Automated Reasoning with Graphical models Rina Dechter Bren school of ICS University of California Irvine ICS 90 November 2016 Agenda My work in AI How did I get to AI 2 ICS90 2016 Knowledge representation and Reasoning ID: 572957
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Slide1
Artificial Intelligence in UC-Irvine:Automated Reasoning with Graphical models
Rina DechterBren school of ICSUniversity of California, Irvine
ICS 90
November 2016Slide2
AgendaMy work in AIHow did I get to AI?
2ICS-90, 2016Slide3
Knowledge representation and Reasoning3
Represent knowledge
Machine learning
Modeling knowledge
Knowledge
acquisition
Reason about the knowledge
Answer queries
Makes decisions
Executes actions
ICS-90, 2016Slide4
4Artificial Intelligence Tasks
Areas:1. Automated theorem proving2. Planning and Scheduling3. Machine Learning4. Robotics5.
Diagnosis/place recognition6. Explanation
Frameworks:
1. Propositional Logic
2. Constraint Networks
3. Belief Networks
4. Markov Decision Processes
Graphical ModelsSlide5
5Artificial Intelligence Tasks
Areas:1. Automated theorem proving2. Planning and Scheduling3. Machine Learning4. Robotics5. Diagnosis
6. Explanation Frameworks:
1. Propositional Logic
2. Constraint Networks
3. Belief Networks
4. Markov Decision Processes
Graphical ModelsSlide6
Sample Applications for Graphical ModelsICS-90, 2016
6Slide7
Sample Applications for Graphical Models
Learning, Modeling, Representation
Reasoning
ICS-90, 2016
7Slide8
Sudoku –
Constraint Satisfaction
Each row, column and major block must be alldifferent
“Well posed” if it has unique solution:
27 constraints
2 3
4 6
2
Variables
: empty slots
Domains
= {1,2,3,4,5,6,7,8,9}
Constraints
:
27 all-different
Constraint
Propagation
Inference
ICS-90, 2016
8Slide9
A B
red green
red yellow
green red
green yellow
yellow green
yellow red
Map coloring
Variables: countries (A B C etc.)
Values: colors (
red
green
blue
)
Constraints:
C
A
B
D
E
F
G
Constraint Networks
Constraint graph
A
B
D
C
G
F
E
Task: find a solution
Count solutions, find a good one
ICS-90, 2016
9Slide10
Constrained OptimizationICS-90, 2016
10Slide11
Combinatorial Optimization
Planning & SchedulingComputer Vision
Find an optimal schedule for the satellitethat maximizes the number of photographstaken, subject to on-board recording capacity
Image classification: label pixels in
an image by their associated object class
[He et al. 2004; Winn et al. 2005]
ICS-90, 2016
11Slide12
Constraint Optimization Problemsfor Graphical Models
A
B
D
Cost
1
2
3
3
1
3
2
2
2
1
3
0
2
3
1
0
3
1
2
5
3
2
1
0
G
A
B
C
D
F
Primal graph
=
Variables
--> nodes
Functions, Constraints - arcs
f(A,B,D) has scope {A,B,D}
F(a,b,c,d,f,g)= f1(a,b,d)+f2(d,f,g)+f3(b,c,f)
ICS-90, 2016
12Slide13
Big Part of Reasoning is Diagnosis13
Diagnosis: What has happened here?We want to understand, to make sense from the environmentWe want to do “plan recognition”ICS-90, 2016
Two student carry a book and walk…
A student is looking into another student notebookSlide14
ICS-90, 201614
Application: circuit diagnosisProblem: Given a circuit and its unexpected output, identify faulty components. The problem can be modeled as a constraint optimization problem and
solved…somehow. Slide15
ICS-90, 201615
Probabilistic Inference smoking
A
S
T
V
X
D
B
C
tuberculosis
X-ray
visit to Asia
Lung cancer
bronchitis
dyspnoea
(shortness of breath)
abnormality
in lungs
Query: P(T = yes | S = no, D = yes) = ?
medical
diagnosisSlide16
ICS-90, 2016
16Slide17
ICS-90, 201617
Monitoring Intensive-Care PatientsThe “alarm” network - 37 variables, 509 parameters (instead of 237)
PCWP
CO
HRBP
HREKG
HRSAT
ERRCAUTER
HR
HISTORY
CATECHOL
SAO2
EXPCO2
ARTCO2
VENTALV
VENTLUNG
VENITUBE
DISCONNECT
MINVOLSET
VENTMACH
KINKEDTUBE
INTUBATION
PULMEMBOLUS
PAP
SHUNT
ANAPHYLAXIS
MINOVL
PVSAT
FIO2
PRESS
INSUFFANESTH
TPR
LVFAILURE
ERRBLOWOUTPUT
STROEVOLUME
LVEDVOLUME
HYPOVOLEMIA
CVP
BPSlide18
18
Example: Car DiagnosisICS-90, 2016Slide19
19 Example: Printer Troubleshooting
ICS-90, 2016Slide20
Bayesian Networks: Representation(Pearl, 1988)
P(S, C, B, X, D) = P(S) P(C|S) P(B|S) P(X|C,S) P(D|C,B)
lung Cancer
Smoking
X-ray
Bronchitis
Dyspnoea
P(D|C,B)
P(B|S)
P(S)
P(X|C,S)
P(C|S)
CPD:
C B P(D|C,B)
0 0 0.1 0.9
0 1 0.7 0.3
1 0 0.8 0.2
1 1 0.9 0.1
Belief Updating:
P (
lung cancer
=yes |
smoking
=no,
dyspnoea
=yes ) = ?
Most probable explanation (mpe)
ICS-90, 2016
20Slide21
2 1
? ?
? ?
A a
B b
A A
B b
3
4
A | ?
B | ?
? ?
?
?
5
6
A | a
B | b
6 individuals
Haplotype:
{2, 3}
Genotype
: {6}
Unknown
Linkage Analysis
ICS-90, 2016
21Slide22
ICS-90, 201622
Bayesian Network for RecombinationS23m
L
21f
L
21m
L
23m
X
21
S
23f
L
22f
L
22m
L
23f
X
22
X
23
S
13m
L
11f
L
11m
L
13m
X
11
S
13f
L
12f
L
12m
L
13f
X
12
X
13
y
3
y
2
y
1
Locus 1
Locus 2
P(e|
Θ
) ?
Deterministic relationships
Probabilistic relationshipsSlide23
23
L
11m
L
11f
X
11
L
12m
L
12f
X
12
L
13m
L
13f
X
13
L
14m
L
14f
X
14
L
15m
L
15f
X
15
L
16m
L
16f
X
16
S
13m
S
15m
S
16m
S
15m
S
15m
S
15m
L
21m
L
21f
X
21
L
22m
L
22f
X
22
L
23m
L
23f
X
23
L
24m
L
24f
X
24
L
25m
L
25f
X
25
L
26m
L
26f
X
26
S
23m
S
25m
S
26m
S
25m
S
25m
S
25m
L
31m
L
31f
X
31
L
32m
L
32f
X
32
L
33m
L
33f
X
33
L
34m
L
34f
X
34
L
35m
L
35f
X
35
L
36m
L
36f
X
36
S
33m
S
35m
S
36m
S
35m
S
35m
S
35m
Linkage Analysis: 6 People, 3 Markers
Modeling: coming up with the Bayesian network
Reasoning: finding the most likely location of a Gene by an Algorithm
ICS-90, 2016Slide24
ICS-90, 201624
xk-1
zk-1
z
k
x
k
Time k-1
Time k
x=<location, velocity>
GPS reading z
Cookie Reading y
r
k-1
r
k
g
k-1
g
k
Goal g
Route taken by the person r
The
Probabilistic Activity Model
w
k
w
k-1
d
k-1
d
k
Time-of-day d
Day-of-week w
Liao et al (2004), Gogate and Dechter (2005)
Modeling = LearningSlide25
ICS-90, 201625
Example of Route
Route Seen
Route Predicted
Grocery storeSlide26
ICS-90, 201626
Automated reasoning tasksPropositional satisfiability Constraint satisfactionPlanning and scheduling
Probabilistic inference Decision-theoretic planningEtc.
Reasoning is
NP-hard
Approximations Slide27
27
Sample Domains for Graphical MoldelsWeb Pages and Link AnalysisLinkage analysisCommunication Networks (Cell phone Fraud Detection)
Natural Language Processing (e.g. Information Extraction and Semantic ParsingObject Recognition and Scene Analysis
Battle-space Awareness
Epidemiological Studies
Citation Networks
Geographical Information Systems
Intelligence Analysis (Terrorist Networks)
Financial Transactions (Money Laundering)
Computational Biology
…
ICS-90, 2016
27Slide28
Complexity of Automated ReasoningConstraint satisfactionCounting solutions
Combinatorial optimizationBelief updatingMost probable explanation Decision-theoretic planning
Reasoning is
computationally hard
Complexity is
Time and space(memory)
ICS-90, 2016
28Slide29
ICS-90, 201629
Handling complex tasksIdentifying tractable structuresApproximationsUsing dependency graph structureStructure inherent in relationships.Slide30
30 A Road Map
Methods
Tasks
ICS-90, 2016Slide31
31
OverviewWhat are graphical modelsExact Algorithms: Inference and Search
Approximate algorithms: mini-bucket, belief propagation, constraint propagation
AND/OR search for combinatorial optimization
Current focus:
AND/OR search and Compilation
Approximation by Sampling and belief propagation
ICS-90, 2016
31Slide32
Distributed Belief Propagation
1
2
3
4
4
3
2
1
5
5
5
5
5
How many people?
The essence of belief propagation is to make global information be shared locally by every entity
ICS-90, 2016
32Slide33
Sudoku –
Constraint Satisfaction
Each row, column and major block must be alldifferent
“Well posed” if it has unique solution:
27 constraints
2 3
4 6
2
Variables
: empty slots
Domains
= {1,2,3,4,5,6,7,8,9}
Constraints
:
27 all-different
Constraint
Propagation
Inference
ICS-90, 2016
33Slide34
Constraint PropagationSound
Incomplete Always converges (polynomial)
A
B
C
D
3
2
1
A
3
2
1
B
3
2
1
D
3
2
1
C
<
<
<
=
A < B
1
2
2
3
A < D
1
2
2
3
D < C
1
2
2
3
B = C
1
1
2
2
3
3
ICS-90, 2016
34Slide35
Distributed Belief Propagation
Causal support
Diagnostic support
ICS-90, 2016
35Slide36
Loopy Belief Propagation
ICS-90, 2016
36Slide37
A
AB
AC
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
A
P(A)
1
.2
2
.5
3
.3
…
0
A
B
P(B|A)
1
2
.3
1
3
.7
2
1
.4
2
3
.6
3
1
.1
3
2
.9
…
…
0
A
B
D
P(D|A,B)
1
2
3
1
1
3
2
1
2
1
3
1
2
3
1
1
3
1
2
1
3
2
1
1
…
…
…
0
D
F
G
P(G|D,F)
1
2
3
1
2
1
3
1
…
…
…
0
B
C
F
P(F|B,C)
1
2
3
1
3
2
1
1
…
…
…
0
A
C
P(C|A)
1
2
1
3
2
1
…
…
0
A
1
2
3
A
B
1
2
1
3
2
1
2
3
3
1
3
2
A
B
D
1
2
3
1
3
2
2
1
3
2
3
1
3
1
2
3
2
1
D
F
G
1
2
3
2
1
3
B
C
F
1
2
3
3
2
1
A
C
1
2
3
2
A
A
B
A
C
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
Belief network
Flat constraint network
Flattening the Bayesian Network
ICS-90, 2016
37Slide38
A
B
P(B|A)
1
2
>0
1
3
>0
2
1
>0
2
3
>0
3
1
>0
3
2
>0
…
…
0
A
B
1
2
1
3
2
1
2
3
3
1
3
2
A
h
1
2
(A)
1
>0
2
>0
3
>0
…
0
B
h
1
2
(B)
1
>0
2
>0
3
>0
…
0
B
h
1
2
(B)
1
>0
3
>0
…
0
A
1
2
3
B
1
2
3
B
1
3
Updated belief:
Updated relation:
A
B
Bel
(A,B)
1
3
>0
2
1
>0
2
3
>0
3
1
>0
…
…
0
A
B
1
3
2
1
2
3
3
1
A
AB
AC
ABD
BCF
DFG
B
4
5
3
6
2
B
D
F
A
A
A
C
1
Belief Zero Propagation = Arc-Consistency
ICS-90, 2016
38Slide39
A
P(A)
1
.2
2
.5
3
.3
…
0
A
C
P(C|A)
1
2
1
3
2
1
…
…
0
A
B
P(B|A)
1
2
.3
1
3
.7
2
1
.4
2
3
.6
3
1
.1
3
2
.9
…
…
0
B
C
F
P(F|B,C)
1
2
3
1
3
2
1
1
…
…
…
0
A
B
D
P(D|A,B)
1
2
3
1
1
3
2
1
2
1
3
1
2
3
1
1
3
1
2
1
3
2
1
1
…
…
…
0
D
F
G
P(G|D,F)
1
2
3
1
2
1
3
1
…
…
…
0
A
A
B
A
C
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
Flat Network - Example
ICS-90, 2016
39Slide40
A
P(A)
1
>0
3
>0
…
0
A
C
P(C|A)
1
2
1
3
2
1
…
…
0
A
B
P(B|A)
1
3
1
2
1
>0
2
3
>0
3
1
1
…
…
0
B
C
F
P(F|B,C)
1
2
3
1
3
2
1
1
…
…
…
0
A
B
D
P(D|A,B)
1
3
2
1
2
3
1
1
3
1
2
1
3
2
1
1
…
…
…
0
D
F
G
P(G|D,F)
2
1
3
1
…
…
…
0
A
A
B
A
C
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
IBP Example – Iteration 1
ICS-90, 2016
40Slide41
A
P(A)
1
>0
3
>0
…
0
A
C
P(C|A)
1
2
1
3
2
1
…
…
0
A
B
P(B|A)
1
3
1
3
1
1
…
…
0
B
C
F
P(F|B,C)
3
2
1
1
…
…
…
0
A
B
D
P(D|A,B)
1
3
2
1
3
1
2
1
…
…
…
0
D
F
G
P(G|D,F)
2
1
3
1
…
…
…
0
A
A
B
A
C
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
IBP Example – Iteration 2
ICS-90, 2016
41Slide42
A
P(A)
1
>0
3
>0
…
0
A
C
P(C|A)
1
2
1
3
2
1
…
…
0
A
B
P(B|A)
1
3
1
…
…
0
B
C
F
P(F|B,C)
3
2
1
1
…
…
…
0
A
B
D
P(D|A,B)
1
3
2
1
3
1
2
1
…
…
…
0
D
F
G
P(G|D,F)
2
1
3
1
…
…
…
0
A
A
B
A
C
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
IBP Example – Iteration 3
ICS-90, 2016
42Slide43
A
P(A)
1
1
…
0
A
C
P(C|A)
1
2
1
3
2
1
…
…
0
A
B
P(B|A)
1
3
1
…
…
0
B
C
F
P(F|B,C)
3
2
1
1
…
…
…
0
A
B
D
P(D|A,B)
1
3
2
1
…
…
…
0
D
F
G
P(G|D,F)
2
1
3
1
…
…
…
0
IBP Example – Iteration 4
A
A
B
A
C
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
ICS-90, 2016
43Slide44
A
P(A)
1
1
…
0
A
C
P(C|A)
1
2
1
…
…
0
A
B
P(B|A)
1
3
1
…
…
0
B
C
F
P(F|B,C)
3
2
1
1
…
…
…
0
A
B
D
P(D|A,B)
1
3
2
1
…
…
…
0
D
F
G
P(G|D,F)
2
1
3
1
…
…
…
0
A
B
C
D
F
G
Belief
1
3
2
2
1
3
1
…
…
…
…
…
…
0
IBP Example – Iteration 5
A
A
B
A
C
AB
D
BC
F
DF
G
B
4
5
3
6
2
B
D
F
A
A
A
C
1
ICS-90, 2016
44Slide45
AgendaMy work in AIHow did I get to AI?BSc. in Math and Statistics: (Israel, HUJI 1973)MS. Applied math: (Israel, in Weitzman Institute, 1975 )
I stayed in math because I was afraid of programming PHD. CS, UCLA, 1985Started in Computer networks… more theory (Kleinrock, the father of the internet)Then was fascinated by the vision of AI … overcame my fear of (some) programming.
45ICS-90, 2016Slide46
My WorkConstraint networks: Graph-based parameters and algorithms for constraint satisfaction, tree-width and cycle-
cutset, summarized in “Constraint Processing”, Morgan Kaufmann, 2003Probabilistic networks: Transferring these ideas to Probabilistic network, helping unifying the principles.
Current work: Mixing probabilistic and deterministic network
ICS-90, 2016
46Slide47
Thank youAutomated Reasoning Group
Dan Frost
Eddie
Schwalb
Kalev
Kask
Irina
Rish
Bozhena
Bidyuk
Robert
Mateescu
Radu
Marinescu
Vibhav
Gogate
Emma
Rollon
Lars
Otten
Natalia
Flerova
Andrew
Gelfand
William Lam
Junkyu
Lee
Filjor
BrokaSlide48
Students’s Thesis and current projectsVibhav
Gogate, 2009: Sampling algorithms for probabilistic graphical models with determinism, 2009Radu Marinescu, 2008: AND/OR search strategies for combinatorial Optimization in Graphical models, 2008.
Robert Mateescu, 2007: AND/OR search spaces for Graphical Models, 2007
Bozhena
Bidyuk
, 2006
: Exploiting graph-
cutset
for Sampling-based approximations in Bayesian networks, 2006
Kalev
Kask
, 2001
: Approximation algorithms for graphica models,
Irina Rish, 1999
: Efficient Reasoning in Graphical Models, 1999Eddie Schwalb, 1998: Temporal reasoning with Constraints, 1998.
Dan Frost, 1997: Algorithms and Heuristics for Constraint Satisfaction Problems
Current Projects:Lars Otten: Exploring Parallelism in Graphical modelsEmma Rollon: Developing bounds for
liklihood
computation
Kalev
Kask
: Using
diskspace
for reasoning
Applications: Linkage analysis, learning driving patterns from
GPS data
48
ICS-90, 2016Slide49
The EndThank You Slide50
Iterative (Loopy) Belief ProapagationBelief propagation is exact for poly-trees
IBP - applying BP iteratively to cyclic networksNo guarantees for convergence
Works well for many coding networks
ICS-90, 2016
50Slide51
BP on Loopy GraphsPearl (1988): use of BP to loopy networks
McEliece, et. Al 1988: IBP’s success on coding networks Lots of research into convergence … and accuracy (?), but:Why IBP works well for coding networksCan we characterize other good problem classes
Can we have any guarantees on accuracy (even if converges)
ICS-90, 2016
51Slide52
Artificial Intelligence in UC-Irvine:Automated Reasoning with Graphical models
Rina DechterBren school of ICSUniversity of California, Irvine
Students and
Collaborators
:
Natasha
Fllerova
William Lam
Kalev
Kask
Bozhena
BidyukRadu Marinescu,
Robert MateescuVibhav
GogateLars OttenDavid Larkin
Eddie SchwalbIrina RishDan Frost
ICS 90
February 2014Slide53
The Turing Test(Can Machine think? A. M. Turing, 1950)
RequiresNatural languageKnowledge representationAutomated reasoningMachine learning (vision, robotics) for full test
ICS-90, 2016
53Slide54
Judea Pearl: Turing Award, 2011Slide55
Combinatorial Auctions ExampleBIDSB1 = {1, 2, 3, 4}B2 = {2, 3, 6}B3 = {1, 4, 5}
B4 = {2, 8}B5 = {5, 6}PRICESP1 = 8P2 = 6P3 = 5P4 = 2P5 = 2
Constraint Optimization Problem
Variables
:
b
1
, b
2
, b
3
, b
4
, b
5
(i.e., bids)
Domains
: {0, 1}
Constraints: R12, R
13
, R
14
, R
24
, R
25
, R
35
Cost
functions
:
r(b
1
), r(b
2
), r(b
3
), r(b
4
), r(b
5
)
TASK: Find a non-conflicting set of bids with maximum total profit
ICS-90, 2016
55Slide56
Combinatorial Optimization
CommunicationsBioinformatics
Assign frequencies to a set of radio linkssuch that
interferencies
are minimized
Find a joint haplotype configuration for
all members of the pedigree which
maximizes the probability of data
ICS-90, 2016
56