n mthmtcs, sttstcs, fnnc, nd cmptr scnc, prtclrly n mchn lrnng nd nvrs prblms, rglrztn s prcss tht cnvrts th nswr f prblm t smplr n. t s ftn sd n slvng ll-psd prblms r t prvnt vrfttng.
lthgh rglrztn prcdrs cn b dvdd n mny wys, th fllwng dlntn s prtclrly hlpfl:
xplct rglrztn s rglrztn whnvr n xplctly dds trm t th ptmztn prblm. Ths trms cld b prrs, pnlts, r cnstrnts. xplct rglrztn s cmmnly mplyd wth ll-psd ptmztn prblms. Th rglrztn trm, r pnlty, mpss cst n th ptmztn fnctn t mk th ptml sltn nq.
mplct rglrztn s ll thr frms f rglrztn. Ths nclds, fr xmpl, rly stppng, sng rbst lss fnctn, nd dscrdng tlrs. mplct rglrztn s ssntlly bqts n mdrn mchn lrnng pprchs, ncldng stchstc grdnt dscnt fr trnng dp nrl ntwrks, nd nsmbl mthds (sch s rndm frsts nd grdnt bstd trs).
n xplct rglrztn, ndpndnt f th prblm r mdl, thr s lwys dt trm, tht crrspnds t lklhd f th msrmnt, nd rglrztn trm tht crrspnds t prr. By cmbnng bth sng Bysn sttstcs, n cn cmpt pstrr, tht nclds bth nfrmtn srcs nd thrfr stblzs th stmtn prcss. By trdng ff bth bjctvs, n chss t b mr lgnd t th dt r t nfrc rglrztn (t prvnt vrfttng). Thr s whl rsrch brnch dlng wth ll pssbl rglrztns. n prctc, n slly trs spcfc rglrztn nd thn fgrs t th prbblty dnsty tht crrspnds t tht rglrztn t jstfy th chc. t cn ls b physclly mtvtd by cmmn sns r nttn.
n mchn lrnng, th dt trm crrspnds t th trnng dt nd th rglrztn s thr th chc f th mdl r mdfctns t th lgrthm. t s lwys ntndd t rdc th gnrlztn rrr, .. th rrr scr wth th trnd mdl n th vltn st (tstng dt) nd nt th trnng dt.
n f th rlst ss f rglrztn s Tkhnv rglrztn (rdg rgrssn), rltd t th mthd f lst sqrs.