Njira ya Bootstrap mu Ziwerengero
Pendauluan
Ziwerengero ndi sayansi yomwe cholinga chake ndi kusonkhanitsa, kusanthula, kutanthauzira, ndi kupereka deta. Kusanthula ziwerengero nthawi zambiri kumadalira malingaliro ena kapena malingaliro a kuthekera omwe amafunikira zitsanzo zazikulu kuti apange ziwerengero zolondola. Komabe, nthawi zambiri, kupeza zitsanzo zazikulu sikothandiza kapena kosatheka. Apa ndi pomwe njira yoyambira, njira yosinthira zitsanzo, imakhala yothandiza kwambiri.
Njira yogwiritsira ntchito bootstrap idayambitsidwa koyamba ndi Bradley Efron mu 1979 ndipo yakhala imodzi mwa njira zodziwika kwambiri mu ziwerengero chifukwa cha kusinthasintha kwake komanso kuthekera kwake kopanga ziwerengero zolondola za magawo ambiri a anthu popanda kupanga malingaliro enieni ogawa. Nkhaniyi ifotokoza mfundo zoyambira za njira yogwiritsira ntchito bootstrap, njira zake zogwiritsira ntchito, ndi zitsanzo zingapo za momwe imagwiritsidwira ntchito mu ziwerengero.
Mfundo Zoyambira za Njira ya Bootstrap
Njira ya bootstrap ndi njira yopanda ma parametric yomwe imatithandiza kuwerengera kufalikira kwa ziwerengero (monga, apakati, apakati, kusiyana) mwa kusanthulanso deta yathu yoyambirira. Mfundo yaikulu ya njira iyi ndikugwiritsa ntchito deta yomwe ilipo (chitsanzo choyambirira) kuti tiyerekezere ma data ambiri atsopano ndi zitsanzo zobwerezabwereza.
Nazi njira zoyambira zomwe zatengedwa mu njira ya bootstrap:
1. Chitsanzo: Kuchokera ku deta yoyambirira ya kukula kwa N, bwerezaninso nthawi ya N ndikusintha. Izi zikutanthauza kuti zinthu zomwe zasankhidwa kuti ziwunikidwe zitha kusankhidwa kangapo.
2. Werengani Ziwerengero: Werengani ziwerengero zomwe mukufuna (monga, apakati, apakati) pa chitsanzo chilichonse.
3. Bwerezani Njirayi: Bwerezani masitepe 1 ndi 2 kangapo (monga B=1000 kapena kuposerapo) kuti mupeze kugawa kwa bootstrap kwa ziwerengero zomwe mukufuna.
4. Kuyerekeza ndi Kutsiliza: Gwiritsani ntchito kugawa kwa bootstrap kumeneku kuti mupange nthawi zodalirika, kuyesa malingaliro, kapena kupanga ziwerengero zina zoyerekeza.
Magawo Okhazikitsa Bootstrap
Njira ya bootstrap ingathe kufotokozedwa mwatsatanetsatane m'magawo otsatirawa:
1. Kubwerezanso zitsanzo
Kuyesanso ndi kusintha ndiye mfundo yaikulu ya njira ya bootstrap. Pogwiritsa ntchito deta yoyambirira, timapanga ma data ambiri atsopano, otchedwa bootstrap samples. Chitsanzo chilichonse cha bootstrap ndi zotsatira za sampuli ya nthawi ya N kuchokera ku deta yoyambirira ya kukula kwa N, koma ndi kusintha, kotero kuti zinthu zomwe zili mu chitsanzo choyambirira zitha kuwoneka kangapo mu zitsanzo za bootstrap.
Chitsanzo:
Ngati tili ndi deta yoyambirira \[3, 5, 7, 9\], ndiye kuti chitsanzo chimodzi chotheka cha bootstrap chingakhale \[3, 9, 9, 5\].
2. Kuwerengera Ziwerengero za Bootstrap
Pa chitsanzo chilichonse cha bootstrap, werengani ziwerengero zomwe mukufuna. Tiyerekeze kuti tili ndi chidwi ndi avareji, tingawerenge avareji ya chitsanzo chilichonse cha bootstrap. Ngati tibwereza njirayi nthawi B, tidzakhala ndi ziwerengero za B za avareji.
3. Kupanga Kugawa kwa Bootstrap
Mwa kuphatikiza ziwerengero zonse zowerengedwa kuchokera ku zitsanzo za B bootstrap, timapanga kugawa kwa bootstrap kwa ziwerengero zomwe tikufuna. Kugawa kumeneku kumagwiritsidwa ntchito kuyerekeza kugawa kwa zitsanzo za ziwerengero.
4. Kuzindikira kwa Ziwerengero
Kuchokera ku kugawa kwa bootstrap uku, titha kupanga ziwerengero zosiyanasiyana. Mwachitsanzo, titha kudziwa nthawi yodalirika potenga ma percentiles kuchokera ku kugawa kwa bootstrap kapena kuyesa malingaliro poyang'ana mtengo wa p womwe wapezeka kuchokera ku kugawa kumeneku.
Chitsanzo cha Kugwiritsa Ntchito Njira ya Bootstrap
Kuti tipeze chithunzi chomveka bwino, tiyeni tiwone zitsanzo zina za momwe njira ya bootstrap imagwiritsidwira ntchito m'malo ogwirira ntchito.
Chitsanzo 1: Nthawi Yodzidalira Yapakati
Tiyerekeze kuti tili ndi zitsanzo za kulemera kwa thupi la anthu 10 motere: \[60, 62, 67, 70, 65, 68, 64, 60, 66, 63].
1. Kuchokera mu deta iyi, timatenga zitsanzo 1000 za bootstrap za kukula komweko, mwachitsanzo:
– Chitsanzo 1: \[62, 67, 70, 67, 64, 62, 63, 65, 68, 60\]
– Chitsanzo 2: \[60, 62, 70, 70, 63, 64, 63, 65, 68, 62\]
- ndi zina zotero…
2. Kuchokera ku chitsanzo chilichonse cha bootstrap, timawerengera avareji:
– Avereji ya chitsanzo 1: (62+67+70+67+64+62+63+65+68+60) / 10
– Avereji ya chitsanzo 2: (60+62+70+70+63+64+63+65+68+62) / 10
- ndi zina zotero…
3. Mwa kubwereza sitepe iyi ka 1000, tidzapeza zolemera zapakati pa 1000.
4. Ndi avareji ya deta iyi ya 1000, timapanga kugawa kwa bootstrap ndikutenga ma percentiles a 2.5 ndi 97.5 kuti tipange nthawi yodzidalira ya 95%.
Chitsanzo 2: Mayeso a Multiple Median Hypothesis
Tiyerekeze kuti tikufuna kuyesa ngati ma median a ma data awiri ndi ofanana. Tingagwiritse ntchito bootstrapping kuti tipange kugawa kwa kusiyana kwa ma median.
1. Tengani zitsanzo za bootstrap kuchokera ku deta iliyonse yoyambirira.
2. Werengani kusiyana kwapakati pa chitsanzo chilichonse cha bootstrap.
3. Pangani kugawa kwa kusiyana kwapakati pa bootstrap.
4. Onani ngati ziro zili mkati mwa nthawi yodalirika ya kugawa.
Ubwino ndi Zofooka za Njira ya Bootstrap
Kelebihan
– Zosagwiritsa ntchito mfundo: Sizimafuna malingaliro okhudza kugawa deta.
- Kugwira Ntchito kwa Zitsanzo Zing'onozing'ono: Kugwira Ntchito ngakhale kwa zitsanzo zazing'ono.
- Yosinthasintha: Ingagwiritsidwe ntchito pa ziwerengero zosiyanasiyana kuphatikizapo mean, median, regression coefficient, ndi zina zotero.
- Kusavuta Kugwiritsa Ntchito: Ndi kupita patsogolo kwa ukadaulo wa makompyuta, njira ya bootstrap ndi yosavuta kugwiritsa ntchito pogwiritsa ntchito mapulogalamu owerengera monga R kapena Python.
Zolepheretsa
- Mtengo wa Makompyuta: Zingafunike zinthu zambiri zamakompyuta makamaka ndi deta yayikulu kapena zitsanzo zambiri za bootstrap (B).
- Kusiyanasiyana kwa Zitsanzo: Zoyenera zokha zitsanzo zomwe zikuyimira mokwanira chiwerengero choyambirira.
– Sichiteteza ku tsankho: Ngati deta yoyambirira ili ndi tsankho, ndiye kuti zitsanzo zonse za bootstrap zidzakhala ndi tsankho lomwelo.
Mapeto
Njira ya bootstrap imapereka yankho lamphamvu komanso losinthasintha pamavuto ambiri owerengera ziwerengero. Popeza imatha kuwerengera bwino kugawa kwa ziwerengero zosiyanasiyana popanda kuganizira kugawa kulikonse, njira ya bootstrap yakhala chida chofunikira kwambiri pakusanthula deta. Ngakhale kuti ili ndi zofooka, ubwino wake nthawi zambiri umaposa mtengo wa makompyuta. Ikagwiritsidwa ntchito moyenera, njira ya bootstrap ingapereke chidziwitso chokwanira komanso cholondola pa kusanthula ziwerengero.
