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SUMMARY:Adaptive Monte Carlo on multivariate binary sampling spaces - Prof
  Nicolas Chopin\, ENSAE
DTSTART:20101012T131500Z
DTEND:20101012T141500Z
UID:TALK26526@talks.cam.ac.uk
CONTACT:Rachel Fogg
DESCRIPTION:Authors: Christian Schäfer (CREST\, CEREMADE)\, Nicolas Chopi
 n (CREST)\n\nA Monte Carlo algorithm is said to be adaptive if it can adju
 st automatically its current proposal distribution\, using past simulation
 s. The choice of the parametric family that defines the set of proposal di
 stributions is critical for a good performance. We treat the problem of co
 nstructing such parametric families for adaptive sampling on multivariate 
 binary spaces. A practical motivation for\nthis problem is variable select
 ion in a linear regression context\, where we need to either find the best
  model\, with respect to some criterion\, or to sample from a Bayesian pos
 terior distribution on the\nmodel space. In terms of adaptive algorithms\,
  we focus on the Cross-Entropy (CE) method for optimisation\, and the Sequ
 ential Monte Carlo (SMC) methods for sampling. Raw versions of both SMC an
 d CE\nalgorithms are easily implemented using binary vectors with independ
 ent components. However\, for high-dimensional model choice problems\, the
 se straightforward proposals do not yields satisfactory\nresults. The key 
 to advanced adaptive algorithms are binary parametric families which take 
 at least the linear dependencies between components into account. We revie
 w suitable multivariate binary models\nand make them work in the context o
 f SMC and CE. Extensive computational studies on real life data with a hun
 dred covariates seem to prove the necessity of more advanced binary famili
 es\, to make adaptive Monte Carlo procedures efficient. Besides\, our nume
 rical results encourage the use of SMC and CE methods as alternatives to t
 echniques based on Markov chain exploration.\n\nPaper available on arxiv: 
 http://arxiv.org/abs/1008.0055\n
LOCATION:LR5\, Engineering\, Department of
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