Fo DA.

Linear

L 25. Classifiers

labelsInput XCIRDTee - i. a Bn

A- E x, ,x ,

.

. . - Ayi EE - I

, -113

Goal : function g: Rd - IR

So . if Xi ,g , has g - t I

^ them gcxi ) > o

on . gcxi ) co

÷¥i¥÷÷. " sis

linear functiong : lRd→lR

×clRd x= C x" ? x

"

,. . .

xd ) )

g ( x ) = do + a x' "tax

" I mind del

= Lot ftp.x5 )mood a -

- K .- . - ra )

b. web,

w

= be 8¥,

w ; x" )

weird

= Lw,

x ) t b offset : distance from

7 origin O to classifiernormal of classifier

make unit vector

a gcxS=Lx,w > t b

④④

O-gFxzt-cw.x.su/Rdd--e⑦- 2.9 + 2. o

④ IM I - ageogdo

④ A -0

O = ( o.o . . . o )= 0.8>0

① ④

g G) 70 gcxto

How do we findw ,b⇒gw.b

-

• Bg linear regression

XEIR'd

→ I EIR" " 'd " )

I,

. = I i. x; )

Cb,w)=aelRd# ga Cx ) - La,

G. xD

Solve w/ at ( FF )"

Ey

This is optimizing C minimizing )

gso II ( gacxil - gi )

'

if increase IRg

X,

= +2

¥¥*m¥¥iµf¥s-gate IRD

- i -

toQQ-9¥penalizedfr beingclassified

too well

Bastion Welts

I ( ga ,

C x. d) = II ( t - Hi( signal = sign

¢ 91 i identity function

fiudaproxg? I ( True ) -- 1 if tlffaise) -

- O

= He of misclassified points .

Can I solve w/ gradient descent ?

NO ,not convex

no gradient .

Lossfunction-

proxyfu A

f G) =L( galas)) - EIllga.ki.gs)run = it,

lyfzi ) Zi - Gigabit" "

II. fiery film -

- HerZi = gigxlxi ) Sigala)

if go. =

- I then we want

gicxi) small co

if so - t ' lung, ÷;!,o)→ IITo

"

li⇐,gDdbgga? zit gigolo )

Dez ) = { o it

720 = yen,AS

iI if Z ! co

¥-0ZiZiEIRbi

ga Cx )

,, Himh

¥.fee - ¥

Max ( o,

I - ⇒

weed! sailediD, ai.

z! - z

o Of ER

other Loss Functions

¥÷¥i÷÷÷÷÷÷÷÷'

Solve logisticloss w/ GD

-

↳ logistician