PPT-Directed Graphical Models

aka Bayesian Networks 1 Matt Gormley Lecture 21 November 9 2016 School of Computer Science Readings Bishop 81 and 822 Mitchell 611 Murphy 10 10601B Introduction to Machine Learning. We call the tail of the head of and uv the ends of If there is an edge with tail and head then we let uv denote such an edge and we say that this edge is directed from to Loops Parallel Edges and Simple Digraphs An edge uv in a digraph is a 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. Graphical Model Inference. View observed data and unobserved properties as . random variables. Graphical Models: compact graph-based encoding of probability distributions (high dimensional, with complex dependencies). Graphs 1. Graphs. Definition:. Two types: . Undirected. Directed. Examples/Applications. Transportation Networks. Source: pages.cs.wisc.edu. Shortest path?. Vacuum World (from AI). Source: . centurion2.com. Analysis. Aaron J. Fisher, Ph.D.. Assistant Professor. Department of Psychology. University of California, Berkeley. Nomothetic Problems I. Nomothetic . analyses generalize to the . population. (at best) – not . Tamara L Berg. CSE 595 Words & Pictures. Announcements. HW3 . online tonight. Start thinking about project ideas . Project . proposals in class Oct 30 . . Come to office hours . Oct. 23-25 . to discuss . Ricardo Silva, Charles Blundell and Yee . Whye. . Teh. University College London. AISTATS 2011 – Fort Lauderdale, FL. Directed Graphical Models. X. 1. X. 2. U. X. 3. X. 4. X. 2. X. 4. X. 2. X. Automated Reasoning with Graphical models. Rina. Dechter. Bren school of ICS. University of California, Irvine. ICS 90 . November 2016. Agenda. My work in AI. How did I get to AI?. 2. ICS-90, 2016. Knowledge representation and Reasoning. Directed Mixed Graph Models. Ricardo Silva. Statistical Science/CSML, University . College London. ricardo@stats.ucl.ac.uk. Networks: Processes and Causality, Menorca 2012. Graphical Models. Graphs provide a language for describing independence constraints. Generalized covariance matrices and their inverses. Menglong Li. Ph.d. of Industrial Engineering. Dec 1. st. 2016. Outline. Recap: Gaussian graphical model. Extend to general graphical model. Model setting. William W. Cohen. Machine Learning 10-601. Motivation for Graphical Models. Recap: A paradox of . i. nduction. A black crow seems to support the hypothesis “all crows are black”.. A pink highlighter supports the hypothesis “all non-black things are non-crows”. Nanyun. (Violet). Peng. Ryan Cotterell. Jason Eisner. J. ohns. . Hopkins. . University. . 1. Attention!. Don’t care about phonology?. . Listen anyway. This is a general method for . inferring strings. Comparison of Strategies for Scalable Causal Discovery of Latent Variable Models from Mixed Data Vineet Raghu , Joseph D. Ramsey, Alison Morris, Dimitrios V. Manatakis, Peter Spirtes, Panos K. Chrysanthis, Clark Glymour, and Panayiotis V. Benos Part 1: Overview and Applications . Outline. Motivation for Probabilistic Graphical Models. Applications of Probabilistic Graphical Models. Graphical Model Representation. Probabilistic Modeling. 1. when trying to solve a real-world problem using mathematics, it is common to define a mathematical model of the world, e.g..