PPT-Bayes Models Outline I. Conditional independence

Figures are from the textbook site II Naïve Bayes model III Revisiting the wumpus world I Combining Evidence What happens when we have two or more pieces of evidences Suppose we know the full joint distribution. Pieter . Abbeel. UC Berkeley EECS. Many slides adapted from . Thrun. , . Burgard. and Fox, Probabilistic Robotics. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . Need to write what you know as propositional formulas. Theorem proving will then tell you whether a given new sentence will hold given what you know. Three kinds of queries. Is my . knowledgebase . consistent? (i.e. is there at least one world where everything I know is true?) . Bayes. Nets. Lecture 4. Getting a Full Joint Table Entry from a Bayes Net. Recall:. A . table entry for . X. 1 . = x. 1. ,…,. X. n. . = . x. n. . is simply P(. x. 1. ,…,. x. n. ) which can be calculated based on the . Classification. Naïve . Bayes. . c. lassifier. Nearest-neighbor classifier. Eager . vs. Lazy learners. Eager learners: learn the model as soon as the training data becomes available. Lazy learners: delay model-building until testing data needs to be classified. 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 . Computer Science cpsc322, Lecture 26. (Textbook . Chpt. 6.1-2). Nov. , . 2013. Lecture Overview. Recap with Example. Marginalization. Conditional Probability. Chain Rule. Bayes. ' Rule. Marginal Independence. Generative vs. Discriminative models. Christopher Manning. Introduction. So far we’ve looked at “generative models”. Language models, Naive Bayes. But there is now much use of conditional or discriminative probabilistic models in NLP, Speech, IR (and ML generally). Jonathan Lee and Varun Mahadevan. Programming Project: Spam Filter. Due: Check the Calendar. Implement a Naive Bayes classifier for classifying emails as either spam or ham.. You may use C, Java, Python, or R; . Jonathan Lee and Varun Mahadevan. Independence. Recap:. Definition: Two events X and Y are . independent. . if and only if. . . . Equivalently, if . , then. ..  . Conditional Independence. Definition: Two . Human and Machine Learning. Mike . Mozer. Department of Computer Science and. Institute of Cognitive Science. University of Colorado at Boulder. Today’s Plan. Hand back Assignment 1. More fun stuff from motion perception model. .  . .  . .  . .  . .  . .  . Announcements. Assignments:. HW9 (written). Due Tue 4/2, 10 pm. Optional Probability (online). Midterm:. Mon 4/8, in-class. Course Feedback:. See Piazza post for mid-semester survey. Bayes nets encode joint distributions as product of conditional distributions on each variable:. P. (. X. 1. ,..,X. n. ) = . . i. . P. (. X. i. . | . Parents. (. X. i. )). P(B). true. false. 0.001. Bayes Net Syntax. A set of nodes, one per variable . X. i. A directed, acyclic graph. A conditional distribution for each node given its . parent variables. . in the graph. CPT. (conditional probability table); each row is a distribution for child given values of its parents. Bayes. and Independence. Computer Science cpsc322, Lecture 25. (Textbook . Chpt. . 6.1.3.1-2). Nov, 5, 2012. Lecture Overview. Recap Semantics of Probability. Marginalization. Conditional Probability.