ps 57 Machne Leann School of EES Washnon Sae Unves ps 57 - Machne Leann
Assume nsances of classes ae lneal sepaable Esmae paamees of lnea dscmnan If ( - -) > hen + Else - ps 57 - Machne Leann
lassfcaon (K classes) choose f ( ) K ma ( ) Lkelhood-based classfcaon Esmae pos ( ) and lkelhoods p( ) Defne () n ems of he poseos ( ) ( ) Reques knolede of pes of denses ps 57 - Machne Leann 3
Dscmnan-based classfcaon Lean model of boundaes beeen classes, nsead of denses of bounded eons ( ) Whee ae model paamees of he bounda ps 57 - Machne Leann 4
Smple Reques onl O(d) space o soe and O(d) me fo classfcaon Weh ndcaes mpoance of feaue lnea model befoe n moe complcaed model, d ps 57 - Machne Leann 5
If lnea model nsuffcen, could consde hhe-ode dscmnans Moe me and space equemens Ma ovef (bas/vaance dlemma) Alenave: lnea model of non-lnea feaues z, z, z3, z4, z5 Ne feaues z compse bass funcons k () ps 57 - Machne Leann 6
Weh veco defnes a hpeplane dvdn he nsance space no o eons f hoose ohese ps 57 - Machne Leann 7
K > classes Lean one hpeplane fo each class sepaan fom all ohe classes, hoose f K ma ps 57 - Machne Leann 8
Lean one hpeplane fo each pa of classes K(K-)/ hpeplanes, don' cae hoose, f mamzes, o f f ohese ps 57 - Machne Leann 9
If p( ) ~ N(, Σ), hen, hee, Σ, and ( ) can be esmaed fom he daa o class case: o-class case: 5 and / /.5 f choose Odds of Lo odds of, o ps 57 - Machne Leann ohese and,
Fo o nomal classes h common covaance ma, s lnea p p / / / / / ep / ep d d p hee ps 57 - Machne Leann
Invese of s he sc o smod funcon smod ep and can be esmaed fom he daa (see pevous slde) Smod ansfoms dscmnan value o a poseo pobabl ps 57 - Machne Leann
Losc (Smod) funcon an ehe alculae ()= +, choose f () > alculae =smod( + ), choose f >.5 ps 57 - Machne Leann 3
Dscmnan-based classfcaon seeks mnmzn eo E(X) on ann se X * a mn E ( X ) Use eave opmzaon mehod aden descen o fnd When E() s dffeenable, compue aden veco E E E E,,..., d ps 57 - Machne Leann 4
Sa h andom Updae n he oppose decon of he aden veco E, Dsance of updae deemned b sep sze (o leann faco) ɳ onnue updae unl aden s zeo Ma be a local mnmum ps 57 - Machne Leann 5
E ( ) E, E ( + ) + η ps 57 - Machne Leann 6
Deve a dffeenable eo funcon o-class: Assume lkelhood ao s lnea p o p p p p o hee o hee ˆ ps 57 - Machne Leann 7 ep
o-class case ( = o ): ~ Benoull, X ep X l E l, X oss Enop E, X ps 57 - Machne Leann 8
ann n -class case: Gaden descen d E, X E da d a smod If E E d,...,, ps 57 - Machne Leann 9
ann n -class case: Gaden descen Inal ehs andom and nea zeo Avods ovefn due o usn elevan feaues = ps 57 - Machne Leann
Evoluon of flne and smod a,, and eaons ps 57 - Machne Leann
K ) (, ~ Mul, X o K p p Le K be efeence class K K,...,, ep ep ˆ Sofma l, X E, X ps 57 - Machne Leann
ps 57 - Machne Leann 3
ps 57 - Machne Leann 4
=== lassfe model (full ann se) === SmpleLosc: lass : 9.99 + [peallenh] * -9.9696 + [pealdh] * -5.7 lass : -6.5 + [sepallenh] *.67 + [sepaldh] *.8 + [peallenh] * -.74 + [pealdh] * -.8 98.67% accuac ( msakes) lass : -34.94 + [sepallenh] * -.4 + [sepaldh] * -3.76 + [peallenh] h] * 6.7 + [pealdh] *.89 ps 57 - Machne Leann 5
Assume classes can be sepaaed b a hpeplane Even f no lneal-sepaable, can sll fnd a ood lnea dscmnan Gaden descen used o lean ehs defnn hpeplanes Losc dscmnaon ps 57 - Machne Leann 6