Bayesian networks in AI

Jul 04, 2023

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The article on "Bayesian Networks in AI" provided by LeewayHertz explores the concept and applications of Bayesian networks in the field of artificial intelligence. It highlights how Bayesian networks utilize probability theory to model and analyze complex relationships between variables, enabling intelligent decision-making, risk assessment, and predictive analytics. The article likely delves deeper into the technical aspects and benefits of using Bayesian networks in AI systems.

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Bayesian networks in AI

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Bayesian Networks

Bayesian Networks. Alan Ritter. Problem: Non-IID Data. Most real-world data is not IID (like coin flips) Multiple correlated variables Examples: Pixels in an image Words in a document Genes in a microarray We saw one example of how to deal with this Markov Models + Hidden Markov Models.

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Bayesian Networks

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Bayesian Networks

Bayesian Networks. Team Orange : Harrison, Sheehan, McGregor, & Law. History. Reverend Thomas Bayes (1702-1761) British theologian and mathematician who wrote the basic law of probability (now called Bayes Rule)

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Bayesian Networks

Bayesian Networks. What is the likelihood of X given evidence E? i.e. P(X|E) = ?. Issues. Representational Power allows for unknown, uncertain information Inference Question: What is Probability of X if E is true. Processing: in general, exponential Acquisition or Learning

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Learning In Bayesian Networks

Learning In Bayesian Networks. Learning Problem. Set of random variables X = {W, X, Y, Z, …} Training set D = { x 1 , x 2 , …, x N } Each observation specifies values of subset of variables x 1 = {w 1 , x 1 , ?, z 1 , …} x 2 = { w 2 , x 2 , y 2 , z 2 , …}

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Bayesian Networks

Bayesian Networks. Some Applications of BN. Medical diagnosis Troubleshooting of hardware/software systems Fraud/uncollectible debt detection Data mining Analysis of genetic sequences Data interpretation, computer vision, image understanding. Battery. Gas. Radio. SparkPlugs. Starts.

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Bayesian Networks

M.I. Jaime Alfonso Reyes ´Cortés. Bayesian Networks. Es un grafo dirigido acíclico conexo más una distribución de probabilidad sobre sus variables . Red Bayesiana. Existen distintos tipos de redes Bayesianas: Naive Bayes : Redes simples. Forma de “V” => 2^n estados en el nodo inferior

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Bayesian Networks

Bayesian Networks. Significance of Conditional independence. Consider Grade(CS101), Intelligence, and SAT Ostensibly, the grade in a course doesn’t have a direct relationship with SAT scores but good students are more likely to get good SAT scores , so they are not independent…

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Bayesian networks

Bayesian networks. More commonly called graphical models A way to depict conditional independence relationships between random variables A compact specification of full joint distributions. Structure. Nodes: random variables Can be assigned (observed) or unassigned (unobserved)

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Bayesian networks

Bayesian networks. Chapter 14 . Outline. Syntax Semantics. Bayesian networks. A simple, graphical notation for conditional independence assertions and hence for compact specification of full joint distributions Syntax: a set of nodes, one per variable

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Bayesian networks

Bayesian networks. Chapter 14 Section 1 – 2. Outline. Syntax Semantics. Bayesian networks. A simple, graphical notation for conditional independence assertions and hence for compact specification of full joint distributions Syntax: a set of nodes, one per variable

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Bayesian Networks

Bayesian Networks. A causal probabilistic network , or Bayesian network , is an directed acyclic graph (DAG) where nodes represent variables and links represent dependency relations , e.g. of the type cause-effect, between variables

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Bayesian networks

Bayesian networks. Chapter 14 Slide Set 2. Constructing Bayesian networks. 1. Choose an ordering of variables X 1 , … , X n 2. For i = 1 to n add X i to the network select parents from X 1 , … ,X i-1 such that P (X i | Parents(X i )) = P (X i | X 1 , ... X i-1 ). Example.

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Bayesian Networks

Reverend Thomas Bayes (1702-1761). Bayesian Networks. Probability theory BN as knowledge model Bayes in Court Dazzle examples Conclusions. Jenneke IJzerman, Bayesiaanse Statistiek in de Rechtspraak, VU Amsterdam, September 2004.

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Bayesian networks

Bayesian networks. Weather data. What is the Bayesian Network corresponding to Naïve Bayes?. “Effects” and “Causes” vs. “Evidence” and “Class”. Why Naïve Bayes has this graph? Because when we compute in Naïve Bayes: P(play=yes | E) = P(Outlook=Sunny | play=yes) *

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Bayesian Networks

Bayesian Networks. Russell and Norvig: Chapter 14 CMCS421 Fall 2006. sensors. environment. ?. agent. actuators. I believe that the sun will still exist tomorrow with probability 0.999999 and that it will be a sunny day with probability 0.6. Probabilistic Agent. Problem.

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Bayesian Networks

Bayesian Networks. Introduction. A problem domain is modeled by a list of variables X 1 , …, X n Knowledge about the problem domain is represented by a joint probability P(X 1 , …, X n ). Introduction. Example: Alarm

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Bayesian Networks

Bayesian Networks. Aldi Kraja Division of Statistical Genomics. Bayesian Networks and Decision Graphs. Chapter 1. Causal networks are a set of variables and a set of directed links between variables Variables represent events (propositions) A variable can have any number of states

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Bayesian Networks

Bayesian Networks. Material used Halpern: Reasoning about Uncertainty. Chapter 4 Stuart Russell and Peter Norvig: Artificial Intelligence: A Modern Approach 1 Random variables 2 Probabilistic independence 3 Belief networks 4 Global and local semantics 5 Constructing belief networks

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Bayesian Networks

Bayesian Networks. Tamara Berg CS 590-133 Artificial Intelligence. Many slides throughout the course adapted from Svetlana Lazebnik , Dan Klein, Stuart Russell, Andrew Moore, Percy Liang, Luke Zettlemoyer , Rob Pless , Killian Weinberger, Deva Ramanan. Announcements.

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BAYESIAN NETWORKS

BAYESIAN NETWORKS IN MODEL AND DATA INTEGRATION AND DECISION MAKING IN RIVER BASIN MANAGEMENT USING Consideration of opportunities for Bayes networks in predictive water quality modelling Olli Malve ( M. Sc. ) Water Resources Research and Management Citations from

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Bayesian Networks

Bayesian Networks. CS 271: Fall 2007 Instructor: Padhraic Smyth. Logistics. Remaining lectures Bayesian networks (today) 2 on machine learning No lecture next Tuesday Dec 4 th (out of town) Homeworks #5 (Bayesian networks) is due Thursday

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