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2011”N6ŒŽ17“úi‹àj 15:00-17:30
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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
Derivative-Free Estimation of the Score Vector and Observed Information Matrix with Application to State-Space Models
Abstract
We present an original approach to obtain gderivative-freeh
estimate of the score vector and observed information matrix for general statistical models. For state-space 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 derivative-free estimates of the score vector and observed information matrix which are computed using the optimal smoother associated to a modified version of the original state-space 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 Metropolis-Hastings 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 MCMC-based inference for iHMM and state clustering.
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