Chinangwa chechinyorwa ndechekupa rutsigiro kune kutanga data masayendisiti. IN Takatsanangura nzira nhatu dzekugadzirisa mutsara wekudzoreredza equation: analytical mhinduro, gradient descent, stochastic gradient descent. Zvadaro kune mhinduro yekuongorora takashandisa fomula . Muchinyorwa chino, sezvinoratidzwa nemusoro, tichapembedza kushandiswa kwefomula iyi kana, nemamwe mazwi, tichazvitora isu pachedu.
Sei zvine musoro kubhadhara zvakanyanya kune formula ?
Iko neiyo matrix equation iyo muzviitiko zvakawanda munhu anotanga kujairana nemutsara kudzoreredza. Panguva imwecheteyo, maverengero akadzama ekuti formula yakatorwa sei haiwanzo.
Semuenzaniso, mumakosi ekudzidza muchina kubva kuYandex, kana vadzidzi vakaunzwa kunguva dzose, vanopihwa kushandisa mabasa kubva kuraibhurari. sklearn, nepo pasina izwi rinotaurwa nezve matrix inomiririra yegorgorithm. Iri panguva ino apo vamwe vateereri vangada kunzwisisa nyaya iyi zvakadzama - nyora kodhi pasina kushandisa akagadzirira-akagadzirwa mabasa. Uye kuti uite izvi, iwe unofanirwa kutanga wapa iyo equation neinojairika mune matrix fomu. Ichi chinyorwa chichabvumira avo vanoda kugona hunyanzvi hwakadaro. Ngatitangei.
Mamiriro ekutanga
Target zviratidzo
Tine huwandu hwezvatinovavarira. Semuenzaniso, iyo inotarirwa chiratidzo inogona kunge iri mutengo wechero asset: oiri, goridhe, gorosi, dhora, nezvimwe. Panguva imwecheteyo, nehuwandu hwechinangwa chechiratidzo chetsika tinoreva nhamba yekucherechedza. Kucherekedza kwakadaro kungave, semuenzaniso, mitengo yemafuta pamwedzi yegore, ndiko kuti, isu tichava negumi nembiri. Ngatitange kusuma notation. Ngatiratidze kukosha kwega kwega kwechiratidzo chetariro se . Pakazara tine kucherechedza, zvinoreva kuti tinogona kumiririra zvatinoona se .
Regressors
Isu tichafungidzira kuti pane zvinhu izvo kusvika pamwero wakati zvinotsanangura kukosha kwechiratidzo chechinangwa. Semuenzaniso, dhora / ruble exchange rate inokonzerwa zvakasimba nemutengo wemafuta, Federal Reserve rate, etc. Zvinhu zvakadaro zvinonzi regressors. Panguva imwecheteyo, kukosha kwechiratidzo chega chega kunofanirwa kuenderana neregressor kukosha, ndiko kuti, kana isu tine gumi nemaviri tarisiro zviratidzo zvemwedzi wega wega muna 12, saka isu tinofanirawo kuva negumi nemaviri regressor values ββyenguva imwe chete. Ngatiratidzei kukosha kweumwe neumwe regressor . Kwatiri ngazvivepo regressors (i.e. zvinhu zvinopesvedzera zvibodzwa zvechiratidzo). Izvi zvinoreva kuti maregressors edu anogona kuratidzwa sezvinotevera: kune 1st regressor (semuenzaniso, mutengo wemafuta): , ye2nd regressor (semuenzaniso, iyo Fed rate): , Nokuti"-th" regressor:
Kutsamira kwezvinangwa zvinotarirwa pane regressors
Ngatitorei kuti kutsamira kwechiratidzo chechiratidzo kubva ku regressors"th" kutarisa kunogona kuratidzwa kuburikidza nemutsara wekudzokorora equation yefomu:
kupi - "-th" regressor kukosha kubva pa1 kuenda ,
- nhamba ye regressors kubva pa1 kusvika
- angular coefficients, iyo inomiririra mari iyo iyo yakaverengerwa chinangwa chiratidzo ichachinja paavhareji kana regressor ichichinja.
Mune mamwe mazwi, isu tiri vemunhu wese (kunze ) yeregressor isu tinosarudza "yedu" coefficient , wobva wawedzera coefficients nemaitiro ezvidzoreso "th" kuona, semhedzisiro tinowana imwe fungidziro "-th" chinongedzo chechiratidzo.
Saka, tinofanira kusarudza coefficients akadaro , uko ukoshi hwebasa redu rekufungidzira ichave iri padyo sezvinobvira kune inotarirwa chiratidzo kukosha.
Kuongorora kunaka kweiyo approximating function
Isu tichaona iyo yemhando yekuongorora kweiyo approximating basa tichishandisa nzira shoma masikweya. Iyo yemhando yekuongorora basa mune iyi kesi inotora inotevera fomu:
Isu tinofanirwa kusarudza kukosha kwakadaro kweiyo coefficients $w$ iyo kukosha kwayo achava muduku kuna vose.
Kushandura equation kuita matrix fomu
Vector kumiririra
Kutanga, kuita kuti hupenyu hwako huve nyore, iwe unofanirwa kuterera kune mutsara regression equation uye cherechedza kuti yekutanga coefficient. haina kuwanzwa nechero regressor. Panguva imwecheteyo, kana isu tichishandura iyo data kuita matrix fomu, mamiriro ataurwa pamusoro anoomesa zvakanyanya kuverenga. Panyaya iyi, zvinokurudzirwa kuunza imwe regressor yekutanga coefficient uye kuenzanisa kune imwe. Kana kuti, zvese"enzanisa kukosha kweiyi regressor kune imwe - shure kwezvose, kana yakawedzerwa neimwe, hapana chichachinja kubva pakuona kwechigumisiro chekuverenga, asi kubva pakuona kwemitemo yezvigadzirwa zvematrices, kutambudzwa kwedu. zvichaderedzwa zvakanyanya.
Iye zvino, kwenguva, kuitira kurerutsa zvinyorwa, ngatifungei kuti tine imwe chete "-th" kuona. Zvadaro, fungidzira kukosha kwevadzori "-th" zvakaonekwa sevector . Vector ine dimension , ndizvo mitsara uye 1 column:
Ngatimirirei macoefficients anodiwa sevector , ine dimension :
Linear regression equation ye "-th" kutarisa kunotora fomu:
Basa rekuongorora kunaka kweiyo mutsara modhi richatora fomu:
Ndokumbira utarise kuti zvinoenderana nemitemo yekuwedzera matrix, isu taida kufambisa iyo vector .
Matrix anomiririra
Nekuda kwekuwanza mavheji, tinowana nhamba: , izvo zvinotarisirwa. Nhamba iyi ndiyo fungidziro "-th" chinongedzo chechiratidzo. Asi isu tinoda fungidziro ye kwete chete kukosha kwechinangwa, asi ese. Kuti tiite izvi, ngatinyore pasi zvese ""th" regressors mune matrix fomati . Iyo matrix inoguma ine dimension :
Ikozvino iyo mutsara regression equation inotora fomu:
Ngatiratidzei kukosha kwezvinotarirwa zviratidzo (ese ) per vector dimension :
Iye zvino tinogona kunyora equation yekuongorora kunaka kweiyo mutsara modhi mune matrix fomati:
Chaizvoizvo, kubva pane iyi fomula tinowana fomula inozivikanwa kwatiri
Zvinoitwa sei? Mabhuraketi anovhurwa, kusiyanisa kunoitwa, mhedzisiro yekutaura inoshandurwa, nezvimwewo, uye izvi ndizvo chaizvo zvatichaita izvozvi.
Matrix shanduko
Ngativhure mabhureki
Ngatigadzirirei equation yekusiyanisa
Kuti tiite izvi, tichaita dzimwe shanduko. Mumaverengero anotevera zvichava nyore kwatiri kana vector ichamiririrwa pakutanga kwechigadzirwa chimwe nechimwe muequation.
Shanduko 1
Zvakaitika sei? Kuti upindure mubvunzo uyu, ingotarisa hukuru hwematrices arikuwanzwa woona kuti pakubuda tinowana nhamba kana zvimwewo. .
Ngatinyore pasi hukuru hwematrix ekutaura.
Shanduko 2
Ngatiinyore nenzira yakafanana neshanduko 1
Pakubuda tinowana equation yatinofanira kusiyanisa:
Isu tinosiyanisa mhando yemhando yekuongorora basa
Ngatisiyanei nekuremekedza kune vector :
Mibvunzo kuti sei hapafanirwe kuve, asi isu tichaongorora mashandiro ekuona zvakatorwa mune mamwe maviri mataurirwo mune zvakadzama.
Musiyano 1
Ngatiwedzerei pakusiyanisa:
Kuti uone zvakabva kune matrix kana vector, unofanirwa kutarisa zviri mukati mavo. Ngatitarisei:
Ngatiratidzei chigadzirwa chematrices kuburikidza nematrix . Matrix square uyezve, ine symmetrical. Izvi zvivakwa zvichatibatsira gare gare, ngatizvirangarirei. Matrix ine dimension :
Ikozvino basa redu nderekuwanza nemazvo mavheji nematrix uye kusawana "kaviri mbiri ishanu," saka ngatitarisei uye tingwarire zvakanyanya.
Zvisinei, takawana kutaura kwakaoma kunzwisisa! Muchokwadi, isu tine nhamba - scalar. Uye zvino, zvechokwadi, tinoenderera mberi nekusiyanisa. Izvo zvinodikanwa kuti uwane kubva kune inobuda kutaura kune yega yega coefficient uye tora dimension vector sekubuda . Zvingoitika, ini ndichanyora pasi maitiro nekuita:
1) siyanisa ne , tinowana:
2) siyanisa ne , tinowana:
3) siyanisa ne , tinowana:
Iyo yakabuda ndiyo yakavimbiswa vector yehukuru :
Kana iwe ukatarisa kune vector zvakanyanya, iwe uchaona kuti kuruboshwe uye rinoenderana kurudyi zvinhu zvevheta zvinogona kuiswa mumapoka nenzira yekuti, semhedzisiro, vector inogona kuparadzaniswa kubva kune yakaratidzwa vector. saizi . Somuenzaniso, (chikamu chekuruboshwe chemutsetse wepamusoro wevector) (chinhu chakanaka chemutsetse wepamusoro wevector) inogona kumiririrwa se uye - se etc. pamutsetse wega wega. Ngatiitei boka:
Ngatitorei vector uye pakubuda kwatinowana:
Zvino, ngatitarisei zvakanyanya pamhedzisiro matrix. Iyo matrix ihuwandu hwematrices maviri :
Ngatiyeukei kuti nguva pfupi yapfuura takaona imwe yakakosha pfuma yematrix - iri symmetrical. Kubva pane iyi pfuma, tinogona kutaura nechivimbo kuti kutaura zvakaenzana . Izvi zvinogona kusimbiswa zviri nyore nekuwedzera chigadzirwa chematrices chinhu nechinhu . Hatingaite izvi pano; avo vanofarira vanogona kuzvitarisa ivo pachavo.
Ngatidzokere pakutaura kwedu. Mushure mekushandura kwedu, zvakazoitika nenzira yataida kuzviona:
Saka, tapedza kusiyanisa kwekutanga. Ngatienderei pakutaura kwechipiri.
Musiyano 2
Ngatitevere nzira yakarohwa. Ichave ipfupi zvakanyanya kupfuura yapfuura, saka usaende kure zvakanyanya kubva pachiratidziri.
Ngatiwedzerei mavheji uye matrix chinhu nechinhu:
Ngatibvisei maviri kubva pakuverenga kwechinguva - haisi kutamba basa guru, zvino tichaidzorera panzvimbo yayo. Ngatiwedzerei mavheji nematrix. Chekutanga, ngatiwedzerei matrix kuti vector , hatina zvirambidzo pano. Isu tinowana saizi vector :
Ngatiite chinotevera chiito - wedzera vector kune inoguma vector. Pakubuda nhamba ichange yakatimirira:
Zvadaro tichazvisiyanisa. Pakubuda tinowana vector ye dimension :
Kundiyeuchidza chimwe chinhu? Izvo ndizvo! Ichi ndicho chigadzirwa chematrix kuti vector .
Nokudaro, kusiyanisa kwechipiri kunopedzwa zvinobudirira.
Pane mhedziso
Iye zvino tava kuziva kuti kuenzana kwakauya sei .
Pakupedzisira, tichatsanangura nzira inokurumidza yekushandura mafomula ekutanga.
Ngationgororei kunaka kweiyo modhi zvinoenderana nediki masikwe nzira:
Ngatisiyanei chirevo chinobuda:
Literature
Nzvimbo dzeInternet:
1)
2)
3)
4)
Mabhuku, kuunganidzwa kwematambudziko:
1) Manotsi echidzidzo chepamusoro masvomhu: yakazara kosi / D.T. Yakanyorwa - 4th ed. - M.: Iris-press, 2006
2) Inoshandiswa regression analysis / N. Draper, G. Smith - 2nd ed. β M.: Finance and Statistics, 1986 (shanduro kubva kuChirungu)
3) Matambudziko ekugadzirisa matrix equations:
Source: www.habr.com