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. 3.1 . The Concept of Probability. 3.2 . Sample Spaces and Events. 3.3 . Some Elementary Probability Rules. 3.4 . Conditional Probability and Independence. 3.5 . Bayes’ Theorem. 3-. 2. Probability Concepts. 4. Introduction. (slide 1 of 3). A key . aspect of solving real business problems is dealing appropriately with uncertainty.. This involves recognizing explicitly that uncertainty exists and using quantitative methods to model uncertainty.. What we learned last class…. We are not good at recognizing/dealing with randomness. Our “random” coin flip results weren’t streaky enough.. If B/G results behave like independent coin flips, we know how many families to EXPECT with 0,1,2,3,4 girls.. 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. Conditional Probability. Conditional Probability: . A probability where a certain prerequisite condition has already been met.. Conditional Probability Notation. The probability of Event A, given that Event B has already occurred, is expressed as P(A | B).. 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. Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . A value between zero and one that describe the relative possibility(change or likelihood) an event occurs.. The MEF announces that in 2012 the change Cambodia economic growth rate is equal to 7% is 80%.. 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 and Probability Distribution Dr Manoj Kumar Bhambu GCCBA-42, Chandigarh M- +91-988-823-7733 mkbhambu@hotmail.com Probability and Probability Distribution: Definitions- Probability Rules –Application of 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.