The following schedule is based on Japanese standard time.
Date: Monday Sep 9th
Time: 13:15 - 14:15 JST
In person location: Room 368, Building No. 6, Faculty of Engineering, Hongo Campus, University of Tokyo
Speaker: Sumeetpal Singh, University of Wollongong
Title: How quickly does the particle filter forget its initialisation?
Abstract. We study the forgetting properties of the particle filter when its state — the collection of particles — is regarded as a Markov chain. Under a strong mixing assumption on the particle filter’s underlying Feynman–Kac model, we find that the particle filter is exponentially mixing, and forgets its initial state in O(logN) ‘time’, where N is the number of particles and time refers to the number of particle filter algorithm steps, each comprising a selection (or resampling) and mutation (or prediction) operation. We present an example which suggests that this rate is optimal. In contrast to our result, available results to-date are extremely conservative, suggesting O(αN) time steps are needed, for some α > 1, for the particle filter to forget its initialisation. We also study the conditional particle filter (CPF) and extend our forgetting result to this context. We establish a similar conclusion, namely, CPF is exponentially mixing and forgets its initial state in O(logN) time. To support this analysis, we establish new time-uniform Lp error estimates for CPF, which can be of independent interest.
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Physical: https://forms.gle/jSYPc6KLgccb5Zro9
Virtual: https://us06web.zoom.us/meeting/register/tZEufuyprDgtGtF_isK7JLWkxbSQJRk8fMxj
Date: Monday July 22nd
Time: 13:15 - 14:15 JST
In person location: ISM D222
Speaker: Takeru Matsuda, University of Tokyo, RIKEN Center for Brain Science
Title: Inadmissibility of the corrected Akaike information criterion
Abstract: For the multivariate linear regression model with unknown covariance, the corrected Akaike information criterion is the minimum variance unbiased estimator of the expected Kullback--Leibler discrepancy. In this study, based on the loss estimation framework, we show its inadmissibility as an estimator of the Kullback--Leibler discrepancy itself, instead of the expected Kullback--Leibler discrepancy. We provide improved estimators of the Kullback--Leibler discrepancy that work well in reduced-rank situations and examine their performance numerically. This result is similar to Stein’s paradox in that the minimum variance unbiased estimator is improved by introducing bias.
参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.
Physical:https://forms.gle/H266hvXQMQQDKr3p7
Virtual: https://us06web.zoom.us/meeting/register/tZAocOuqqT4iE92LHD-VGKqcJqE-EiyJJjv2
Date: Wednesday Jun 5th
Time: 13:15 - 14:15 JST
In person location: ISM D222
Speaker: Dennis Shen, USC Marshall
Title: Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data
Abstract: One dominant approach to evaluate the causal effect of a treatment is through panel data analysis, whereby the behaviors of multiple units are observed over time. The information across time and units motivates two general approaches: (i) horizontal regression (i.e., unconfoundedness), which exploits time series patterns, and (ii) vertical regression (e.g., synthetic controls), which exploits cross‐sectional patterns. Conventional wisdom often considers the two approaches to be different. We establish this position to be partly false for estimation but generally true for inference. In the absence of any assumptions, we show that both approaches yield algebraically equivalent point estimates for several standard estimators. However, the source of randomness assumed by each approach leads to a distinct estimand and quantification of uncertainty even for the same point estimate. This emphasizes that researchers should carefully consider where the randomness stems from in their data, as it has direct implications for the accuracy of inference.
参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.
Physical https://forms.gle/gbEJ6RBWi1FKNMP2A
Virtual https://us06web.zoom.us/meeting/register/tZUucuCspjkvGdB7Q-7OEm-xTUNRM80uuiUL
Date: Monday May 13th
Time: 15:00 - 16:00 JST
In person location: ISM D222
Speaker: Kaoru Irie, University of Tokyo
Title: Gibbs sampler for matrix generalized inverse Gaussian distributions
Abstract: Matrix generalized inverse Gaussian (MGIG) distributions are a multivariate extension of the well-known univariate GIG distributions. Typically, the MGIG distributions are obtained as the full conditional posterior distributions of the variance matrix in many multivariate models, such as the location-scale mixture of multivariate normals. Thus, in implementing Markov chain Monte Carlo (MCMC) algorithms for posterior inference, simulation from the MGIG distributions is required. However, an efficient sampling scheme for the MGIG distributions has not been fully developed. In this study, we propose a novel blocked Gibbs sampler for the MGIG distributions based on the Cholesky decomposition. We show that the full conditionals of the entries of the diagonal and unit lower-triangular matrices are univariate GIG and multivariate normal distributions, respectively. Several variants of the Metropolis-Hastings algorithm can also be considered for this problem, but we mathematically prove that the average acceptance rates become extremely low in particular scenarios. We demonstrate the computational efficiency of the proposed Gibbs sampler through simulation studies and data analysis. This is joint work with Yasuyuki Hamura (Kyoto) and Shonosuke Sugasawa (Keio).
参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.
Physical: https://forms.gle/XMAMc4WMCdXXXyKX8
Virtual: https://us06web.zoom.us/meeting/register/tZYucOChrTwuE9H8rMRgZ9a0Yw596TppqGtt
Date: Monday Apr 22nd
Time: 15:00 - 16:00 JST
In person location: ISM D222
Speaker: 奥戸 道子, 東大情報理工/ Michiko Okudo, University of Tokyo
Title: 事後平均とMAP推定量を漸近的に一致させる matching prior pair
Abstract: ベイズ法に現れる推定量の性質や情報幾何との関連について、最近得られた結果[1]を紹介する。
MAP推定量と事後平均はベイズ法でよく用いられる推定量であるが、本研究ではこの２つが漸近的に一致する事前分布のペアを求める。
ペアの密度が満たす条件を導出し、情報幾何でα-平坦と呼ばれるクラスのモデルでは条件が簡単な形で書けることを紹介する。
指数型分布族や一般化線形モデルを含むいくつかの解析的な例と数値例を紹介する。
この研究は統計数理研究所の矢野恵佑氏との共同研究である。
ベイズ法と情報幾何に関する講演者のこれまでの研究の概観も紹介する予定である。
参考文献：
[1] M. Okudo & K. Yano (2023). Matching prior pairs connecting Maximum A Posteriori estimation and posterior expectation. arXiv preprint arXiv:2312.09586.
参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.
本発表は日本語で開催します．This presentation will be held in Japanese.
Physical https://forms.gle/WwGq8r6ZALkvXNX5A
Virtual https://us06web.zoom.us/meeting/register/tZEtd-mvrjssHtZpbB3kzKRobbkrySP_9WMs
Date: Monday Mar 18th
Time: 13:00 - 14:00 JST
In person location: RIKEN Center for Brain Science, Central Building, C202
Speaker: Omar Chehab, ENSAE-CREST
Title: Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyond
Abstract: Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between a tractable "proposal" distribution and the unnormalized "target" distribution. Promi- nent estimators in this family include annealed importance sampling and annealed noise-contrastive estimation (NCE). Such methods hinge on a number of design choices: which estimator to use, which path of distributions to use and whether to use a path at all; so far, there is no definitive theory on which choices are efficient. Here, we evaluate each design choice by the asymptotic estimation error it produces. First, we show that using NCE is more efficient than the importance sampling esti- mator, but in the limit of infinitesimal path steps, the difference vanishes. Second, we find that using the geometric path brings down the estimation error from an exponential to a polynomial function of the parameter distance between the target and proposal distributions. Third, we find that the arithmetic path, while rarely used, can offer optimality properties over the universally-used geometric path. In fact, in a particular limit, the optimal path is arithmetic. Based on this theory, we finally propose a two-step estimator to approximate the optimal path in an efficient way.
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Physical: https://forms.gle/7nhDTSeJokNdVx8a9
Virtual: https://us06web.zoom.us/meeting/register/tZ0td-GrrjorHt0YpnLKQuqPLxd3lsFgopFb
Date: Thursday Mar 7th
Time: 11:00 - 12:00 JST
In person location: Seminar Room B, 3rd Floor, Building No. 6, Faculty of Engineering, Hongo Campus, University of Tokyo
Speaker: Arnaud Doucet/ Oxford University & Google Deep Mind
Title: Ensemble Rejection Sampling
Abstract: We introduce Ensemble Rejection Sampling, a scheme for exact simulation from the posterior distribution of the latent states of a class of non-linear non-Gaussian state-space models. Ensemble Rejection Sampling relies on a proposal for the high-dimensional state sequence built using ensembles of state samples. Although this algorithm can be interpreted as a rejection sampling scheme acting on an extended space, we show, under regularity conditions, that the expected computational cost to obtain an exact sample increases cubically with the length of the state sequence instead of exponentially as in standard rejection sampling. We demonstrate this methodology by sampling exact state sequences according to the posterior distribution of a stochastic volatility model and a cell model. We also present an application to rare event simulation.
参加希望の方はフォームに登録をお願いします．Kindly register by using the links provided below.
Physical: https://forms.gle/oFNDwoGvwD6WtZAM8
Virtual: https://us06web.zoom.us/meeting/register/tZAtdOGopjgvE9QR0urNFDTxMKMxSyuwWGQ8