fo da linear - school of computingjeffp/teaching/foda/lnotes/foda... · 2020. 11. 23. · linear...
TRANSCRIPT
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