Recitation-EM - 1 Copyright 2001, 2004, Andrew W. Moore...

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Unformatted text preview: 1 Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures Andrew W. Moore Professor School of Computer Science Carnegie Mellon University www.cs.cmu.edu/~awm awm@cs.cmu.edu 412-268-7599 Note to other teachers and users of these slides. Andrew would be delighted if you found this source material useful in giving your own lectures. Feel free to use these slides verbatim, or to modify them to fit your own needs. PowerPoint originals are available. If you make use of a significant portion of these slides in your own lecture, please include this message, or the following link to the source repository of Andrews tutorials: http://www.cs.cmu.edu/~awm/tutorials . Comments and corrections gratefully received. Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 2 Unsupervised Learning You walk into a bar. A stranger approaches and tells you: Ive got data from k classes. Each class produces observations with a normal distribution and variance 2 I . Standard simple multivariate gaussian assumptions. I can tell you all the P(w i )s . So far, looks straightforward. I need a maximum likelihood estimate of the i s . No problem : Theres just one thing. None of the data are labeled. I have datapoints, but I dont know what class theyre from (any of them!) Uh oh!! 2 Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 3 Gaussian Bayes Classifier Reminder ) ( ) ( ) | ( ) | ( x x x p i y P i y p i y P = = = = ( ) ( ) ) ( 2 1 exp || || ) 2 ( 1 ) | ( 2 / 1 2 / x x x x p p i y P i i k i T i k i m = = How do we deal with that? Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 4 Predicting wealth from age 3 Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 5 Predicting wealth from age Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 6 Learning modelyear , mpg ---> maker = m m m m m 2 2 1 2 2 2 12 1 12 1 2 L M O M M L L 4 Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 7 General: O(m 2 ) parameters = m m m m m 2 2 1 2 2 2 12 1 12 1 2 L M O M M L L Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 8 Aligned: O(m) parameters = m m 2 1 2 3 2 2 2 1 2 L L M M O M M M L L L 5 Copyright 2001, 2004, Andrew W. Moore Clustering with Gaussian Mixtures: Slide 9 Aligned: O(m) parameters = m m 2 1 2 3 2 2 2 1 2 L L M M O M M M L L L Copyright 2001, 2004, Andrew W. MooreCopyright 2001, 2004, Andrew W....
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Recitation-EM - 1 Copyright 2001, 2004, Andrew W. Moore...

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