第3回 統計的機械学習セミナー／3rd Statistical Machine Learning Seminar
（主催：統計数理研究所 統計的機械学習NOE・新機軸創発センター)
- 日時
- 2011年6月17日（金） 15:00-17:30
- 会場
- 統計数理研究所 セミナー室5（3階 D313,D314）
※講演は英語で行います
- 講演者
- Arnaud Doucet 氏(University of British Colombia / University of Oxford)
牧野貴樹 氏（東大・生研）
- 世話人
- 福水健次
- 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 “derivative-free”
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.