le a'E ans.e a'Eat will explain this thin in a simpler setting Rank - - PDF document

▶
le
SMART_READER_LITE
LIVE PREVIEW

le a'E ans.e a'Eat will explain this thin in a simpler setting Rank - - PDF document

Oct 22, 2022 156 likes •229 views

Lest lecture generalized regression problem N 10,1 hlOoxi wi is n Qi Xi d Po yi a minimize Ln lol In llyiix.to t 11101 GFOM Ott's x Ff Cu at y FILO Ot X G't lo GE cu ut ut Otl y Assume Xi o N lo kn For any GFOM lot It Thin o le a'E

slide-1
SLIDE 1

Lest lecture

generalized regression problem

yi

hlOoxi wi

is n

Qi

a

d Po

Xi

N10,1

minimize Lnlol

In

llyiix.to

t 11101

GFOM

Ott's x Ff Cu at y

FILO

Ot

ut

XG't lo

Otl

GE cu

ut

y

Thin

Assume Xi

  • N lo kn

Forany GFOM lotIt

  • le

a'Eans.e

a'Eat

will explain this thin in

a simpler setting

Rank

  • ne matrixestimation

X InDOIT t I

j

W GOE n

  • .ilienTidPo

WWT.lWijliajTioiNlo.Yn

Wii i.sn idNlo21n T

minimizeLn

10

IlX thot

HIT 1110

logPolk

GEOM

Ott's XF Yo pt

40 Ot

AMP

Ott's X felon Ot

t.E.obt.sfj.to Os

ft RFK

bt.s h.FI iiCoi oI

ft lo Ot

I felt Off Eh

BayesA

MP

fth

xd EL013 0 1BeZ

xe

slide-2
SLIDE 2

Se

i

e

L

I 3

Set

LFLEC OBEOtrz.cz t

O Po

Z

Nlo l

FEamp

ft

Optamp

e.mn

ifIf

sEm 9iIqI.i

nooT

rI

Reduction Lem_V GFoMlEtJts.oFAMP

tJes.o lot Rt Rst

ft

delO

Ot

GFOM

AMP

Postprocessing

Analysis of

AMP

Thin

If

ft

Lipschitz V

ttnE.n8

  • i.o

at

Law 0 µ 0 2

k

21

Z

Zt

Po

NO Qst

Htt

El 0 felt 0 2

Me 0 21

Q ii.tt

LF

E

Fs

fs

µ 01 2 1

µ

Zs

Intel

1

a

v

v2

rect indep of X W

z

X

i

Inf

i 3

Q

then EE.si

iEinio.aTot

Xffo

Ot

D

slide-3
SLIDE 3

ft

J

J

I

are dependent

act

as if independent

Interest C

2

Po

I 8

1

1 I 8

M

Po

Ite 8 1 tf

e

8 00 Ct Q

t Q

00

CV

X

Tn

VnEn

infinite tree of degree n

Hoilien Tin Po

Xij

Doing

Wig

Nij

een

  • l N lokn

Iii

it

Message passing

u i

Izzi Xie fecwe.si

utensil

murmur meme

Fi y

O

Wem i tem EE Ti j

Doe

EE VCTi j

H nti

Em Fits e

2

Qi Ui

U

j

0 140 2 1 Mt0 27

slide-4
SLIDE 4

Optimality of Bayes AMP Sufficient to prove LB for estimation onTn

Message passing

is

a local alg

uti j

End

Xen i

m

c BiH

Optimal

local algorithm

E

E Ooi

Xen

mk

Bc.lt

Can be implemented

as

a message

passingalgorithm

Belief Propagation

Wdy shouldwe expect state evolution

Do

D

Ott'swffof.at IId f

101 Os

t s

ft

0191 Otthfty

it Wfe

Ott'tfidesfs lo

O'J Conditioning

  • n Eye

Condition

  • n

x

W fo

x

Wfl

xt wft

Xt _W ft

Xt Ix

it

Fe Lfo ft I

t

Wl

g

PENTTI 1 Ethel Stt

rank _n t

M

X t.FI

gttldp.tw

P ftt Mke El ft

Fide f

WTPt

Ed

f

Ident

slide-5
SLIDE 5

f

I

e