Photo

Random Data Lab. Inc.    ( 日本語 )

BLOG   Linkedin    Twitter

orcid.org/0000-0002-2699-2883

Contact

Random Data Lab., Tokyo 121-0062 Japan

hayato DOT takahashi AT ieee DOT org

hayato DOT h-takahashi AT sakura DOT ne DOT jp

Research Summary

Title: Bayesian definition of random sequences with respect to conditional probabilities.
Author: Hayato Takahashi
Abstract: We study Martin-Löf random (ML-random) points on computable probability measures on sample and parameter spaces(Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of conditional blind randomness. We show that variants of conditional blind randomness are ill-defined from the Bayes statistical point of view. We prove that if the sets of random sequences of uniformly computable parametric models are pairwise disjoint then there is a consistent estimator for the model. Finally, we present an algorithmic solution to a classical problem in Bayes statistics, i.e. the posterior distributions converge weakly to almost all parameters if and only if the posterior distributions converge weakly to all ML-random parameters.

Information and Computation, Article 105041 Vol 292, 2023

Title: Computational limits to nonparametric estimation for ergodic processes.
Author: Hayato Takahashi
Abstract: A new negative result for nonparametric estimation of binary ergodic processes is shown. The problem of estimation of distribution with any degree of accuracy is studied. Then it is shown that for any countable class of estimators there is a zero-entropy binary ergodic process that is inconsistent with the class of estimators. Our result is different from other negative results for universal forecasting scheme of ergodic processes.

arxiv:1002.1559

Title: Universal parameterized family of distributions of runs
Author: Hayato Takahashi
Abstract: We present explicit formulae for parameterized families of distributions of the number of nonoverlapping words and increasing nonverlapping words in independent and identically distributed (i.i.d.) finite valued random variables, respectively. Then we provide an explicit formula for a parameterized family of distributions of the number of runs, which generalizes \(\mu\)-overlapping distributions for \(\mu\geq 0\) in i.i.d.~binary valued random variables. We also demonstrate that of runs whose size are exactly given numbers (Mood 1940). The number of arithmetic operations required to compute our formula for generalized distributions of runs for fixed number of parameters and fixed range is linear order of sample size.

https://arxiv.org/pdf/2302.14356.pdf NEW

Recent presentation

Papers

Awards

SITA Young Researcher Award 2004

Development of Open System Performance Evaluation Tools, NEC Award 1997.

Projects

Research Representative, KAKENHI Project,
Randomness Theory and Statistical Tests for Pseudo Random Numbers, 2012-2016.

Research Representative, ISM Cooperative Research Program, General Cooperative Research 2,
Ergodic theory, information theory, computer science and related areas, 2010-2012.

Professional Affiliations

IEEE Senior Member

IEICE SITA, Society of Information Theory and Its Applications

The Mathematical Society of Japan

AMS Reviewer

Japanese Society for Bioinformatics