PPT-Probability Theory for ML

1 Matt Gormley Lecture 2 August 31 2016 School of Computer Science Readings Mitchell Ch 1 2 61 63 Murphy Ch 2 Bishop Ch 1 2 10601 Introduction to Machine Learning Reminders. Through this class we will be relying on concepts from probability theory for deriving machine learning algorithms These notes attempt to cover the basics of probability theory at a level appropriate for CS 229 The mathematical theory of probability Continued Fractions. Lisa Lorentzen. Norwegian University of Science and Technology. Continued fraction:. Convergence:. Möbius. transformations:. Convergence:. Catch:. L (1986). General convergence:. Hedonism. . Key players and ideas?. B’s Theory of Motivation. W. hat . is it?. Moral Fact. What is it?. Initial . Ideas. Derivation. : How is the value or norm (idea of goodness which will come from it) derived?. tunity to of six a total of the of being a winner of the and "the last of the of other think that on each is essentially what we mean "heads on toss" are event occurred of the have no of the a poker i Jennifer Trueblood, James . Yearsley. , Peter . Kvam. , Jerome . Busemeyer. , and . Zheng. (Joyce) Wang. Supported by NSF . (SES 0818277, 1153846, 1326275) & AFOSR (FA9550-12-1-00397) . Today’s agenda. ENGR 4323/5323. Digital and Analog Communication. Engineering and Physics. University of Central Oklahoma. Dr. Mohamed Bingabr. Chapter Outline. Concept of Probability. Random Variables. Statistical Averages (MEANS). Machine Learning. Chapter 1: Introduction. Example. Handwritten Digit Recognition. Polynomial Curve Fitting . Sum-of-Squares Error Function. 0. th. Order Polynomial. 1. st. Order Polynomial. 3. rd. March 23, 2010. Outline. Intro & Definitions. Why learn about probabilities and risk?. What is learned?. Expected Utility. Prospect Theory. Scalar Utility Theory. Choices, choices, choices.... In the lab, reinforcement is often uniform. Slide . 2. Probability - Terminology. Events are the . number. of possible outcome of a phenomenon such as the roll of a die or a fillip of a coin.. “trials” are a coin flip or die roll. Slide . A bar is . obeying the law . when it has the following property:. If any of the patrons are below the age of 18, then that person is not drinking alcohol.. Legal or Illegal?. Patron. Age. Drink. Alice. Probability Theory Section Summary Assigning Probabilities Probabilities of Complements and Unions of Events Conditional Probability Independence Random Variables Assigning Probabilities Let S be a sample space of an experiment with a finite number of outcomes. We assign a probability Probability Space of Two Die. σ-. Algebra (. ℱ. ). Sample Space (Ω). [...]. E5={(1,4),(2,3),(3,2),(4,1)}. [...]. Probability Measure Function (P). P. E5. 0.11. Probability Measure Function (P). . Mixture of Transparencies created by:. Dr. . Eick. and Dr. Russel. Reasoning and Decision Making Under Uncertainty. Quick Review Probability Theory . Bayes’ Theorem and Naïve Bayesian Systems. Bayesian Belief Networks. and . RATIONALITY – Some general comments. 2. 3. Decision Theory. Formidable foundations. Probability and reasoning about the future. Rational decision making. Deeply rooted in the Enlightenment. Major leaps in the mid-20.