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Linear regression ndeimwe yeakakosha algorithms yenzvimbo dzakawanda dzine chekuita nekuongorora data. Chikonzero cheizvi chiri pachena. Iyi iri nyore uye inonzwisisika algorithm, iyo yakakonzera kushandiswa kwayo kwakapararira kwemakumi mazhinji, kana asiri mazana emakore. Pfungwa ndeyokuti isu tinotora mutsara wekutsamira kweimwe shanduko pane seti yezvimwe zvinosiyana, uye toedza kudzoreredza kutsamira uku.
Asi chinyorwa ichi hachisi chekushandisa mutsara kudzoreredza kugadzirisa matambudziko anoshanda. Pano isu tichatarisa zvinonakidza maficha ekushandiswa kweakagoverwa algorithms kupora kwayo, iyo yatakasangana nayo pakunyora muchina wekudzidza module mu. . Idiki diki svomhu, kudzidza muchina, uye kugoverwa komputa kunogona kukubatsira iwe kufunga maitiro ekuita mutsara regression kunyangwe data rako richigoverwa muzviuru zvemanodhi.
Tiri kutaura nezvei?
Isu takatarisana nebasa rekudzoreredza kutsamira kwemutsara. Se data yekupinza, seti yemavheji ezvinonzi akazvimirira akasiyana anopihwa, rimwe nerimwe rine chekuita nehumwe kukosha kweiyo inotsamira shanduko. Iyi data inogona kumiririrwa muchimiro chematiriki maviri:
Zvino, sezvo kutsamira kuchifungidzirwa, uyezve, mutsara, isu tichanyora fungidziro yedu muchimiro chechigadzirwa chematrices (kurerutsa kurekodha, pano uye pazasi zvinofungidzirwa kuti nguva yemahara ye equation yakavanzwa kumashure. , uye koramu yekupedzisira yematrix ine mayunitsi):
Inonzwika zvakanyanya senge system yemutsara equation, handizvo? Zvinoita senge, asi kazhinji panenge pasisina mhinduro kuhurongwa hwakadaro hweequations. Chikonzero cheichi ruzha, chiripo munenge chero data chaiyo. Chimwe chikonzero chinogona kunge chiri kushaikwa kwekutsamira kwemutsara sekudaro, izvo zvinogona kurwiswa nekuunza mamwe machinjiro asina mutsara anoenderana neaya ekutanga. Chimbofunga muenzaniso unotevera:
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Uyu muenzaniso wakapfava wekudzokororwa kwemutsara unoratidza hukama hweimwe shanduko (pamwe neaxis ) kubva kune imwe shanduko (pamwe neaxis ) Kuti hurongwa hwemitsara yemitsara inoenderana nemuenzaniso uyu ive nemhinduro, mapoinzi ese anofanirwa kunge ari pamutsetse wakatwasuka wakafanana. Asi ichocho hachisi chokwadi. Asi havanyepe pamutsetse wakatwasanuka chaizvo nekuda kweruzha (kana nekuti fungidziro yehukama hwemutsara yaive isiriyo). Nekudaro, kuitira kudzoreredza hukama hwemutsara kubva kune chaiyo data, zvinowanzodikanwa kuunza imwezve fungidziro: iyo data yekupinza ine ruzha uye ruzha urwu rune. . Iwe unogona kuita fungidziro nezve mamwe marudzi ekuparadzira ruzha, asi muhuwandu hwakawanda hwezviitiko ndiko kugoverwa kwakajairika kunotariswa, izvo zvinozokurukurwa zvakare.
Maximum mukana nzira
Saka, takafungidzira kuvepo kweruzha runowanzo kugovaniswa. Chii chekuita mumamiriro ezvinhu akadaro? Panyaya iyi mumasvomhu pane uye anoshandiswa zvakanyanya . Muchidimbu, kukosha kwayo kuri mukusarudza uye kuwedzera kwayo kunotevera.
Isu tinodzokera kudzoreredza hukama hwemutsara kubva kune data neruzha rwakajairika. Ziva kuti hukama hunofungidzirwa hwemutsara ndiyo tarisiro yemasvomhu kugovera kwagara kuriko. Panguva imwecheteyo, mukana wekuti inotora imwe kukosha kana imwe, zvichienderana nekuvapo kwezvinhu zvinoonekwa , sezvinotevera:
Ngatichitsivai zvino ΠΈ Izvo zvakasiyana zvatinoda ndezvi:
Chasara kuwana vector , apo mukana uyu mukuru. Kuti uwedzere basa rakadaro, zviri nyore kutanga kutora logarithm yayo (iyo logarithm yebasa ichasvika pakakwirira panzvimbo imwechete nebasa racho pacharo):
Izvo, zvakare, zvinouya pasi pakuderedza basa rinotevera:
Nenzira, iyi inonzi nzira . Kazhinji zvese zviri pamusoro apa zvinosiiwa uye nzira iyi inongoshandiswa.
QR kuparara
Hushoma hwebasa riri pamusoro rinowanikwa nekutsvaga poindi iyo gradient yebasa iri razero. Uye iyo gradient ichanyorwa sezvinotevera:
inzira yematrix yekugadzirisa dambudziko rekudzikisa rinoshandiswa mudiki diki nzira. Panyaya iyi, tinonyora zvakare equation mune matrix fomu:
Saka tinoparadza matrix ku matrices ΠΈ uye ita shanduko dzakatevedzana (iyo QR decomposition algorithm pachayo haizotariswe pano, chete kushandiswa kwayo zvine chekuita nebasa riripo):
Matrix iri orthogonal. Izvi zvinotibvumira kubvisa basa :
Uye kana ukatsiva pamusoro , zvobva zvaita . Tichifunga izvozvo ndeyepamusoro petriangular matrix, inoita seizvi:
Izvi zvinogona kugadziriswa uchishandisa nzira yekutsiva. Element iri se , yapfuura element iri se uye zvichingodaro.
Zvakakosha kucherechedza pano kuti kuoma kweiyo algorithm inoguma nekuda kwekushandiswa kweQR decomposition yakaenzana . Uyezve, zvisinei nekuti iyo matrix yekuwedzera mashandiro akanyatsoenderana, hazvigoneke kunyora inoshanda yakagoverwa shanduro yealgorithm iyi.
Gradient Descent
Paunenge uchitaura nezvekuderedza basa, zvinogara zvakakodzera kuyeuka nzira ye (stochastic) gradient descent. Iyi inzira yakapfava uye inoshanda yekudzikisa yakavakirwa pakudzokorora kuverengera gradient yebasa pane imwe nzvimbo wobva waichinjisa munzira yakatarisana negradient. Nhanho imwe neimwe yakadaro inounza mhinduro pedyo nekuderera. Iyo gradient ichiri kutaridzika zvakafanana:
Iyi nzira zvakare yakanyatso enzanirana uye yakagovaniswa nekuda kweiyo mutsara zvivakwa zve gradient opareta. Ziva kuti mufomula iri pamusoro, pasi pechiratidzo chehuwandu pane mazwi akazvimirira. Mune mamwe mazwi, tinogona kuverenga gradient takazvimiririra kune ese ma indices kubva pakutanga kusvika , mukufambirana neizvi, verenga gradient ye indices ne up to . Wobva wawedzera ma gradients anoguma. Mhedzisiro yekuwedzera ichave yakafanana kana isu takabva taverenga gradient ye indices kubva kune yekutanga kusvika . Nekudaro, kana iyo data ikagoverwa pakati pezvimedu zvakati wandei zve data, gradient inogona kuverengerwa yakazvimirira pachidimbu chega chega, uyezve mhedzisiro yezviverengero izvi inogona kupfupikiswa kuti uwane yekupedzisira mhedzisiro:
Kubva pakuona kwekuita, izvi zvinoenderana neparadigm . Panhanho imwe neimwe yekudzika kwe gradient, basa rinotumirwa kune yega data node kuverenga gradient, ipapo iwo akaverengerwa gradients anounganidzwa pamwechete, uye mhedzisiro yehuwandu hwavo inoshandiswa kugadzirisa mhedzisiro.
Zvisinei nekureruka kwekuita uye kugona kuita muMepuReduce paradigm, gradient descent inewo zvinokanganisa. Kunyanya, huwandu hwematanho anodiwa kuti uwane convergence yakanyanya kukwirira zvichienzaniswa nedzimwe nzira dzakanyanya hunyanzvi.
LSQR
ndiyo imwe nzira yekugadzirisa dambudziko, iyo inokodzera zvese kudzoreredza mutsara regression uye yekugadzirisa masisitimu emutsetse equation. Chinhu chayo chikuru ndechekuti inosanganisa zvakanakira matrix nzira uye nzira yekudzokorora. Kuitwa kweiyi nzira kunogona kuwanikwa mumaraibhurari ese ari maviri uye mukati . Tsanangudzo yenzira iyi haizopiwi pano (inogona kuwanikwa muchinyorwa ) Pane kudaro, nzira icharatidzwa kugadzirisa LSQR kuurayiwa munzvimbo yakagoverwa.
Iyo LSQR nzira yakavakirwa pa . Iyi inzira yekudzokorora, imwe neimwe iteration ine matanho anotevera:
Asi kana tikafunga kuti matrix yakaganhurwa yakatwasuka, ipapo imwe neimwe iteration inogona kumiririrwa sematanho maviri MepuReduce. Nenzira iyi, zvinokwanisika kudzikisa kufambiswa kwedata panguva yega yega iteration (mavheji chete ane hurefu hwakaenzana nenhamba yezvisingazivikanwe):
Iyi ndiyo nzira inoshandiswa pakuita linear regression in .
mhedziso
Kune akawanda mutsara regression kudzoreredza algorithms, asi haasi ese anogona kuiswa mumamiriro ese. Saka QR decomposition yakanakira mhinduro chaiyo pane madiki data seti. Gradient descent iri nyore kushandisa uye inobvumidza iwe nekukurumidza kuwana mhinduro yekufungidzira. Uye LSQR inosanganisa akanakisa zvivakwa zveaviri algorithms, sezvo ichigona kugovaniswa, inochinjika nekukurumidza kana ichienzaniswa nekudzika kwegradient, uye zvakare inobvumira kumisa kwekutanga kweiyo algorithm, kusiyana neQR kuora, kuwana mhinduro.
Source: www.habr.com