[PPT] - Reasoning with Graphical Models Class 1 Rina Dechter Darwiche PowerPoint Presentation

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Reasoning with Graphical Models Class 1 Rina Dechter

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Darwiche chapters 1,3 Dechter‐Morgan&claypool book: Chapters 1‐2 Pearl chapter 1‐2

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Congressional Breifing: AI at UCI

Congressional Briefing, December 2019 2

Rina Dechter

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Congressional Briefing, December 2019 3

The Primary AI Challenges

Machine Learning focuses on

replicating humans learning

Automated reasoning focuses on

replicating how people reason.

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 BP

A neural network A Graphical Model

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Congressional Briefing, December 2019 4

Automated Reasoning

Lawyer Policy Maker Medical Doctor

Queries:

Prediction: what will happen?
Diagnosis: what happened?
Situation assessment: What is going on?
Planning, decision making: what to do?

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Automated Reasoning

Queries:

Prediction
Diagnosis
Situation assessment
Planning, decision making

answers

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Knowledge is huge, so How to identify what’s relevant?

Graphical Models

Congressional Briefing, December 2019

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Graphical Models

Example: diagnosing liver disease (Onisko et al., 1999)

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Automated Reasoning:

Develop methods to answer these questions.
Learning the models: from experts and data.

Congressional Briefing, December 2019

Queries:

Prediction
Diagnosis
Situation assessment
Planning, decision making

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Global Seismic Monitoring Compliance for the Comprehensive Nuclear‐Test‐Ban Treaty (CTBT) (Nimar, Russel, Sudderth, 2011)

Congressional Briefing, December 2019 8

278 monitoring stations (147 seismic)

CNTBT:A Graphical Model Application

The IDC (International Data Centers)

perates continuously and in real time,

performing signal processing

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Congressional Briefing, December 2019 9

Given: continuous waveform measurements from a global network of seismometer stations

Global Seismic Monitoring for the Comprehensive Nuclear‐Test‐Ban Treaty (Nimar, Russel, Sudderth, 2011)

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Congressional Briefing, December 2019

Input: obsreved detection Output: a bulletin listing seismic events, with

Time
Location (latitude, longitude)
Depth
Magnitude

Global Seismic Monitoring for the Comprehensive Nuclear‐Test‐Ban Treaty (Nimar, Russel, Sudderth, 2011)

Result: 60% reduction in error compared with human experts. Reasoning methods infers the most likely set of seismic events given the observed detections,

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Complexity of Automated Reasoning

Prediction
Diagnosis
Planning and scheduling
Probabilistic Inference
Explanation
Decision‐making

200 400 600 800 1000 1200 1 2 3 4 5 6 7 8 9 10 f(n) n

Linear / Polynomial / Exponential

Line ar

Reasoning is computationally hard

Complexity is exponential

Congressional Briefing, December 2019

Approximation, anytime

Bounded error

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AI Renaissance

Deep learning

– Fast predictions – “Instinctive”

Probabilistic models

– Slow reasoning – “Logical / deliberative” Tools: Tensorflow, PyTorch, … Tools: Graphical Models, Probabilistic programming, Markov Logic, …

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Text Books, Outline, Requirements

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Class page

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Outline of classes

Part 1: Introduction and Inference
Part 2: Search
Parr 3: Variational Methods and Monte‐Carlo Sampling

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E K F L H C B A M G J D ABC BDEF DGF EFH FHK HJ KLM

1 1 1 1 1 1 1 1 1 1 1 1 0101010101010101010101010101010101010101010101010101010101010101 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1

E C F D B A

1

Context minimal AND/OR search graph

A

OR AND

B

OR AND OR

E

OR

F F

AND

01

AND

0 1 C D D 01 0 1 1 E C D D 0 1 1 B E F F 0 1 C 1 E C

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Probabilistic Graphical models

Describe structure in large problems

– Large complex system – Made of “smaller”, “local” interactions – Complexity emerges through interdependence

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Probabilistic Graphical models

Describe structure in large problems

– Large complex system – Made of “smaller”, “local” interactions – Complexity emerges through interdependence

Examples & Tasks

– Maximization (MAP): compute the most probable configuration

[Yanover & Weiss 2002] [Bruce R. Donald et. Al. 2016]

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Protein Structure prediction: predicting the 3d structure from given

sequences

PDB: Protein design (backbone) algorithms enumerate a

combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC).

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Probabilistic Graphical models

Describe structure in large problems

– Large complex system – Made of “smaller”, “local” interactions – Complexity emerges through interdependence

Examples & Tasks

– Summation & marginalization

grass plane sky grass cow

Observation y Observation y Marginals p( xi | y ) Marginals p( xi | y )

and “partition function”

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e.g., [Plath et al. 2009]

Image segmentation and classification:

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Graphical models

Describe structure in large problems

– Large complex system – Made of “smaller”, “local” interactions – Complexity emerges through interdependence

Examples & Tasks

– Mixed inference (marginal MAP, MEU, …)

Test Drill Oil sale policy Test result Seismic structure Oil underground Oil produced Test cost Drill cost Sales cost Oil sales Market information

Influence diagrams &

ptimal decision‐making

(the “oil wildcatter” problem)

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e.g., [Raiffa 1968; Shachter 1986]

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In more details…

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Bayesian Networks (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)

Θ) (G, BN 

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

Posterior marginals, probability of evidence, MPE
P( D= 0) = ∑

P(S)· P(C|S)· P(B|S)· P(X|C,S)· P(D|C,B

,,,

MAP(P)= 𝑛𝑏𝑦,,, P(S)· P(C|S)· P(B|S)· P(X|C,S)· P(D|C,B) Combination: Product Marginalization: sum/max

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An early example From medical diagnosis

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Alarm network

Bayes nets: compact representation of large joint distributions

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 BP

The “alarm” network: 37 variables, 509 parameters (rather than 237 = 1011 !) [Beinlich et al., 1989]

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A B

red green red yellow green red green yellow yellow green yellow red

Example: map coloring

Variables - countries (A,B,C,etc.) Values - colors (red, green, blue) Constraints:

etc. , E D D, A B, A   

C A B D E F G

Constraint Networks

A B E G D F C

Constraint graph

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Propositional Reasoning

If Alex goes, then Becky goes:
If Chris goes, then Alex goes:
Question:

Is it possible that Chris goes to the party but Becky does not?

Example: party problem

B A  A C 

e? satisfiabl , , the Is 



   C B, A C B A theory nal propositio 

A B C

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Probabilistic reasoning (directed)

Alex is‐likely‐to‐go in bad weather
Chris rarely‐goes in bad weather
Becky is indifferent but unpredictable

Questions:

Given bad weather, which group of individuals is most

likely to show up at the party?

What is the probability that Chris goes to the party

but Becky does not?

Party example: the weather effect

P(W,A,C,B) = P(B|W) · P(C|W) · P(A|W) · P(W) P(A,C,B|W=bad) = 0.9 · 0.1 · 0.5

P(A|W=bad)=.9

W A

P(C|W=bad)=.1

W C

P(B|W=bad)=.5

W B W P(W) P(A|W) P(C|W) P(B|W) B C A

W A P(A|W) good .01 good 1 .99 bad .1 bad 1 .9

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Mixed Probabilistic and Deterministic networks

P(C|W) P(B|W) P(W) P(A|W) W B A C

Query: Is it likely that Chris goes to the party if Becky does not but the weather is bad?

PN CN

) , , | , ( A C B A bad w B C P   

A→B

C→A

B A C P(C|W) P(B|W) P(W) P(A|W) W B A C

A→B C→A

B A C

Alex is‐likely‐to‐go in bad weather Chris rarely‐goes in bad weather Becky is indifferent but unpredictable

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Example domains for graphical models

Natural Language processing

– Information extraction, semantic parsing, translation, topic models, …

Computer vision

– Object recognition, scene analysis, segmentation, tracking, …

Computational biology

– Pedigree analysis, protein folding and binding, sequence matching, …

Networks

– Webpage link analysis, social networks, communications, citations, ….

Robotics

– Planning & decision making

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Complexity of Reasoning Tasks

Constraint satisfaction
Counting solutions
Combinatorial optimization
Belief updating
Most probable explanation
Decision‐theoretic planning

200 400 600 800 1000 1200 1 2 3 4 5 6 7 8 9 10 f(n) n

Linear / Polynomial / Exponential

Linear Polynomial Exponential

Reasoning is computationally hard

Complexity is Time and space(memory)

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Tree‐solving is easy

Belief updating (sum-prod) MPE (max-prod)

CSP – consistency (projection-join) #CSP (sum-prod)

P(X) P(Y|X) P(Z|X) P(T|Y) P(R|Y) P(L|Z) P(M|Z)

) (X mZX ) (X mXZ ) (Z mZM

) (Z mZL

) (Z mMZ ) (Z mLZ ) (X mYX ) (X mXY

) (Y mTY ) (Y mYT ) (Y mRY ) (Y mYR

Trees are processed in linear time and memory

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Transforming into a Tree

By Inference (thinking)

– Transform into a single, equivalent tree of sub‐ problems

By Conditioning (guessing)

– Transform into many tree‐like sub‐problems.

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Inference and Treewidth

E K F L H C B A M G J D ABC BDEF DGF EFH FHK HJ KLM

treewidth = 4 - 1 = 3 treewidth = (maximum cluster size) - 1 Inference algorithm: Time: exp(tree-width) Space: exp(tree-width)

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Conditioning and Cycle cutset

C P J A L B E D F M O H K G N C P J L B E D F M O H K G N

A

C P J L E D F M O H K G N

B

P J L E D F M O H K G N

C Cycle cutset = {A,B,C}

C P J A L B E D F M O H K G N C P J L B E D F M O H K G N C P J L E D F M O H K G N C P J A L B E D F M O H K G N

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Search over the Cutset

A=yellow A=green B=red B=blue B=red B=blue B=green B=yellow

C K G L D F H M J E C K G L D F H M J E C K G L D F H M J E C K G L D F H M J E C K G L D F H M J E C K G L D F H M J E

Inference may require too much memory
Condition on some of the variables

A C B K G L D F H M J E

Graph Coloring problem

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Inference

exp(w*) time/space

A D B C E F

1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E C F D B A

1

Search

Exp(w*) time O(w*) space

E K F L H C B A M G J D ABC BDEF DGF EFH FHK HJ KLM A=yellow A=green B=blue B=red B=blue B=green C K G L D F H M J E A C B K G L D F H M J E C K G L D F H M J E C K G L D F H M J E C K G L D F H M J E

Search+inference: Space: exp(q) Time: exp(q+c(q)) q: user controlled

Bird's‐eye View of Exact Algorithms

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Inference

exp(w*) time/space

A D B C E F

1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E C F D B A

1

Search

Exp(w*) time O(w*) space

E K F L H C B A M G J D ABC BDEF DGF EFH FHK HJ KLM A=yellow A=green B=blue B=red B=blue B=green C K G L D F H M J E A C B K G L D F H M J E C K G L D F H M J E C K G L D F H M J E C K G L D F H M J E

Search+inference: Space: exp(q) Time: exp(q+c(q)) q: user controlled

Context minimal AND/OR search graph 18 AND nodes

A

OR AND

B

OR AND OR

E

OR

F F

AND

0 1

AND

1 C D D 0 1 1 1 E C D D 1 1 B E F F 1 C 1 E C

Bird's‐eye View of Exact Algorithms

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A D B C E F

1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E C F D B A

1

E K F L H C B A M G J D ABC BDEF DGF EFH FHK HJ KLM A=yellow A=green B=blue B=red B=blue B=green C K G L D F H M J E A C B K G L D F H M J E C K G L D F H M J E C K G L D F H M J E C K G L D F H M J E

Inference

Bounded Inference

Search Sampling

Search + inference: Sampling + bounded inference

Bird's‐eye View of Approximate Algorithms

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Context minimal AND/OR search graph 18 AND nodes

A

OR AND

B

OR AND OR

E

OR

F F

AND

0 1

AND

1 C D D 0 1 1 1 E C D D 1 1 B E F F 1 C 1 E C

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Outline

Basics of probability theory
DAGS, Markov(G), Bayesian networks
Graphoids: axioms of for inferring conditional

independence (CI)

D‐separation: Inferring CIs in graphs

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Outline

Basics of probability theory
DAGS, Markov(G), Bayesian networks
Graphoids: axioms of for inferring conditional

independence (CI)

Capturing CIs by graphs
D‐separation: Inferring CIs in graphs

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Examples: Common Sense Reasoning

Zebra on Pajama: (7:30 pm): I told Susannah: you have a nice pajama, but it was just

a dress. Why jump to that conclusion?: 1. because time is night time. 2. certain designs look like pajama.

Cars going out of a parking lot: You enter a parking lot which is quite full (UCI), you

see a car coming : you think ah… now there is a space (vacated), OR… there is no space and this guy is looking and leaving to another parking lot. What other clues can we have?

Robot gets out at a wrong level: A robot goes down the elevator. stops at 2nd floor

instead of ground floor. It steps out and should immediately recognize not being in the right level, and go back inside.

Turing quotes

– If machines will not be allowed to be fallible they cannot be intelligent – (Mathematicians are wrong from time to time so a machine should also be allowed)

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Why Uncertainty?

AI goal: to have a declarative, model‐based, framework that allows computer

system to reason.

People reason with partial information
Sources of uncertainty:

– Limitation in observing the world: e.g., a physician see symptoms and not exactly what goes in the body when he performs diagnosis. Observations are noisy (test results are inaccurate) – Limitation in modeling the world, – maybe the world is not deterministic.

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Why/What/How Uncertainty?

Why Uncertainty?

– Answer: It is abandant

What formalism to use?

– Answer: Probability theory

How to overcome exponential representation?

– Answer: Graphs, graphs, graphs… to capture irrelevance, independence, causality

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The Burglary Example

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Earthquake Burglary Radio Alarm Call

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Alpha and beta are events

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Burglary is independent of Earthquake

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Earthquake is independent of burglary

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Example

P(B,E,A,J,M)=?

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Bayesian Networks: Representation

= 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)

P(S, C, B, X, D)

Conditional Independencies Efficient Representation

Θ) (G, BN 

CPD:

C B D=0 D=1 0 0 0.1 0.9 0 1 0.7 0.3 1 0 0.8 0.2 1 1 0.9 0.1

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