d.IO CitxTxD2 Cx5 CxY Old linear time better than OCdD Products - - PDF document

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d.IO CitxTxD2 Cx5 CxY Old linear time better than OCdD Products - - PDF document

of as HI tt It t XOR Tinear WT X predictor WT cffx E feature expansion Feature Expansion e Rd Quadratic Expansion x Xi XI DIX EXd I Exa x IX Xz DIX Xz d2Xd i.X d.IO CitxTxD2 Cx5 CxY Old linear time better than OCdD Products of


slide-1
SLIDE 1
  • f

as

HI

tt t It

XOR

Tinear

predictor

WT X

WT cffx

E feature expansion

Feature

Expansion

x

eRd

Quadratic Expansion

x

I

DIX Exa

EXd

Xi

XI

IX Xz DIX Xz d2Xdi.X

d.IO

Cx5

CxY

CitxTxD2

betterthan OCdD

Old

linear time Products of

all

subsets

Cx

Its

X2 SEED

X Xie

Xd

XX

Xd iXD

Xi XD

c ped

d

slide-2
SLIDE 2

465

It citing

D

How hard

f

Old Old time

465

expf HIEI

Gaussian kernel

44

per

Old linear

lnxER.EC

exptI

EzfEI

kernel A

kernel

function

K XXX

R

is

a

symmetric

function

such that

for any

Xi

XnEX

the

Gram

matrix

G

JEqiir

klx.mx

is

positive

semidefinite

I

IRn

How

to

show

KC

is

a kernel

Easy way

Find

  • f

mapping

such that

I

kCxxD

new features

similarity measure

C

slide-3
SLIDE 3

implies

the

definition

Gig

dCxi5dCxg

G

E'Io

Io

Axis

xD P.s.cl

tf

GTE off

Io 8 220

Examples

Ktx x

Xix

when is

this useful

need

Polynomial

kcx.xj

CI xtx.dk

Gaussian Kerney

Radial Basis Function

RBF

z

kCxixD

exp

t

282

  • ther

examples

in the

note

Dual

SVM

maax

Zai

I fea

8

9

Exp

S't

OE The C

KCxing

For RBF

w

lives

in

Pf

w't EI Yi Xi okra

slide-4
SLIDE 4

For

a

new

test point

X

wittol

Ii

y

1 fxz54td

kcx.mx

kerned

c

7

similarity Build

new

kernels from old kernels

ktx.yj

ckf.my

for

c

so

k

kernel

Klay

Kathy

t Kday

If

ker.no

EkCx.y1

kcCx.y kafx.y

  • ther

examples

in notes

kernTRidgeRgessin

I

beD

Ridge Reg

if

CATA

XIN A b

Alternative

form

i

GIFHAIYAT

foerenaoteproof

AT CGT AID

to

GEIR

Gigs

Xj

I

slide-5
SLIDE 5

ii

ATCGIE.iq

tE0GaToag

v w

Atv

Ziva Xi

New

test

point

X

prediction

xtid

EV.x

X.am

I

01651

kcx.x.jo

lx5ii

Z VioCxTofk

taxi