bukhethwe ukwenzela ukubala kakuhle. Ulungelelwaniso oluphezulu luboniswa kuzo zombini ii-SIF (iibhokisi zebhokisi ezimfusa) kunye ne-K-SIF yezichazi-magama ezibini, okt Brownian kunye neCosine (iibhokisi zebhokisi eziblowu neorenji). Ke ngoko, ukukhetha ubuncinci benqanaba lokunqunyulwa kuyacetyiswa ukuphucula ukusebenza kakuhle kokubala. Kwi-algorithms efanayo, ulungelelwaniso oluphantsi kancinci luchongiwe kwimeko yeenkqubo zeMerton, kodwa kusekho amanqanaba angama-0.8, kungoko kuxhasa ibango elilinganayo. Kwimeko ye-K-SIF ngesichazi-magama se-Gaussian (iibhokisi zebhokisi eziluhlaza), umahluko ophezulu kakhulu ufunyenwe malunga neziphumo zonxulumano kuzo zonke iimeko ezintathu ezivavanyiweyo. Ngaphezu koko, kwimeko yeenkqubo ze-Merton-jump diffusion, iziphumo zibonisa ukulungelelaniswa okuphantsi, okuhambelana nezinye iziphumo. Ngoko ke, kwimeko ye K-SIF ngesichazi-magama esinjalo, ubunzulu kufuneka bukhethwe ngononophelo kuba iiparamitha ezahlukeneyo zinokukhokelela kubhaqo olungcono lwemizuzu yenkqubo engaphantsi.

C.2. Ukomelela kwingxolo

Le nxalenye inika imifuniselo eyongezelelweyo ukomelela kwinzuzo yengxolo ye (K) -SIF phezu kwe-FIF, enxulumene neCandelo 4.2 lomzimba oyintloko wephepha. Ulungelelwaniso lokulinganisa idatha luhamba ngolu hlobo lulandelayo. Sichaza iseti yedatha yokwenziwa ye-100 yemisebenzi egudileyo enikwe ngu

apho ε(t) ∼ N (0, 0.5). Sikhetha ngokungenamkhethe i-10% kwakhona kwaye senze iijika ezingxolayo kancinci ngokongeza ingxolo encinci kwelinye isithuba sokuphumla xa kuthelekiswa nelokuqala, okt.

apho ε(t) ∼ N (0, 0.1).

Umzobo 7 ubonelela ngesishwankathelo sokubonwa kwedatha eyenziweyo kwiphaneli yokuqala. Iigophe ezili-10 ezingaqhelekanga zicwangciswe ngombala obomvu, ngelixa i-10 ithathwa njengengxolo encinci yedatha eqhelekileyo icwangciswe ngeblue. Eminye i-curves, ithathwa njengedatha eqhelekileyo, inikezelwa ngegrey. Umbono kukuqonda indlela ukhetho lwesichazi-magama oluyiphembelela ngayo i-K-SIF kunye ne-FIF ekubhaqweni kwedatha enengxolo encinci yesiqhelo ngokuchasene nengxolo engaqhelekanga. Iziphumo ze-K-SIF kunye ne-FIF zibonelelwa kwiphaneli yesibini, yesithathu neyesine yoMfanekiso 7, ngokulandelelanayo.

Sibala i-K-SIF nesichazi-magama saseBrownian, k = 2 kunye no-ω = 10 kunye ne-FIF ye-α = 0 kunye no-α = 1 kunye nesichazi-magama saseBrownian. Imibala yeephaneli imele amanqaku angaqhelekanga abelwe igophe ngalinye kuloo algorithm ethile. Kweyesibini (K-SIF) kunye neyokugqibela (FIF nge-α = 0) iiphaneli, amanqaku angaqhelekanga ayanda ukusuka kumthubi ukuya kumnyama bhulowu, okt ijika elimnyama aliqhelekanga kwaye umthubi uqhelekile, ngelixa, kwiploti yesithathu (FIF ene-α). = 1) ichasene, okt igophe elimnyama liqhelekile kwaye umthubi awuqhelekanga.

Kuyenzeka ukuba uqaphele ukuba i-K-SIF inokuchonga njani ngempumelelo idatha enengxolo nengaqhelekanga ngolo hlobo. Ewe, ngelixa idatha engaqhelekanga inemibala eluhlaza okwesibhakabhaka, ezo zinomsindo zibonisa amanqaku ombala omthubi. Endaweni yoko, kwi-FIF ene-α = 1 (iphaneli yesithathu) zombini ezingaqhelekanga kunye neegophe ezingxolayo kancinci zichongwa njengedatha eqhelekileyo (inikwe isikali esibuyiselwe umva kunye nemibala eluhlaza okwesibhakabhaka). Xa kuziwa kwi-FIF nge-α = 0 (iphaneli yokugqibela neyesine), zombini idatha engaqhelekanga kunye nenengxolo ifakwe amanqaku njengeegophe ezingaqhelekanga. Yiyo loo nto, iFIF enezicwangciso zombini zeparamitha ye-α, ayinakubonelela ngamanqaku ahlukileyo kwingxolo kunye nedatha enengxolo encinci. K-SIF, endaweni yoko, yenza ngempumelelo umsebenzi onjalo.

C.3. Ukutshintshela iSeti yedatha yeziganeko

Eli candelo libonelela ngokubonwa kweseti yedatha esetyenziswe 'kwiziganeko zokutshintshatshintsha' kwicandelo lesi-4.2 lephepha elingundoqo. Umzobo 8 ubonisa idatha eyenziweyo. Phawula ukuba sichaza iseti yedatha yokwenziwa ye-100 yemisebenzi egudileyo enikwe ngu

ngo-t ∈ [0, 1] kunye no-q balingana kwi- [1, 1.4]. Emva koko, silinganisa ukwenzeka kweziganeko ngokongeza ingxolo yeGaussian kwiindawo ezahlukeneyo zemisebenzi. Sikhetha ngokungakhethiyo i-90% yazo kwaye songeze amaxabiso e-Gaussian kwisithuba esisezantsi, okt.

apho ε(t) ∼ N (0, 0.8). Siyithathela ingqalelo i-10% eseleyo njengengaqhelekanga ngokongeza 'iziganeko' ezifanayo kwelinye ixeshana elingaphantsi xa lithelekiswa nelokuqala, okt.

apho ε(t) ∼ N (0, 0.8). Emva koko siye sakha iziganeko ezibini ezifanayo ezenzeka kwiindawo ezahlukeneyo zemisebenzi, ekhokelela ekuhlukaniseni izinto ezingaqhelekanga.

C.4. Ixesha lokubala le-K-SIF, i-SIF kunye ne-FIF

C.5. I-K-SIF kunye ne-SIF: Ucalulo olungcono lwe-Anomalies xa kuthelekiswa ne-FIF

Kweli candelo, sakha umfuniselo wethoyi owongezelelweyo ukubonisa amandla ocalucalulo e (K-)SIF ngaphezulu kwe-FIF. Silinganisa i-100 yeendlela ze-Brownian ezicwangcisiweyo ezine-90% yedatha eqhelekileyo kunye ne-drift µ = [0, 0] kunye nokutenxa okusemgangathweni σ = [0.1, 0.1], kunye ne-10% yedatha engaqhelekanga kunye ne-drift µ = [0, 0] kunye nomgangatho ukutenxa σ = [0.4, 0.4].

Umzobo we-10 ubonisa umlinganiso omnye wale datha. Qaphela ukuba, iindlela ezimfusa zibonisa idatha eqhelekileyo, ngelixa, kwi-orenji, engaqhelekanga endaweni yoko imelwe. Kule datha, sibala iFIF (nge α = 1 kunye nesichazi-magama saseBrownian), K-SIF (nge

k = 2, ω = 10 kunye nesichazi-magama saseBrownian) kunye ne-SIF (nge-k = 2 kunye ne-ω = 10). Ukubonisa amanqaku abuyiswe yi-algorithsm, sinika uMfanekiso 11. Qaphela ukuba, iiplani zibonisa amanqaku ezi ndlela ze-100, emva kokuba zihlelwe. Yiyo loo nto, i-x-axis ibonelela ngesalathiso samanqaku acwangcisiweyo, ngelixa i-axis ka-y imele amaxabiso amanqaku. Ngokuphathelele ukulinganisa, siceba ngemfusa amanqaku edatha eqhelekileyo kunye ne-orenji amanqaku edatha engaqhelekanga. Iiphaneli zintathu zibhekisa kwi-FIF, K-SIF kunye ne-SIF, ngokulandelelanayo.

Kuyenzeka ukuqaphela ukuba amanqaku e-K-SIF kunye ne-SIF ahlula kakuhle idatha engaqhelekanga kunye neyesiqhelo, ngokutsiba kumanqaku avakaliswayo, okt amanqaku edatha eqhelekileyo akude kakhulu kumanqaku angaqhelekanga. idatha. Ukuba umntu ugxile kwi-FIF endaweni yoko, ucalucalulo lwezo ziphazamiso lubonakala lucela umngeni; iphaneli yokuqala ibonisa, enyanisweni, ngokuqhubekayo ngokwemiqathango yamanqaku abuyiswe yi-algorithm ye-AD, engahluli idatha eqhelekileyo kunye nengaqhelekanga.

Isishwankathelo, i-algorithms ecetywayo exhasa i-kernel yesiginitsha (K-SIF) kunye nolungelelwaniso lwesiginitsha (SIF) lubonisa iziphumo ezithembeke ngakumbi kolu cwangciso lovavanyo, lucebisa ukusebenza kwabo ekuqondeni okungaqhelekanga ngaphakathi kweseti yedatha eyenziweyo. Ukubona ulandelelwano lweziganeko ezenzekayo luphawu olufundisa kakhulu kunokubandakanya inkalo esebenzayo kwi-algorithm yokufumanisa okungaqhelekanga. Lo mbandela kufuneka uphandwe ngakumbi kwaye uphononongwe, ngakumbi kwiindawo zesicelo apho idatha elandelelanayo, efana nochungechunge lwexesha, ithathelwa ingqalelo.

C.6. IDatha yeBenchmark yoFundo olungaqhelekanga

C.7. Imvelaphi kumsebenzi woBunzulu beDatha

Izixhobo zobalo ezaziwa njengobunzulu bedatha zisebenza njengamanqaku afanayo ngaphakathi kulo mxholo. Ubunzulu bedatha bunikeza ukutolika kwejometri ecacileyo, amanqaku oodolo ukusuka kwiziko ngaphandle ngokubhekiselele kunikezelo olunokwenzeka (Tukey, 1975; Zuo kunye neSerfling, 2000). Ngokwejometri, ubunzulu bedatha bulinganisa ubunzulu besampulu ngaphakathi kosasazo olunikiweyo. Ngaphandle kokufumana ingqwalasela kuluntu lwamanani, ubunzulu bedatha buye bahoywa kakhulu luluntu lokufunda ngomatshini. Iinkcazo ezininzi ziye zacetywa, njengezinye iindlela kwisiphakamiso sokuqala, ubunzulu be-halfspace obuziswe kwi (Tukey, 1975). Phakathi kwezinye ezininzi ezi ziquka: ubunzulu obulula (uLiu, 1988), ubunzulu bentelekelelo (uLiu noSingh, 1993), ubunzulu bezonoid (Koshevoy kunye noMosler, 1997), ubunzulu bokubuyela umva (Rousseeuw noHubert, 1999), indawo ubunzulu (uVardi noZhang, 2000) okanye ubunzulu be-AI-IRW (Clemen ´ c¸on et al., 2023) ezahlukeneyo kwiipropathi zabo kunye nokusetyenziswa. Ubunzulu bedatha bufumana usetyenziso oluninzi olunjengokuchaza iimethrikhi ezomeleleyo phakathi kokusasazwa okunokwenzeka (u-Staerman et al., 2021b) ekhuphisana neemetrics ezisekwe kuthutho olufanelekileyo (uStaerman et al., 2021a), ukufumana uhlaselo oluchasene nombono wekhompyuter (Picot et al., 2022) ; Dadalto et al., 2023) okanye ukufumanisa i-hallucination kwi-NLP transformers (Colombo et al., 2023; Darrin et al., 2023; Colombo et al., 2022) kunye neLLM (Himmi et al., 2024).