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Genetics NumericalAnalysis AppliedProbability Optimization MM algorithms As in, “MM, I wonder what these algorithms have to do with genetics!” David Hunter DepartmentofStatistics PennStateUniversity Langefest, February 9, 2007 UCLA2007 MMalgorithms Genetics NumericalAnalysis AppliedProbability Optimization MM algorithms As in, “MM, I wonder what these algorithms have to do with genetics!” David Hunter DepartmentofStatistics PennStateUniversity Langefest, February 9, 2007 UCLA2007 MMalgorithms Genetics NumericalAnalysis AppliedProbability Optimization Outline 1 Genetics What is an MM algorithm? Why is any EM algorithm an MM algorithm? 2 Numerical Analysis A bit of history 3 Applied Probability An example from the “bag of tricks”: Deﬁnition of convexity Application to transmission tomography 4 Optimization Illustrative example: Finding a sample quantile UCLA2007 MMalgorithms Genetics NumericalAnalysis AppliedProbability Optimization Two people I met in 1995 UCLA2007 MMalgorithms Genetics NumericalAnalysis AppliedProbability Optimization Gratuitous baby pictures (1999) UCLA2007 MMalgorithms Genetics NumericalAnalysis WhatisanMMalgorithm? AppliedProbability WhyisanyEMalgorithmanMMalgorithm? Optimization Section One UCLA2007 MMalgorithms Every EM algorithm is an MM algorithm, so MM algorithms are evidently common. But what is an MM algorithm? Genetics NumericalAnalysis WhatisanMMalgorithm? AppliedProbability WhyisanyEMalgorithmanMMalgorithm? Optimization What do MM algorithms have to do with genetics? Let’s check the index! UCLA2007 MMalgorithms But what is an MM algorithm? Genetics NumericalAnalysis WhatisanMMalgorithm? AppliedProbability WhyisanyEMalgorithmanMMalgorithm? Optimization What do MM algorithms have to do with genetics? Let’s check the index! Every EM algorithm is an MM algorithm, so MM algorithms are evidently common. UCLA2007 MMalgorithms Genetics NumericalAnalysis WhatisanMMalgorithm? AppliedProbability WhyisanyEMalgorithmanMMalgorithm? Optimization What do MM algorithms have to do with genetics? Let’s check the index! Every EM algorithm is an MM algorithm, so MM algorithms are evidently common. But what is an MM algorithm? UCLA2007 MMalgorithms Choose a starting point x 0 Construct a majorizing function of f(x) at x . 0 Minimize the majorizer (at x ). 1 Repeat. So “MM” stands for “Majorize-Minimize”. Genetics NumericalAnalysis WhatisanMMalgorithm? AppliedProbability WhyisanyEMalgorithmanMMalgorithm? Optimization What is an MM algorithm? Goal: Solve difﬁcult minimization problem, like minimizing the function shown here in black. UCLA2007 MMalgorithms

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Genetics Numerical Analysis Applied Probability Optimization MM algorithms As in, “MM, I wonder what these algorithms have to do with genetics!” David Hunter

MM algorithms - As in, ``MM, I wonder what these algorithms have PDF

78 Pages·2007·2.03 MB·English

by David Hunter

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Genetics Numerical Analysis Applied Probability Optimization MM algorithms As in, “MM, I wonder what these algorithms have to do with genetics!” David Hunter

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Author:	David Hunter
Publication Year:	2007
Pages:	78
Language:	English
File Size:	2.03
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