steyininte udaaharanam

theerumaana sidhaanthathilum esttimeshan sidhaanthathilum, steyininte udaaharanam (steyins prathibhasam allengil steyins paradox ennum ariyappedunnu) oresamayam moonno athiladhikamo paaraamettarukal kanakkaakkumbol, sharashari kooduthal krithyathayulla samyojitha esttimettarukal (athaayath, kuranja prathekshikkunna sharashari square pishak) undenna nireekshanamaanu. 1955ll eee prathibhasam kandethiya stanford sarvakalaashaalayile chaals steyininte perilaanu ithu ariyappedunnathu.
oru "samyojitha" esttimettarinte sharashari-chathura pishak opttimais cheiyunnathu vyakthigatha paaraamettarukalude prathyeka esttimettarukalude pishakukal opttimais cheiyunnathinu thulyamalla ennathaanu oru avabodhajanyamaaya vishadeekaranam. praayogikamaayi paranjaal, samyojitha pishak yadhaarthathil thaalpparyamullathaanenkil, adisthaana paaraamettarukal swathanthramaanengilum oru samyojitha esttimettar upayogikkanam. pakaram oraalkk oru vyakthigatha paaraameettar kanakkakkaan thaalpparyamundengil, oru samyojitha esttimettar upayogikkunnathu sahayikkilla, vaasthavathil ithu kooduthal moshamaan.
aupachaarika prasthavana.
thaazhepparayunnath vairudhyathinte ettavum lalithamaaya roopamaanu, nireekshanangalude ennam kanakkaakkenda paaraamettarukalude ennathinu thulyamaaya prathyeka cases. formula _ 1 ennathu formula _ 2 anjjaatha paaraamettarukal adangiya oru vector ayirikkatte. eee paaraamettarukal kanakkakkaan, oro paaraameettar formulakkum orotta alaveduppu formula 3 nadathunnu, athinte falamaayi dairkhya formula 6-nte vekttar formula 5 undaakunnu. alavukal swathanthravum, sharashari formula 1, vyathiyaanam 1, i ennivayulla gausiyan random veriyabilukalaanennu ariyaamenn karuthuka.iii.formula _ 8. athinaal, oro paaraamettarum orotta shabda alavu upayogichu kanakkakkunnu, oro alavum thulyamaayi krithyamalla.
eee saahacharyangalil, oro alavukalum athinte anubandha paaraamettarinte oru esttimettaayi upayogikkunnathu avabodhajanyavum saadhaaranavumaanu. saadhaarana" theerumaana niyamam ennu vilikkappedunna eee formula _ 9 ennu ezhuthaam, ithu paramavadhi saadhyatha kanakkaakkunna (emm. ell. iii) aanu. atharamoru esttimettarinte gunanilavaaram alakkunnathu athinte risk functionaanu. saadhaaranayaayi upayogikkunna risk function, formula _ 10 aayi nirvachichirikkunna sharashari square eraraanu. athbhuthakaramennu parayatte, formula _ 2 aayirikkumbol sharashari square erarinte kaaryatthil "saadhaarana" theerumaana niyamam sub opttimal (asweekaarya) aanennu maarunnu. mattoru vidhathil paranjaal, ivide charcha cheytha krameekaranatthil, formula _ 1-nte moolyam enthuthanneyaayaalum "ellaayppozhum" kuranja sharashari square error nedunna badal esttimettarukal nilavilundu. oru nischitha "formula _ 1" nuu oraalkk ellaayppozhum "formula _ 1" mathramulla oru thikanja "esttimettar" nirvachikkaan kazhiyum, ennaal eee esttimettar "formula _ 1" nte mattu moolyangalkku moshamayirikkum. 
steyins paradoxinte esttimettarukal, oru nischitha "formula _ 1" nuu, chila "formula _ 5" nuu "saadhaarana" theerumaana niyamam "formula _ 5" nekkaal mikachathaanenkilum mattullavarkk theerchayaayum moshamaan. sharashari avar mikachavaraanennu maathrame parayaanaakoo. kooduthal krithyamaayi paranjaal, oru esttimettar formula _ 19 mattoru esttimettar formula _ 20-ll aadhipathyam pularthunnuvennu parayappedunnu, formula _ 1-nte ellah moolyangalkkum, formula _ 19-nte apakadasaadhyatha formula _ 20-nte apakadasaadhyathayekkaal kuravo thulyamo aanenkil, "" asamathvam eathenkilum formula _ 1-nuu karshanamaanengil. mattoru esttimettar athil aadhipathyam pularthunnillenkil oru esttimettar sveekaaryamaanennu parayappedunnu, allengil athu "asweekaaryamaanu". athinaal, steyininte udaaharanam lalithamaayi inipparayunna reethiyil prasthaavikkam "multiveriyettu gausiyan vitharanathinte sharaashariyude" saadhaarana "theerumaana niyamam sharashari square error riskinu keezhil sveekaaryamalla."
lalithavum praayogikavumaaya pala esttimettarukalum "saadhaarana" theerumaana niyamathekkaal mikacha prakadanam kaivarikkunnu. ettavum ariyappedunna udaaharanam jaims-stain esttimettaanu, athu oru prathyeka poyintilekku (uthbhavam polulla) "formula _ 5" aaa pooyintil ninnulla "formula _ 5" nte doorathinu vipareeta anupaathathil churukkunnu. eee phalatthinte thelivu varaykkaan steyinte udaaharanathinte thelivu kaanuka. oru badal thelivu laari braun moolamaanu "formula _ 6"-dimensional multiveriyettu normal meane vektarinte saadhaarana esttimettar "formula _ 6"-dimensional brouniyan chalanam aavarthichaal maathrame sveekaaryamaakoo ennu addeham theliyichu. formula _ 2-nuu brouniyan chalanam aavarthikkathathinaal, formula _ 2-nuu millie sveekaaryamalla.
avabodhajanyamaaya oru vishadeekaranam.
formula _ 1-nte eathenkilum prathyeka moolyathinu puthiya esttimettar vyakthigatha sharashari square pishakukalude formula _ 32-ll onnengilum mechappeduthum, ithu budhimuttulla kaaryamalla-udaaharanathinu, formula _ 1 −1 num 1 num edayilaanengil, "formula _ 34" aanenkil, formula _ 5-neey 0-0-0 (i) aayi rekheeyamaayi churukkunna oru esttimettar.iii.formula _ 36, threashold formula _ 37 ulla sophtt threasholding) formula _ 5 nekkaal kuranja sharashari square error undaakum. ennaal formula _ 1-nte mattu moolyangalundu, athinu eee esttimettar formula _ 5-nekkaal moshamaan. steyin esttimettarinteyum steyin paradox nalkunna mattullavarudeyum thanthram, avar shift krameekarikkunnath ellaayppozhum (eathenkilum formula _ 1 vektarinu) oru formulayengilum ulla reethiyil aanu, athinte sharashari square error mechappeduthunnu, koodaathe mattoru formula _ 43 nuu sambhavikkaanidayulla sharashari square erarile eathenkilum degradation nikathunnathinekkaal athinte mechappeduthal kooduthalaanu. prashnam, formula _ 1 ariyaathe, "formula _ 6" sharashari square erarukalil eathaanu mechappeduthiyathennu ningalkariyilla ennathaanu, athinaal ningalkk aaa paaraamettarukalkk maathram steyin esttimettar upayogikkaan kazhiyilla.
mukalil paranja krameekaranatthinte oru udaaharanam telecommunicationule chaanal esttimettil sambhavikkunnu, udaaharanathinu, vyathyastha gadakangal mothatthilulla chaanal prakadanatthe badhikkunnu. 
prathyaaghaathangal.
saadhaarana" theerumaana niyamam avabodhajanyavum saadhaaranayaayi upayogikkappedunnathumaayil steyininte udaaharanam athishayakaramaan. vaasthavathil, paramavadhi saadhyatha kanakkaakkal, mikacha leanier nishpakshamaaya kanakkaakkal, kuranja chathurangalude kanakkaakkal, opttimal ekviveriyant kanakkaakkal ennivayulppede esttimettar nirmmaanathinulla niravadhi reethikal ellaam "saadhaarana" esttimettaril kalaashikkunnu. ennirunnaalum, mukalil charcha cheythathupole, eee esttimettar sub opttimal aanu.
udaaharanam.
steyininte udaaharanathinte avabodhajanyamallaatha swabhaavam prakadippikkaan, inipparayunna yadhaartha loka udaaharanam pariganikkuka. pariganikkuka yuu. ezz gothamb vilavu, vilavu wimbledon tennies toornamentile kaanikalude ennam, soopparmaarkkattil ninnu kramarahithamayi thiranjeduttha oru candy baarinte bharam enningane bandhamillaattha moonnu maanadandangal nammal kanakkaakkumenn karuthuka. eee alavukalil oronninteyum swatantra gausiyan alavukal namukkundennu karuthuka. bandhamillaattha moonnu alavukal oresamayam upayogichu moonnu paaraamettarukalude vektarinu mikacha kanakk (sharashari) nedaan kazhiyumennu steyininte udaaharanam ippol nammodu parayunnu.
wimpledonile kaanikalude ennavum candy baarinte bharavum polulla bandhamillaattha mattu chila sthithivivarakkanakkukal alakkunnathiloode namukk enganeyengilum gothamb vilavu mikacha reethiyil kanakkakkaan kazhiyumennu aadya kaazhchayil thanne thonnunnu. ennirunnaalum, gothamb vilavu svayam oru mikacha esttimettar njangalkk labhichitilla, pakshe moonnu random veriyabilukaludeyum maarggangalude vektarinaayi njangal oru esttimettar nirmmichittundu, athu "motham" apakadasaadhyatha kuraykkunnu. vektarinte oru gadakathile mosham esttimettinte vila mattoru gadakathile mikacha esttimettu vazhi nikathappedunnathaanu ithu sambhavikkunnath. koodaathe, puthiya esttimettar upayogichu labhicha moonnu kanakkakkiya sharashari moolyangalude oru prathyeka koottam saadhaarana koottathekkaal (alanna moolyangal) mikachathaayirikkanamennilla. sharashari puthiya esttimettar maathramaan mikachathu.
rekhaachithram cheytha thelivu.
theerumaana niyama soothravaakyam _ 46-nte apakadasaadhyatha pravartthanam
ippol theerumaana niyamam pariganikkuka
ivide formula _ 51. formula _ 53 nekkaal mikacha theerumaana niyamamaan formula _ 52 ennu nammal kanikkum. risk function
- formula _ 57-leeii oru quadratic. oru pothu "nannayi perumaarunna" function formula _ 58 pariganikkunnathiloodeyum bhagangal upayogichu samyojanam upayogikkunnathiloodeyum namukk madhya padam lalithamakkaam. formula _ 59-nuu, valia formula _ 61-nuu vendathra pathukke valarunna thudarchayaayi deferentiable formula _ 60-nuu namukk undu
athinaal,
(eee phalathe steyins lemma ennu vilikkunnu.) ippol, nammal thiranjedukkunnu
formula _ 60 "nannayi perumariya" avastha paalikkukayaanenkil (athu cheiyunnilla, pakshe ithu pariharikkan kazhiyum-chuvade kaanuka), namukk undaayirikkum.
angane
thudarnnu formula _ 52-nte risk functionilekku madanguka
formula _ 57 leeii eee quadratic formula _ 51 ll minimise cheythirikkunnu,
ithu theerchayaayum formula _ 77-neey thripthippeduthunnu, formula _ 53 oru sveekaaryamallaatha theerumaana niyamamaan.
athinte upayogathe nyaayeekarikkan avasheshikkunnu
eee function formula _ 80-ll ekavachanamaayathinaal thudarchayaayi deferentiable allah. ennirunnaalum, function
ithu thudarchayaayi deferentiable aanu, beejaganitam pinthudarukayum formula _ 82 anuvadikkukayum cheytha sesham oraalkk athe phalam labikkum.

