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Seminars & Lectures

* TITLE

Sex as Gibbs sampling: a Markov chain Monte-Carlo model of evolution, using a direct product of Dirichlet processes

* SPEAKERS

Name	Affiliation	E-mail
Christopher Watkins	University of London	chrisw(at)cs.rhul.ac.kr

* HOST(Applicant)

Name	Affiliation	E-mail
Junghyo Jo	APCTP	jojunghyo(at)apctp.org

* DATE / TIME

2014-01-07, 14:00

* PLACE

512 Seminar Room

* ABSTRACT

Evolution by natural selection is a learning algorithm of remarkable power; we propose a model of evolution using the techniques of machine learning.
We specify a probability model explicitly by considering the population of genomes as a Markov random field. We then observe that a standard Markov chain Monte Carlo (MCMC) sampling method -- blocked Gibbs sampling within Metropolis-Hastings -- is simply a genetic algorithm. In genetic terminology, this model is a modification of the well-known Moran process for evolution with overlapping generations. Although this result is rather simple, we have so far been unable to find it in the literature. The implications seem quite deep, and generate many questions and directions for research.
First, this model of evolution is similar to non-parametric Bayesian inference. The stationary distribution over populations factorises as the product of two terms: the first term is the probability of generating the population by pure genetic drift with no selection; the second term is the product of the fitnesses of the genomes. This expression is analogous to that for a Bayesian posterior distribution, and a population in equilibrium is analogous to a sample from a posterior distribution.
Second, standard MCMC techniques can be used to construct alternative sampling algorithms that converge to the same stationary distribution. It may therefore be possible to create `super-evolutionary\' algorithms that are faster than conventional evolution in interesting cases.
Third, the Markov chain of populations satisfies detailed balance, and the equilibrium distribution may be studied using techniques from statistical physics.
Finally, this model is embarrassingly simple. If genetic algorithms are just Gibbs-sampling, then how has evolution been so successful in producing complex organisms? Gibbs-sampling is known to be one of the slowest MCMC methods -- how can this bad MCMC method have produced life on earth, even over geological time? If there is time, I will suggest three possible answers...

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