April 22
2013, 4:30 PM 302- 308
Evolution is a
powerful learning algorithm, and it is an important scientific problem to
find an explanation of how evolution is so effective. This talk will consider from first
principles how to model evolution as sampling from an explicitly probability
distribution, rather than as a randomised
algorithm. An old approach from population genetics -- the Moran model -- is
adapted to model a population as a Markov random field, so that the
stationary distribution of the population can be expressed in closed form,
for any fitness function. Breeding is modelled as blocked Gibbs sampling, and the sequence of
populations is a reversible Markov chain that satisfies the detailed balance
condition. An advantage of this approach is that the stationary distribution
of the population -- or in genetic terms, the mutation-selection equilibrium
-- is explicitly given, and the problem becomes to find a suitable MCMC
method to sample from this distribution. Conventional genetic breeding is one
possible algorithm -- but many other MCMC methods could also be used, and
these also provably converge to the same stationary distribution. Some
preliminary experimental results from work in progress will be presented. |