Inhloso ye-athikili ukunikeza ukwesekwa kososayensi abaqalayo bedatha. IN Siveze izindlela ezintathu zokuxazulula isibalo sokuhlehla komugqa: isixazululo sokuhlaziya, ukwehla kwe-gradient, ukwehla kwe-stochastic gradient. Bese kuthi ngesixazululo sokuhlaziya sisebenzise ifomula . Kulesi sihloko, njengoba isihloko sibonisa, sizokuthethelela ukusetshenziswa kwale fomula noma, ngamanye amazwi, sizozitholela yona ngokwethu.
Kungani kunengqondo ukunaka kakhulu ifomula ?
Kungenxa ye-matrix equation lapho ezimweni eziningi umuntu eqala ukujwayelana nokuhlehla komugqa. Ngesikhathi esifanayo, izibalo ezinemininingwane yokuthi ifomula yatholwa kanjani azivamile.
Isibonelo, ezifundweni zokufunda ngomshini kusuka ku-Yandex, lapho abafundi bethulwa ngokujwayelekile, banikezwa ukusebenzisa imisebenzi evela kumtapo wolwazi. sklearn, kuyilapho kungashiwo igama mayelana nokumelwa kwe-matrix ye-algorithm. Kungalesi sikhathi lapho abanye abalaleli bengafuna ukuqonda kabanzi lolu daba - bhala ikhodi ngaphandle kokusebenzisa imisebenzi eseyenziwe ngomumo. Futhi ukwenza lokhu, kufanele uqale wethule i-equation nge-regulator ngendlela ye-matrix. Lesi sihloko sizovumela labo abafisa ukufunda amakhono anjalo. Ake siqale.
Izimo zokuqala
Izinkomba eziqondiwe
Sinebanga lamanani esiqondiwe. Isibonelo, inkomba eqondiwe ingaba inani lanoma iyiphi impahla: uwoyela, igolide, ukolweni, idola, njll. Ngesikhathi esifanayo, ngenani lamanani ezinkomba eziqondiwe sisho inani lokubhekwa. Ukubheka okunjalo kungaba, isibonelo, amanani entengo kawoyela njalo ngenyanga ngonyaka, okungukuthi, sizoba namanani ahlosiwe angu-12. Ake siqale ukwethula i-notation. Ake sikhombise inani ngalinye lenkomba eqondiwe njenge . Sekukonke sinakho esikuqaphelayo, okusho ukuthi singamela lokho esikuqaphelayo njenge .
Ama-Regressors
Sizothatha ngokuthi kunezici okuthi ngokwezinga elithile zichaze amanani wenkomba eqondiwe. Isibonelo, izinga lokushintshaniswa kwe-dollar/ruble lithonywa kakhulu intengo yamafutha, izinga le-Federal Reserve, njll. Izici ezinjalo zibizwa ngokuthi ama-regressors. Ngasikhathi sinye, inani lenkomba ngayinye eqondiwe kufanele lihambisane nenani le-regressor, okungukuthi, uma sinezinkomba eziyi-12 zenyanga ngayinye ngo-2018, kufanele futhi sibe namanani e-regressor angu-12 ngesikhathi esifanayo. Ake sikhombise amanani we-regressor ngayinye ngokuthi . Makube khona kithi ama-regressors (isb. izici ezinomthelela kumanani ezinkomba eziqondiwe). Lokhu kusho ukuthi ama-regressors ethu angethulwa kanje: ku-1st regressor (isibonelo, intengo kawoyela): , ye-2nd regressor (isibonelo, isilinganiso se-Fed): , Ngokuba"-th" isihlehlisi:
Ukuncika kwezinkomba eziqondiwe kuma-regressors
Ake sicabange ukuthi ukuncika kwenkomba eqondiwe kusuka kuma-regressors "th" ukubona kungavezwa ngezibalo zokuhlehla zomugqa zefomu:
kuphi - "-th" inani le-regressor ukusuka ku-1 kuye ,
- inani lama-regressors ukusuka ku-1 kuye
β ama-angular coefficients, amele inani inkomba yethagethi ebaliwe izoshintsha ngokwesilinganiso lapho isihlehli sishintsha.
Ngamanye amazwi, singawo wonke umuntu (ngaphandle ) kweregressor sinquma i-coefficient "yethu". , bese uphindaphinda ama-coefficients ngamavelu ama-regressors "th" observation, ngenxa yalokho sithola isilinganiso esithile "-th" inkomba eqondiwe.
Ngakho-ke, sidinga ukukhetha ama-coefficient anjalo , lapho amanani okusebenza kwethu okusondele izotholakala eduze ngangokunokwenzeka kumanani ezinkomba eziqondiwe.
Ukuhlola ikhwalithi yomsebenzi oseduze
Sizonquma ukuhlolwa kwekhwalithi yomsebenzi oseduze sisebenzisa indlela yezikwele ezincane kakhulu. Umsebenzi wokuhlola ikhwalithi kulesi simo uzothatha ifomu elilandelayo:
Sidinga ukukhetha amanani anjalo ama-coefficients $w$ inani lawo kuyoba encane.
Ukuguqula isibalo sibe yifomu le-matrix
Ukumelwa kweVector
Okokuqala, ukwenza impilo yakho ibe lula, kufanele unake i-linear regression equation futhi uqaphele ukuthi i-coefficient yokuqala. ayiphindaphindwa nganoma yisiphi isihlehli. Ngesikhathi esifanayo, lapho siguqulela idatha kufomu le-matrix, isimo esishiwo ngenhla sizofaka izibalo zibe nzima kakhulu. Mayelana nalokhu, kuhlongozwa ukwethula esinye isihlehliseli se-coefficient yokuqala bese ulinganisa nokukodwa. Noma kunalokho, wonke "linganisa inani le-th yalesi regressor kwelinye - emva kwakho konke, lapho iphindaphindwa ngomunye, akukho lutho oluzoshintsha kusukela ekubukeni komphumela wezibalo, kodwa ngokombono wemithetho yomkhiqizo wamatrices, ukuhlushwa kwethu izoncishiswa kakhulu.
Manje, okwamanje, ukuze senze izinto zibe lula, ake sicabange ukuthi sinenye kuphela "-th" ukubona. Bese, cabanga amanani ama-regressors "-th" ukubonwa njengevektha . I-Vector inobukhulu , okungukuthi imigqa nekholomu engu-1:
Masimele ama-coefficient adingekayo njengevekhtha , enobukhulu :
Isibalo sokuhlehla komugqa sokuthi "-th" ukubuka kuzothatha ifomu:
Umsebenzi wokuhlola ikhwalithi yemodeli yomugqa uzothatha ifomu:
Sicela uqaphele ukuthi ngokuhambisana nemithetho yokuphindaphinda kwe-matrix, besidinga ukuguqula i-vector .
Ukumelwa kwe-matrix
Njengomphumela wokuphindaphinda ama-vector, sithola inombolo: , okulindelekile. Le nombolo iwukulinganisa "-th" inkomba eqondiwe. Kodwa sidinga ukulinganisa hhayi nje inani elilodwa eliqondiwe, kodwa wonke. Ukwenza lokhu, asibhale phansi konke ""th" ama-regressors ngefomethi ye-matrix . I-matrix ewumphumela inobukhulu :
Manje isibalo sokuhlehla komugqa sizothatha ifomu:
Ake sikhombise amanani ezinkomba eziqondiwe (zonke ) ngevekhtha ngayinye ubukhulu :
Manje sesingabhala isibalo sokuhlola ikhwalithi yemodeli yomugqa ngefomethi ye-matrix:
Empeleni, kule fomula siphinde sithole ifomula eyaziwa yithi
Kwenziwa kanjani? Abakaki bayavulwa, ukuhlukaniswa kuyenziwa, izinkulumo eziwumphumela ziyaguqulwa, njll., futhi yilokhu esizokwenza manje.
Ukuguqulwa kwe-matrix
Asivule amabakaki
Ake silungiselele i-equation yokuhlukanisa
Ukuze senze lokhu, sizokwenza izinguquko ezithile. Ezibalweni ezilandelayo kuzoba lula kakhulu kithi uma ivekhtha izomelwa ekuqaleni komkhiqizo ngamunye esibalweni.
Ukuguqulwa 1
Kwenzeke kanjani? Ukuze uphendule lo mbuzo, vele ubheke osayizi bakamatikuletsheni abaphindaphindwayo futhi ubone ukuthi ekuphumeni sithola inombolo noma ngenye indlela. .
Masibhale phansi osayizi bezinkulumo ze-matrix.
Ukuguqulwa 2
Masiyibhale ngendlela efanayo nenguquko 1
Kokukhiphayo sithola isibalo okufanele sisehlukanise:
Sihlukanisa umsebenzi wokuhlola ikhwalithi yemodeli
Ake sihlukanise ngokuhlonipha i-vector :
Imibuzo ukuthi kungani akufanele kube khona, kodwa sizohlola ukusebenza kokuthola okuphuma kokunye kwezinye izinkulumo ezimbili ngokuningiliziwe.
Umehluko 1
Masinwebe ekuhlukaniseni:
Ukuze unqume okuphumayo kwe-matrix noma i-vector, udinga ukubheka ukuthi yini engaphakathi kuyo. Ake sibheke:
Ake sikhombise umkhiqizo wamatrices nge-matrix . I-Matrix isikwele futhi ngaphezu kwalokho, i-symmetrical. Lezi zakhiwo zizoba usizo kithi kamuva, masizikhumbule. I-Matrix inobukhulu :
Manje umsebenzi wethu uwukuphindaphinda kahle ama-vector nge-matrix futhi singatholi "okuphindwe kabili kabili kuya kwesihlanu," ngakho-ke masigxilise ingqondo futhi siqaphele kakhulu.
Nokho, siye sazuza inkulumo eyinkimbinkimbi! Eqinisweni, sithole inombolo - isikala. Futhi manje, empeleni, siqhubekela phambili ekuhlukaniseni. Kuyadingeka ukuthola okuphuma kokunye komusho owumphumela we-coefficient ngayinye futhi uthole i-vector yobukhulu njengokukhiphayo . Uma kwenzeka, ngizobhala phansi izinqubo ngesenzo:
1) hlukanisa nge , sithola:
2) hlukanisa nge , sithola:
3) hlukanisa nge , sithola:
Okukhiphayo yivekhtha ethenjisiwe yosayizi :
Uma ubhekisisa i-vector, uzoqaphela ukuthi izakhi ezingakwesokudla nezihambisana nesokunxele ze-vector zingaqoqwa ngendlela yokuthi, ngenxa yalokho, i-vector ingahlukaniswa nevector eyethulwe. usayizi ... Ngokwesibonelo, (isici esingakwesokunxele somugqa ophezulu we-vector) (into elungile yomugqa ophezulu we-vector) ingamelwa njenge , futhi - Kanjani njll. emgqeni ngamunye. Masihlanganise:
Masikhiphe i-vector futhi ekuphumeni sithola:
Manje, ake sibhekisise i-matrix ewumphumela. I-matrix iyisamba samatrices amabili :
Masikhumbule ukuthi ngaphambili siphawule impahla eyodwa ebalulekile ye-matrix - i-symmetrical. Ngokusekelwe kule ndawo, singasho ngokuqiniseka ukuthi le nkulumo kuyalingana . Lokhu kungaqinisekiswa kalula ngokwandisa umkhiqizo we-elementi ka-matrices nge-elementi . Ngeke sikwenze lokhu lapha; labo abanentshisekelo bangakuhlola ngokwabo.
Ake sibuyele ekuvezeni kwethu. Ngemuva kwezinguquko zethu, kuvele ngendlela ebesifuna ukukubona ngayo:
Ngakho-ke, sesiqedile ukuhlukanisa kokuqala. Ake sidlulele enkulumweni yesibili.
Umehluko 2
Asilandele indlela eshayiwe. Izoba mfishane kakhulu kunangaphambili, ngakho ungahambi kude kakhulu nesikrini.
Masinwebe ama-vector kanye ne-matrix element nge-elementi:
Ake sikususe okubili ekubaleni isikhashana - ayidlali indima enkulu, sizobe sesiyibuyisela endaweni yayo. Masiphindaphinde ama-vector nge-matrix. Okokuqala, masiphindaphinde i-matrix ku-vector , asinayo imikhawulo lapha. Sithola i-vector yesayizi :
Masenze isenzo esilandelayo - phindaphinda i-vector ku-vector ewumphumela. Ekuphumeni inombolo izobe isilindile:
Bese sizoyihlukanisa. Ekuphumeni sithola i-vector of dimension :
Ungikhumbuza okuthile? Kulungile! Lona umkhiqizo we-matrix ku-vector .
Ngakho, ukuhlukaniswa kwesibili kuqedwa ngempumelelo.
Esikhundleni isiphetho
Manje siyazi ukuthi ukulingana kwenzeka kanjani .
Ekugcineni, sizochaza indlela esheshayo yokuguqula amafomula ayisisekelo.
Ake sihlole ikhwalithi yemodeli ngokuhambisana nendlela yezikwele ezincane kakhulu:
Ake sehlukanise isisho esiwumphumela:
Izincwadi
Imithombo ye-inthanethi:
1)
2)
3)
4)
Izincwadi zokufunda, amaqoqo ezinkinga:
1) Amanothi okufundisa ngezibalo eziphezulu: izifundo ezigcwele / D.T. Ibhalwe - 4th ed. - M.: Iris-press, 2006
2) Ukuhlaziywa kokuhlehla okusetshenzisiwe / N. Draper, G. Smith - 2nd ed. β M.: Ezezimali Nezibalo, 1986 (ukuhunyushwa kusuka esiNgisini)
3) Izinkinga zokuxazulula izilinganiso ze-matrix:
Source: www.habr.com