Daphne Koller

Inference'In'Template'Models'

Probabilis5c'Graphical'Models' Sampling'Methods'

Inference'

Daphne Koller

DBN Template Specification

Location’

Failure’

Obs’

Location

Failure

Time'slice't" Time'slice't+1"

Velocity Velocity’

Weather Weather’

Location0

Failure0

Time'slice'0"

Velocity0

Weather0

Obs0

Daphne Koller

Ground Bayesian Network

Can unroll DBN for given trajectory and run inference over ground network

Location0

Failure0

Velocity0

Weather0

Location1

Failure1

Obs1

Velocity1

Weather1

Location2

Failure2

Obs2

Velocity2

Weather2

Obs0

Daphne Koller

Difficulty

Grade Courses'c'

Intelligence

Students's'

D(c1)�

G(s1,c1)�

I(s1)� D(c2)� I(s2)�

G(s1,c2)� G(s2,c1)� G(s2,c2)�

Plate Model

Can unroll plate model for given set of objects and run inference over ground network

Daphne Koller

Belief State Tracking S1

O1

S0 S2

O2

S3

O3

Daphne Koller

Belief State Tracking S1

O1

S0 S2

O2

S3

O3

Daphne Koller

Robot Localization

o

u

o

u

(2)

o

u

... (t) (1) (0)

control signal

robot pose

sensor observation

map

S S S S

(t-1) (1) (0)

(2) (t) (1)

Daphne Koller

Robot Localization

Fox, Burgard, Thrun

Daphne Koller

Computational Issues

Location0

Failure0

Velocity0

Weather0

Location1

Failure1

Obs1

Velocity1

Weather1

Location2

Failure2

Obs2

Velocity2

Weather2

Obs0

Minimal sepset must separate future from past must involve at least all of the persistent variables

Daphne Koller

Entanglement

Location0

Failure0

Velocity0

Weather0

Location1

Failure1

Obs1

Velocity1

Weather1

Location2

Failure2

Obs2

Velocity2

Weather2

Obs0

Location3

Failure3

Obs3

Velocity3

Weather3

Daphne Koller Huang, Koller, Malik, Ogasawara, Rao, Russell, Weber, AAAI 94

LeftClr

RightClr

LatAct

Xdot

FwdAct

Ydot

Stopped

EngStat

FrontBackStat

LeftClr’

RightClr’

LatAct’

Xdot’

FwdAct’

Ydot’

Stopped’

EngStat’

FrontBackStat’

InLane InLane’

SensOK’

FYdotDiff’

FcloseSlow’

BXdot’

BcloseFast’

BYdotDiff’

Fclr’

Bclr’

LftClrSens’

RtClrSens’

TurnSignal’

XdotSens’

YdotSens’

FYdotDiffSens’

FclrSens’

BXdotDiffSens’

BclrSens’

BYdotDiffSens’

Daphne Koller

Welcome'to'Geo101&

Welcome'to'CS101&

low&/&high&easy&/&hard&

Daphne Koller

Collective Webpage Classification

...

Page Category

Word1 WordN

From-

Link ...

Page Category

Word1 WordN

To-

Logistic Links

test

set

err

or

0 0.02 0.04 0.06 0.08

0.1 0.12 0.14 0.16 0.18

CCCFCPCSFCFFFPFSPCPFPPPSSCSFSPSS

Compatibility φ(From,To) FT Classify all pages collectively, maximizing the joint label

probability

(Craven et al, Proc AAAI98; Tasker et al, UAI2002)

Daphne Koller

Summary •  Inference in template and temporal models can

be done by unrolling the ground network and using standard methods

•  Temporal models also raise new inference tasks, such as real-time tracking, which require that we adapt our methods

•  Moreover, ground network is often large and densely connected, requiring careful algorithm design and use of approximate methods

Daphne Koller

Inference'Methods'and'Evalua3on'

Probabilis3c'Graphical'Models' Summary'

Inference'

Daphne Koller

MAP vs Marginals Marginals

•  Less fragile •  Confidence in answers •  Supports decision making

•  Errors are often attenuated

MAP •  Coherent joint assignment •  More tractable model classes •  Some theoretical guarantees

•  Ability to gauge whether algorithm is working

Approximate inference

Daphne Koller

Algorithms for Marginals •  Exact inference

•  Loopy message passing

•  Sampling methods

Daphne Koller

Algorithms for MAP •  Exact inference

•  Optimization methods: – exact or approximate

•  Search-based methods (including sampling)

Daphne Koller

Factors in Approximate Inference •  Connectivity structure •  Strength of influence

•  Opposing influences

•  Multiple peaks in likelihood

Daphne Koller

So, now what? •  Identify “problem regions” in network •  Try to make inference in these regions

more exact – Larger clusters in cluster graph – Proposal moves over multiple variables – Larger “slave” in dual decomposition