‘æ3‰ñ “Œv“I‹@ŠBŠwKƒZƒ~ƒi[^3rd Statistical Machine Learning Seminar
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 Arnaud Doucet Ž(University of British Colombia / University of Oxford)
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 Speaker 1
 Arnaud Doucet (University of British Colombia / University of Oxford)
 Title
 DerivativeFree Estimation of the Score Vector and Observed Information Matrix with Application to StateSpace Models
 Abstract

We present an original approach to obtain gderivativefreeh
estimate of the score vector and observed information matrix for general statistical models.
For statespace models where sequential Monte Carlo computation is required,
these estimates have too high a variance and need to be modified.
In this specific context, we derive new derivativefree estimates of the score vector
and observed information matrix which are computed using the optimal smoother
associated to a modified version of the original statespace model.
We provide quantitative convergence results for these estimates and
their sequential Monte Carlo approximations and demonstrate experimentally that
the score vector estimate proposed here outperforms significantly standard finite difference estimates.
 Speaker 2
 Takaki Makino (University of Tokyo)
 Title
 Restricted Collapsed Draws from Hierarchical Chinese Restaurant Process
 Abstract

Restricted collapsed draws (RCD) sampler is a general Markov chain Monte Carlo sampler of coupled draws
from a hierarchical Chinese restaurant process (HCRP) with restriction.
Models that require simultaneous draws from a hierarchical Dirichlet process with restriction,
such as infinite Hidden markov models (iHMM), were difficult to enjoy benefits of the HCRP
due to combinatorial explosion in calculating distributions of coupled draws.
By constructing a proposal of seating arrangements (partitioning) and stochastically accepts the proposal
by the MetropolisHastings algorithm, the RCD sampler makes accurate sampling for complex combination of draws,
while retaining efficiency of HCRP representation. The RCD sampler enables us not only to provide a series of
sophisticated sampling algorithms for iHMMs, but also to develop complex probabilistic models,
such as hierarchical state clustering of iHMM. This talk presents the idea of the RCD sampler and
experimental results of MCMCbased inference for iHMM and state clustering.