Class 1 Rina Dechter - Donald Bren School of Information ...dechter/courses/ics-276/winter-2020/slides/... · Rina Dechter class1 compsci2020 Darwichechapters 1,3 Dechter‐Morgan&claypoolbook:

Reasoning with Graphical Models

Class 1Rina Dechter

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

Congressional Breifing: AI at UCI

Congressional Briefing, December 2019 2

• Rina Dechter


The Primary AI Challenges

• Machine Learning focuses on replicating humans learning

• Automated reasoning focuses on replicating how people reason.

PCWP COHRBP

HREKG HRSAT

ERRCAUTERHRHISTORY

CATECHOL

SAO2 EXPCO2

ARTCO2

VENTALV

VENTLUNG VENITUBE

DISCONNECT

MINVOLSET

VENTMACHKINKEDTUBEINTUBATIONPULMEMBOLUS

PAP SHUNT

ANAPHYLAXIS

MINOVL

PVSAT

FIO2PRESS

INSUFFANESTHTPR

LVFAILURE

ERRBLOWOUTPUTSTROEVOLUMELVEDVOLUME

HYPOVOLEMIA

CVP

BP

A neural network

A Graphical Model


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?

Automated Reasoning

Queries:• Prediction• Diagnosis• Situation assessment• Planning, decision makinganswers

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

Congressional Briefing, December 2019

Graphical ModelsExample: 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.


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)


278 monitoring stations (147 seismic)

CNTBT:A Graphical Model Application

The IDC (International Data Centers)operates continuously and in real time,performing signal processing


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)


Input: obsreved detectionOutput: 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 likelyset of seismic events given the observed detections,

Complexity of Automated Reasoning• Prediction• Diagnosis• Planning and scheduling• Probabilistic Inference• Explanation • Decision‐making

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Reasoning is computationally hardComplexity is exponential


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

Outline of classes• Part 1: Introduction and Inference

• Part 2: Search

• Parr 3: Variational Methods and Monte‐Carlo Sampling

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Context minimal AND/OR search graph

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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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• 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).



• Examples & Tasks– Summation & marginalization

grass

plane

sky

grass

cow

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

and

“partition function”

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

Image segmentation and classification:

Graphical models• Describe structure in large problems


• Examples & Tasks– Mixed inference (marginal MAP, MEU, …)

Test

Drill Oil salepolicy

Testresult

Seismicstructure

Oilunderground

Oilproduced

Testcost

Drillcost

Salescost

Oil sales

Marketinformation

Influence diagrams &optimal decision‐making

(the “oil wildcatter” problem)

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

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In more details…

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

DyspnoeaP(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 0.90 1 0.7 0.31 0 0.8 0.21 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)= 𝑚𝑎𝑥 , , , P(S)· P(C|S)· P(B|S)· P(X|C,S)· P(D|C,B)

Combination: ProductMarginalization: sum/max

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An early exampleFrom medical diagnosis

Alarm network• Bayes nets: compact representation of large joint distributions

PCWP CO

HRBP

HREKG HRSAT

ERRCAUTERHRHISTORY

CATECHOL

SAO2 EXPCO2

ARTCO2

VENTALV

VENTLUNG VENITUBE

DISCONNECT

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PAP SHUNT

ANAPHYLAXIS

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PVSAT

FIO2PRESS

INSUFFANESTHTPR

LVFAILURE

ERRBLOWOUTPUTSTROEVOLUMELVEDVOLUME

HYPOVOLEMIA

CVP

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The “alarm” network: 37 variables, 509 parameters (rather than 237 = 1011 !)

[Beinlich et al., 1989]

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A Bred greenred yellowgreen redgreen yellowyellow greenyellow red

Example: map coloringVariables - countries (A,B,C,etc.)Values - colors (red, green, blue)Constraints: etc. ,ED D, AB,A

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Constraint Networks

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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

BA

A C

e?satisfiabl ,, theIs C B, ACBA

theorynalpropositio

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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)=.9W A

P(C|W=bad)=.1W C

P(B|W=bad)=.5W B

WP(W)

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

B CA

W A P(A|W)

good 0 .01

good 1 .99

bad 0 .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

),,|,( ACBAbadwBCP

A→B C→AB A CP(C|W)P(B|W)

P(W)

P(A|W)

W

B A C

A→B C→AB A C

Alex is‐likely‐to‐go in bad weatherChris rarely‐goes in bad weatherBecky 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

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LinearPolynomialExponential

Reasoning iscomputationally hardComplexity isTime 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)

)(XmZX

)(XmXZ

)(ZmZM)(ZmZL

)(ZmMZ)(ZmLZ

)(XmYX

)(XmXY

)(YmTY

)(YmYT

)(YmRY

)(YmYR

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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

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treewidth = 4 - 1 = 3treewidth = (maximum cluster size) - 1

Inference algorithm:Time: exp(tree-width)Space: exp(tree-width)

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Conditioning and Cycle cutset

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Cycle cutset = {A,B,C}

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Search over the Cutset

A=yellow A=green

B=red B=blue B=red B=blueB=green B=yellow

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• Inference may require too much memory

• Condition on some of the variablesA

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GraphColoringproblem

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Inference

exp(w*) time/space

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ESearch+inference:Space: exp(q)Time: exp(q+c(q))

q: usercontrolled

Bird's‐eye View of Exact Algorithms

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Inference

exp(w*) time/space

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ESearch+inference:Space: exp(q)Time: exp(q+c(q))

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Bird's‐eye View of Exact Algorithms

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Inference

Bounded Inference

Search

Sampling

Search + inference:

Sampling + bounded inference

Bird's‐eye View of Approximate Algorithms

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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

RadioAlarm

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

DyspnoeaP(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=10 0 0.1 0.90 1 0.7 0.31 0 0.8 0.21 1 0.9 0.1

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End of slides

Documents

Class 1 Rina Dechter - Donald Bren School of Information ...dechter/courses/ics-276/winter-2020/slides/... · Rina Dechter class1 compsci2020 Darwichechapters 1,3 Dechter‐Morgan&claypoolbook: