Reasoning with Graphical Models Class 1 Rina Dechter Darwiche chapters 1,3 Dechter‐Morgan&claypool book: Chapters 1‐2 Pearl chapter 1‐2 class1 compsci2020
Congressional Breifing: AI at UCI • Rina Dechter Congressional Briefing, December 2019 2
The Primary AI Challenges A neural network • Machine Learning focuses on replicating humans learning • Automated reasoning focuses on replicating how people reason. A Graphical Model MINVOLSET PULMEMBOLUS INTUBATION KINKEDTUBE VENTMACH DISCONNECT PAP SHUNT VENTLUNG VENITUBE PRESS MINOVL FIO2 VENTALV ANAPHYLAXIS PVSAT ARTCO2 SAO2 EXPCO2 TPR INSUFFANESTH HYPOVOLEMIA LVFAILURE CATECHOL LVEDVOLUME STROEVOLUME ERRBLOWOUTPUT HR ERRCAUTER HISTORY CVP PCWP CO HREKG HRSAT HRBP BP Congressional Briefing, December 2019 3
Automated Reasoning Medical Doctor Queries: • Prediction: what will happen? • Diagnosis: what happened? Lawyer • Situation assessment: What is going on? • Planning, decision making: what to do? Policy Maker Congressional Briefing, December 2019 4
Automated Reasoning Queries: • Prediction • Diagnosis • Situation assessment answers • Planning, decision making Graphical Models Knowledge is huge, so How to identify what’s relevant? Congressional Briefing, December 2019 5
Graphical Models Example : diagnosing liver disease (Onisko et al., 1999) Queries: • Prediction • Diagnosis • Situation assessment • Planning, decision making Automated Reasoning: • Develop methods to answer these questions. • Learning the models: from experts and data. Congressional Briefing, December 2019 6
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Global Seismic Monitoring Compliance for the Comprehensive Nuclear‐Test‐Ban Treaty (CTBT) (Nimar, Russel, Sudderth, 2011) CNTBT:A Graphical Model Application 278 monitoring stations (147 seismic) The IDC (International Data Centers) operates continuously and in real time, performing signal processing Congressional Briefing, December 2019 8
Global Seismic Monitoring for the Comprehensive Nuclear‐Test‐Ban Treaty (Nimar, Russel, Sudderth, 2011) Given : continuous waveform measurements from a global network of seismometer stations Congressional Briefing, December 2019 9
Global Seismic Monitoring for the Comprehensive Nuclear‐Test‐Ban Treaty (Nimar, Russel, Sudderth, 2011) Input: obsreved detection Output : a bulletin listing seismic events , with • Time • Location (latitude, longitude) • Depth • Magnitude Reasoning methods infers the most likely set of seismic events given the observed detections, Result: 60% reduction in error compared with human experts. Congressional Briefing, December 2019
Complexity of Automated Reasoning • Prediction Approximation, anytime • Diagnosis • Planning and scheduling Bounded error • Probabilistic Inference • Explanation • Decision‐making Linear / Polynomial / Exponential 1200 1000 Reasoning is computationally 800 hard Line 600 f(n) ar Complexity is exponential 400 200 0 1 2 3 4 5 6 7 8 9 10 n Congressional Briefing, December 2019 11
AI Renaissance • Deep learning • Probabilistic models – Fast predictions – Slow reasoning – “Instinctive” – “Logical / deliberative” Tools: Tools: Graphical Models, Tensorflow, PyTorch, … Probabilistic programming, Markov Logic, … class1 compsci2020
Text Books, Outline, Requirements Class page class1 compsci2020
Outline of classes • Part 1: Introduction and Inference ABC DGF G A D B BDEF F C EFH E M K H L FHK J HJ KLM • Part 2: Search OR A A AND 0 1 0 1 OR B B B 0 1 0 1 AND 0 1 0 1 OR C C C C E E E E E 0 1 0 1 0 1 0 1 AND 0 1 0 1 0 1 0 1 C 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 OR D D D D F F F F AND D 01 01 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 F 0101010101010101010101010101010101010101010101010101010101010101 Context minimal AND/OR search graph • Parr 3: Variational Methods and Monte‐Carlo Sampling class1 compsci2020
Probabilistic Graphical models • Describe structure in large problems – Large complex system – Made of “smaller”, “local” interactions – Complexity emerges through interdependence class1 compsci2020
Probabilistic Graphical models • Describe structure in large problems – Large complex system – Made of “smaller”, “local” interactions • Protein Structure prediction : predicting the 3d structure from given – Complexity emerges through interdependence sequences • • Examples & Tasks PDB: Protein design (backbone) algorithms enumerate a combinatorial number of candidate structures to compute the – Maximization (MAP): compute the most probable configuration Global Minimum Energy Conformation (GMEC). [Yanover & Weiss 2002] [Bruce R. Donald et. Al. 2016] class1 compsci2020
Probabilistic Graphical models • Describe structure in large problems – Large complex system – Made of “smaller”, “local” interactions – Complexity emerges through interdependence • Examples & Tasks – Summation & marginalization “partition function” and Image segmentation and classification: Observation y Marginals p( x i | y ) Observation y Marginals p( x i | y ) sky cow plane grass grass e.g., [Plath et al. 2009] class1 compsci2020
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 Test cost cost sales Influence diagrams & optimal decision‐making Oil sale Test Oil Drill result produced policy (the “oil wildcatter” problem) Oil Market Seismic Sales underground information structure cost e.g., [Raiffa 1968; Shachter 1986] class1 compsci2020
In more details… class1 compsci2020
Bayesian Networks (Pearl 1988) An early example P(S) From medical diagnosis BN Smoking (G, Θ) P(C|S) P(B|S) Bronchitis lung Cancer CPD: C B P(D|C,B) 0 0 0.1 0.9 0 1 0.7 0.3 P(X|C,S) P(D|C,B) 1 0 0.8 0.2 X-ray Dyspnoea 1 1 0.9 0.1 Combination: Product P(S, C, B, X, D) = P(S) P(C|S) P(B|S) P(X|C,S) P(D|C,B) Marginalization: sum/max • 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) class1 compsci2020
Alarm network [Beinlich et al., 1989] • Bayes nets: compact representation of large joint distributions The “alarm” network: 37 variables, 509 parameters (rather than 2 37 = 10 11 !) MINVOLSET KINKEDTUBE PULMEMBOLUS INTUBATION VENTMACH DISCONNECT PAP SHUNT VENTLUNG VENITUBE PRESS MINOVL FIO2 VENTALV ANAPHYLAXIS PVSAT ARTCO2 EXPCO2 SAO2 TPR INSUFFANESTH HYPOVOLEMIA LVFAILURE CATECHOL LVEDVOLUME STROEVOLUME ERRCAUTER ERRBLOWOUTPUT HR HISTORY CVP PCWP CO HREKG HRSAT HRBP BP class1 compsci2020
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Constraint Networks Example: map coloring Variables - countries (A,B,C,etc.) Values - colors (red, green, blue) Constraints: A B, A D, D E , etc. Constraint graph A E A B A E red green D red yellow green red D B F green yellow F B yellow green G yellow red C G C class1 828X‐2018
Propositional Reasoning Example: party problem A B • If Alex goes, then Becky goes: • If Chris goes, then Alex goes: C A • Question: Is it possible that Chris goes to B the party but Becky does not? A Is the C propositio nal theory , , B, C satisfiabl e? A B C A class1 828X‐2018
Probabilistic reasoning (directed) Party example: the weather effect • Alex is‐likely‐to‐go in bad weather W A P(A|W=bad)=.9 • Chris rarely‐goes in bad weather W C P(C|W=bad)=.1 • Becky is indifferent but unpredictable W B P(B|W=bad)=.5 Questions: W A P(A|W) • Given bad weather, which group of individuals is most good 0 .01 likely to show up at the party? good 1 .99 P(W) • What is the probability that Chris goes to the party bad 0 .1 W but Becky does not? bad 1 .9 A P(W,A,C,B) = P(B|W) · P(C|W) · P(A|W) · P(W) B C P(A|W) P(A,C,B|W=bad) = 0.9 · 0.1 · 0.5 P(B|W) P(C|W) class1 828X‐2018
Mixed Probabilistic and Deterministic networks Alex is‐likely‐to‐go in bad weather Chris rarely‐goes in bad weather Becky is indifferent but unpredictable PN CN P(W) P(W) W W B B A A C C P(B|W) P(B|W) P(C|W) P(C|W) A→B A→B C→A C→A P(A|W) P(A|W) B B A A C C Query: Is it likely that Chris goes to the party if Becky does not but the weather is bad? ( , | , , ) P C B w bad A B C A class1 828X‐2018
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