PPT-Expectation-Maximization (EM)

1 Matt Gormley Lecture 24 November 21 2016 School of Computer Science Readings 10601B Introduction to Machine Learning Reminders Final Exam in class Wed Dec 7 2 Outline. Hongning Wang. CS@UVa. Today’s lecture. k. -means clustering . A typical . partitional. . clustering . algorithm. Convergence property. Expectation Maximization algorithm. Gaussian mixture model. . (Classroom Rules). RESPECT!. OVERRULING RULE…. Expectation 1 -. Hold your tongue and still your hands while others are talking. Expectation 2 -. Honor the . Golden Rule. Treat others as you would like to be treated. Machine Learning. Last Time. Expectation Maximization. Gaussian Mixture Models. Today. EM Proof. Jensen’s Inequality. Clustering sequential data. EM over . HMMs. EM in any Graphical Model. Gibbs Sampling. Mixture Models and Expectation Maximization. Machine Learning. Last Time. Review of Supervised Learning. Clustering. K-means. Soft K-means. Today. Gaussian Mixture Models. Expectation Maximization. The Problem. SALOME’S SPIRITUALITY. HOPE & EXPECTATION. I. She desires her sons to be . IN. the Kingdom. HOPE & EXPECTATION. II. She desires her . sons . to be . INVOLVED. in the Kingdom. HOPE & EXPECTATION. Zhizhuo. Zhang . Outline. Review of Mixture Model and EM algorithm. Importance Sampling. Re-sampling EM. Extending EM. Integrate Other Features. Result. Review Motif Finding: Mixture modeling. Given a dataset . Profit-Maximization. Economic Profit. A firm uses inputs j = 1…,m to make products i = 1,…n.. Output levels are y. 1. ,…,y. n. .. Input levels are x. 1. ,…,x. m. .. Product prices are p. 1. ,…,p. Machine Learning. April 13, 2010. Last Time. Review of Supervised Learning. Clustering. K-means. Soft K-means. Today. A brief look at Homework 2. Gaussian Mixture Models. Expectation Maximization. The Problem. Machine . Learning . 10-601. , Fall . 2014. Bhavana. . Dalvi. Mishra. PhD student LTI, CMU. Slides are based . on materials . from . Prof. . Eric Xing, Prof. . . William Cohen and Prof. Andrew Ng. Xinran He . and David Kempe. University of Southern . California. {xinranhe, . dkempe. }@usc.edu. 08/15/2016. The adoption of new products . can . propagate between nodes . in the social network. 0.8. PSET2. Concepts. The main functioning system of the economy. Concepts. Traditional Approach. Medium Run. Short Run. Lucas’s Critique. Rational Expectation. Fisher+ Taylor’s approach. Limitation to Rational Expectations. Mean. Breadth. . of. . distribution. 　.  . Breadth. . of. . distribution. 　.  . Breadth. . of. . distribution. 　.  .  . Number of trials. . Times of A.  .  . Calculation of mean.  . contains. The value of 27 is relatively large compared to the closeness in range of the other values in the set. For this question, you were supposed to check out the chart from Let [X]= =xi]= E[X]= =xi]= E[X]= =xi]= E[X]= =xi]= E[X]= =xi]= E[X]= =xi]= E[X]= =xi]= E[X]= =xi]= E[X]= =xi]= E[X]= E[X]= Linearity of Expectation: E[X + Y] = E[X] + E[Y]Example: Birthday Paradoxm balls