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