The following schedule is based on Japanese standard time.
Date: Wednesday May 28th
Time: 11:00 - 12:00 JST
In person location: ISM D222
Speaker: Luke Hardcastle, University College London
Title: Diffusion piecewise exponential models for survival extrapolation using Piecewise Deterministic Monte Carlo
Abstract: In this talk I will introduce the diffusion piecewise exponential model. Piecewise exponential model is a flexible non-parametric approach for time-to-event data, but extrapolation beyond final observation times typically relies on random walk priors and deterministic knot locations, resulting in unrealistic long-term hazards. The diffusion piecewise exponential model, a prior framework consisting of a discretised diffusion for the hazard, that can encode a wide variety of information about the long-term behaviour of the hazard, time changed by a Poisson process prior for knot locations. This allows the behaviour of the hazard in the observation period to be combined with prior information to inform extrapolations. Efficient posterior sampling is achieved using Piecewise Deterministic Markov Processes, whereby we extend existing approaches using sticky dynamics from sampling spike-and-slab distributions to more general transdimensional posteriors. We focus on applications in Health Technology Assessment, where the need to compute mean survival requires hazard functions to be extrapolated beyond the observation period, showcasing performance on datasets for Colon cancer patients.
This is a joint work with Samuel Livingstone and Gianluca Baio and is based on the pre-print: https://arxiv.org/abs/2505.05932
オンライン参加希望の方はフォームに登録をお願いします．If you plan to attend online, kindly register by using the link:
Virtual: https://us06web.zoom.us/meeting/register/G01p2PuKR7C_RxhPBbVQYQ
Date: Friday May 2nd
Time: 13:30 - 14:30 JST
In person Location: Room 126, Graduate School of Mathematical Sciences, University of Tokyo, Komaba Campus
Speaker: 今井 竣祐，京大経済 /Shunsuke Imai, Kyoto University
Title: General Bayesian Semiparametric Inference with Hyvärinen Score
Abstract: This paper proposes a novel framework for semiparametric Bayesian inference on finite-dimensional parameters under existence of nuisance functions. Based on a pseudo-model defined by (profiled) loss functions for the finite dimensional parameters and the Hyv\"arinen score, we propose a general posterior distribution, named semiparametric Hyv\"arinen (SH) posterior. The SH posterior enables us to make inference on the parameters of interest with taking account of uncertainty in the estimation/selection of tuning parameters in estimating the unknown nuisance functions. We establish its theoretical justification of the SH posterior under large samples, and provide posterior computation algorithm. As concrete examples, we provide the posterior inference of partial linear models and single index models, and demonstrate the performance through simulation.
オンライン参加希望の方はフォームに登録をお願いします．If you plan to attend online, kindly register by using the link:
Virtual: https://us06web.zoom.us/meeting/register/3XxtsHwaQVSN7BuINu6E8g
Date: Wednesday Apr 9th
Time: 10:00 - 11:00 JST
In person location: ISM D222
Speaker: 吉田淳一郎，東大数理 / Junichiro Yoshida, University of Tokyo
Title: Penalized estimation for non-identifiable models
Abstract: 識別不可能なモデルの応用例は、有限混合分布や点過程の重ね合わせ、更には深層学習など多岐に渡る一方、それらの漸近理論は複雑であるが故、依然として部分的に未発展であり重要な研究対象となっている。そこで、我々は罰則付き推定を用いることにより、識別不可能なモデルにおいても直接的なパラメータ推定及びモデル選択を可能にし、推定量の漸近正規性及びオラクル性を示した。本発表では、証明の鍵となるアイデアについて話し、時間が許せば、特異点解消定理のような発展的話題についても触れる予定である。
While applications of non-identifiable models range from finite mixture distribution and superposed point process to deep learning, asymptotic theory on them remains partially undeveloped and an important research subject due to its complexity. Here, using penalized estimation, we enable direct parametric estimation and model selection even for non-identifiable models, and show the asymptotic normality and oracle property of the estimator. In this presentation, we will discuss the key ideas of the proof and, if time permits, mention some advanced topics such as resolution of singularities.
オンライン参加希望の方はフォームに登録をお願いします．If you plan to attend online, kindly register by using the link:
Virtual: https://us06web.zoom.us/j/87061904597?pwd=t7asGvNYIbmUx8NrJdI0aCqhBBOgVR.1
Date: Thursday Apr 3rd
Time: 14:30 - 15:30 JST
In person location: ISM D222
Speaker: 塩谷 天章，東大数理 / Takaaki Shiotani, University of Tokyo
Title: Statistical inference for highly correlated stationary point processes and noisy bivariate Neyman-Scott processes
Abstract: 高頻度金融データにおけるlead-lag推定問題を動機として、ガンマカーネルをもち、必ずしもPoissonとは限らないノイズを許容する、2変量Neyman-Scott点過程モデル(NBNSP-G)を導入する。パラメータ推定は2次のcomposite型疑似尤度を用いて行う。しかしながら、推定量の一致性と漸近正規性を証明しようとすると、ガンマカーネルの発散に起因して、既存の漸近理論でよく仮定されるモーメント密度関数の有界性が破綻してしまう。そこで、有界性を緩和し可積分性の条件下で一般の2変量点過程に対する推定量の漸近論を構築し、その系としてNBNSP-Gに対する推定量の一致性と漸近正規性を示した。
Motivated by the lead-lag estimation in high-frequency financial data, we introduce a bivariate Neyman-Scott point process model that employs a gamma kernel and allows for noise that is not necessarily Poisson (NBNSP-G). Parameter estimation is performed using a second-order composite-type likelihood. However, when attempting to prove consistency and asymptotic normality of the estimators, the unboundedness arising from the gamma kernel causes a failure of the boundedness condition on the moment density function that is often assumed in existing asymptotic theory. To address this, we relax the boundedness assumption to an integrability condition and develop an asymptotic theory for estimators of general bivariate point processes. As a corollary, we establish the consistency and asymptotic normality of the estimators for NBNSP-G.
オンライン参加希望の方はフォームに登録をお願いします．If you plan to attend online, kindly register by using the link:
Virtual: https://us06web.zoom.us/meeting/register/iMi6fIJaTQSgAHhoWo-7fQ
Date: Thursday Mar 13th
Time: 13:30 - 14:30 JST
In person location: ISM D222
Speaker: 行德 義弘, 東大数理 / Yoshihiro Gyotoku, University of Tokyo
Title: Nonparametric Point Process Regression
Abstract: 我々は、Muni-Toke Yoshida (2022) で提案された点過程回帰モデルのノンパラメトリックなバージョンを提案し、その汎化誤差に理論的な上界を与えた。この結果は、Schmidt-Hieber (2020) で示された独立同分布観測に対するノンパラメトリック回帰モデルに対する理論を拡張するものである。証明のために、新たな大偏差不等式を導入した。具体的には、強混合性または弱従属性を満たす確率過程に対して Merlevède, Peligrad and Rio (2010) で与えられた不等式を、今回の証明に必要な要件を満たすように改良したものである。本発表では、この改良した不等式の必要性およびその証明の主要なアイディアについても概説する。時間が許せば、深層学習を用いた回帰問題、特に指値注文票の解析への応用についても紹介する。
We propose a nonparametric version of the point process regression model introduced by Muni-Toke Yoshida (2022) and establish a theoretical upper bound on its generalization error. This result extends the nonparametric regression model for independently and identically distributed observations presented in Schmidt-Hieber (2020). To prove our result, we introduce a new large deviation inequality. Specifically, we adapt the inequality provided by Merlevède, Peligrad and Rio (2010) for stochastic processes satisfying either the strong mixing or weak dependence property so that it meets the necessary requirements for our proof. We also outline the necessity and main ideas behind this modified inequality. If time permits, we will present an application of our approach to regression problems in deep learning, focusing on the analysis of limit order book data.
オンライン参加希望の方はフォームに登録をお願いします．If you plan to attend online, kindly register by using the link:
Virtual: https://us06web.zoom.us/meeting/register/JKApnnCBSRWqF1tn1aSaWA