lecture16-annotated - Machine Learning 10-701/15-781, Fall...

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1 Eric Xing © Eric Xing @ CMU, 2006-2008 1 Machine Learning Machine Learning 10 10 -701/15 701/15 -781, Fall 2008 781, Fall 2008 Hidden Markov Model Hidden Markov Model Eric Xing Eric Xing Lecture 16, November 3, 2008 Reading: Chap. 13, C.B book Eric Xing © Eric Xing @ CMU, 2006-2008 2 Dynamic clustering
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2 Eric Xing © Eric Xing @ CMU, 2006-2008 3 Chromosomes of tumor cell: Clustering Tumor Cell States Eric Xing © Eric Xing @ CMU, 2006-2008 4 Array CGH (comparative genomic hybridization) z The basic assumption of a CGH experiment is that the ratio of the binding of test and control DNA is proportional to the ratio of the copy numbers of sequences in the two samples. z But various kinds of noises make the true observations less easy to interpret …
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3 Eric Xing © Eric Xing @ CMU, 2006-2008 5 Copy number profile for chromosome 1 from 600 MPE cell line Copy number profile for chromosome 8 from COLO320 cell line 60-70 fold amplification of CMYC region Copy number profile for chromosome 8 in MDA-MB-231 cell line deletion DNA Copy number aberration types in breast cancer Eric Xing © Eric Xing @ CMU, 2006-2008 6 A real CGH run
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4 Eric Xing © Eric Xing @ CMU, 2006-2008 7 Out problem: how to cluster sequential data? Eric Xing © Eric Xing @ CMU, 2006-2008 8 Hidden Markov Model: from static to dynamic mixture models Dynamic mixture A A A A X 2 X 3 X 1 X T Y 2 Y 3 Y 1 Y T ... ... Static mixture Static mixture A X 1 Y 1 N
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5 Eric Xing © Eric Xing @ CMU, 2006-2008 9 A A A A X 2 X 3 X 1 X T Y 2 Y 3 Y 1 Y T ... ... The sequence: The underlying source: Ploy NT, genomic entities, sequence of rolls, dice, Hidden Markov Models Eric Xing © Eric Xing @ CMU, 2006-2008 10 Example: The Dishonest Casino A casino has two dice: z Fair die P(1) = P(2) = P(3) = P(5) = P(6) = 1/6 z Loaded die P(1) = P(2) = P(3) = P(5) = 1/10 P(6) = 1/2 Casino player switches back-&-forth between fair and loaded die once every 20 turns Game: 1. You bet $1 2. You roll (always with a fair die) 3. Casino player rolls (maybe with fair die, maybe with loaded die) 4. Highest number wins $2
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6 Eric Xing © Eric Xing @ CMU, 2006-2008 11 Puzzles Regarding the Dishonest Casino GIVEN: A sequence of rolls by the casino player 124552 6 4 6 214 6 14 6 13 6 13 666 1 66 4 66 1 6 3 66 1 6 3 66 1 6 3 6 1 6 515 6 1511514 6 1235 6 2344 QUESTION z How likely is this sequence, given our model of how the casino works? z This is the EVALUATION problem in HMMs z What portion of the sequence was generated with the fair die, and what portion with the loaded die? z This is the DECODING question in HMMs z How “loaded” is the loaded die? How “fair” is the fair die? How often does the casino player change from fair to loaded, and back? z This is the LEARNING question in HMMs Eric Xing © Eric Xing @ CMU, 2006-2008 12 A Stochastic Generative Model z Observed sequence: z Hidden sequence (a parse or segmentation): A B 1 4 3 6 6 4 B A A A B B
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7 Eric Xing © Eric Xing @ CMU, 2006-2008 13 Definition (of HMM) z Observation space Alphabetic set: Euclidean space: z Index set of hidden states Index set of hidden states z Transition probabilities between any two states between any two states or z Start probabilities z Emission probabilities associated with each state or in general: A A A A x 2 x 3 x 1
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This note was uploaded on 01/26/2010 for the course MACHINE LE 10701 taught by Professor Ericp.xing during the Fall '08 term at Carnegie Mellon.

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lecture16-annotated - Machine Learning 10-701/15-781, Fall...

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