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Bayesian Networks

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Page 1: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Bayesian Networks

Page 2: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Contents

• Semantics and factorization• Reasoning Patterns• Flow of Probabilistic Influence

Page 3: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Toy Example

• Grade• Course Difficulty• Student Intelligence• SAT• Recommendation

Letter

Page 4: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Variables Dependency Model

Page 5: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Distribution Representation

Page 6: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Chain Rule for Bayesian Network

Page 7: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Chain Rule for Bayesian Network

Page 8: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Chain Rule for Bayesian Network

Page 9: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Chain Rule for Bayesian Network

Page 10: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Bayesian Network

Page 11: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Bayesian Network

Page 12: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Bayesian Network

Page 13: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Bayesian Network

Page 14: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

BN Is a Legal Distribution ? Condition 1

Page 15: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

BN Is a Legal Distribution ? Condition 2

Page 16: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

BN Is a Legal Distribution ? Condition 2

Page 17: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

BN Is a Legal Distribution ? Condition 2

Page 18: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

BN Is a Legal Distribution ? Condition 2

Page 19: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

BN Is a Legal Distribution ? Condition 2

Page 20: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

P Factorizes over G

Page 21: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Genetics Inheritance

Page 22: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

BN for Genetic Inheritance

Page 23: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

The Student BN Network

Page 24: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Casual Reasoning

Page 25: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Casual Reasoning

Page 26: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Casual Reasoning

Page 27: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Evidential Reasoning

Page 28: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Evidential Reasoning

Page 29: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Intercausal Reasoning

Page 30: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Intercausal Reasoning

Page 31: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Intercausal Reasoning

Page 32: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

When can X Influence Y?

Page 33: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Active Trails

Page 34: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

When Can X Influence Y Given Evidence About Z

Page 35: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

When Can X Influence Y Given Evidence About Z

Page 36: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

When Can X Influence Y Given Evidence About Z

Page 37: Bayesian Networks. Contents Semantics and factorization Reasoning Patterns Flow of Probabilistic Influence

Active Trails

IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ...people.csail.mit.edu/haow/paper/TKDE15_RCTR.pdfMatrix factorization [25], [35] and its extensions, such as the probabilistic matrix factorization

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Semantics of Probabilistic Programs - Cornell Universitykozen/Papers/ProbSem.pdf · 2015-07-09 · JOURNAL OF COMPUTER AND SYSTEM SCIENCES 22, 328-350 (1981) Semantics of Probabilistic

Kernelized Probabilistic Matrix Factorization: Exploiting ...tinghuiz/papers/sdm12_kpmf.pdfExploiting Graphs and Side Information Tinghui Zhou Hanhuai Shan Arindam Banerjee Guillermo

Fine-Grained Semantics for Probabilistic Programs · termination, the semantics of each expression and each statement is an s-finite kernel. Informally: Features of probabilistic

Commutative semantics for probabilistic programming · 1.1 A rst introduction to probabilistic programming. To illustrate the key ideas of probabilistic programming, consider the

Computable Semantics and Probabilistic Graphical Models Where Probabilistic Systems and Semantics Rub Elbows Peter Haug, MD Homer Warner Center for Informatics

Formal Semantics of Probabilistic Programming Languages: … · 2017-11-20 · Formal Semantics of Probabilistic Programming Languages: Issues, Results and Opportunities Hongseok

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Probabilistic Semantics and Pragmatics: Uncertainty in ...cocolab.stanford.edu/papers/GoodmanLassiter2015-Chapter.pdfProbabilistic Semantics and Pragmatics 3 1 Probabilistic models

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Structural operational semantics for continuous state ...people.cs.aau.dk/~grbacci/Papers/meas.pdf · Structural operational semantics for continuous state probabilistic processes?

Probabilistic (Logic) Programming Concepts · Typical probabilistic programming languages, on the other hand, employ a variant of Sato’s distribution semantics (Sato, 1995), in

Probabilistic Logic Programming Under the Distribution ...mcs.unife.it/~friguzzi/Papers/RigSwi-WFS16.pdf · Probabilistic Logic Programming Under the Distribution Semantics Fabrizio

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Natural Language Semantics using Probabilistic Logicml/papers/beltagy.proposal14.pdf · 2014. 10. 30. · Natural Language semantics is the study of representing the “meaning”

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Complexity of probabilistic inclusion logic and additive ... · Probabilistic inclusion logic FO(ˇ) Syntax: FO (negation normal form) + ~xˇ~y(only positively) Semantics: De ned

Notes on factorization algebras, factorization homology ... · Notes on factorization algebras, factorization homology and applications ... to factorization algebras, factorization