Tomoyuki Shirai | Last modified date：2020.06.18 |

Professor /
Division of Fundamental mathematics /
Institute of Mathematics for Industry

**Presentations**

1. | Tomoyuki Shirai, Limit theorems for persistence diagrams, The 5th Institute of Mathematical Statistics, Asia Pacific Rim Meeting, 2018.06. |

2. | Tomoyuki Shirai, Limit theorems for persistence diagrams, KTH seminar, 2020.06. |

3. | Tomoyuki Shirai, Limit theorems for determinantal point processes, Probability Conference on Random Matrices and Related Topics, 2019.05. |

4. | Tomoyuki Shirai, Limit theorems for determinantal point processes, International Conference on Mathematical Methods in Physics, 2019.04. |

5. | Takayuki Osogami, Rudy Raymond, Tomoyuki Shirai, Akshay Goel, Takanori Maehara, Dynamic determinantal point processes, 32nd AAAI Conference on Artificial Intelligence, AAAI 2018, 2018.01, The determinantal point process (DPP) has been receiving increasing attention in machine learning as a generative model of subsets consisting of relevant and diverse items. Recently, there has been a significant progress in developing efficient algorithms for learning the kernel matrix that characterizes a DPP. Here, we propose a dynamic DPP, which is a DPP whose kernel can change over time, and develop efficient learning algorithms for the dynamic DPP. In the dynamic DPP, the kernel depends on the subsets selected in the past, but we assume a particular structure in the dependency to allow efficient learning. We also assume that the kernel has a low rank and exploit a recently proposed learning algorithm for the DPP with low-rank factorization, but also show that its bottleneck computation can be reduced from O(M^{2} K) time to O(M K^{2}) time, where M is the number of items under consideration, and K is the rank of the kernel, which can be set smaller than M by orders of magnitude.. |

6. | Tomoyuki Shirai, Limit theorems for persistence diagrams, the Japanese-German Open Conference on Stochastic Analysis (JP-GER Conference 2017), 2017.09, The persistent homology of a stationary point process on R^N is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topological features of the point process such as loops, cavities, etc. in a multiscale way. The key ingredient is the persistence dia- gram, which is an expression of the persistent homology. We prove the strong law of large numbers for persistence diagrams as the window size tends to in- finity and give a sufficient condition for the support of the limiting persistence diagram to coincide with the geometrically realizable region. We also discuss a central limit theorem for persistent Betti numbers.. |

7. | Tomoyuki Shirai, Determinantal point processes associated with de Branges spaces, Various Aspects of Multiple Zeta Functions, 2017.08. |

8. | Tomoyuki Shirai, Determinantal point processes associated with extended kernels and spanning trees on series-parallel graphs, Function theory and dynamics of point processes, 2017.06. |

9. | Hitoshi Nagamatsu, Naoto Miyoshi, Tomoyuki Shirai, Padé approximation for coverage probability in cellular networks, 2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2014, 2014, Coverage probability is one of the most important metrics for evaluating the performance of wireless networks. However, the spatial stochastic models for which a computable expression of the coverage probability is available are restricted (such as the Poisson based or α-Ginibre based models). Furthermore, even if it is available, the practical numerical computation may be time-consuming (in the case of α-Ginibre based model). In this paper, we propose the application of Padé approximation to the coverage probability in the wireless network models based on general spatial stationary point processes. The required Maclaurin coefficients are expressed in terms of the moment measures of the point process, so that the approximants are expected to be available for a broader class of point processes. Through some numerical experiments for the cellular network model, we demonstrate that the Padé approximation is effectively applicable for evaluating the coverage probability.. |

10. | Tetsuro Morimura, Takayuki Osogami, Tomoyuki Shirai, Mixing-time regularized policy gradient, 28th AAAI Conference on Artificial Intelligence, AAAI 2014, 26th Innovative Applications of Artificial Intelligence Conference, IAAI 2014 and the 5th Symposium on Educational Advances in Artificial Intelligence, EAAI 2014, 2014, Policy gradient reinforcement learning (PGRL) has been receiving substantial attention as a mean for seeking stochastic policies that maximize cumulative reward. However, the learning speed of PGRL is known to decrease substantially when PGRL explores the policies that give the Markov chains having long mixing time. We study a new approach of regularizing how the PGRL explores the policies by the use of the hitting time of the Markov chains. The hitting time gives an upper bound on the mixing time, and the proposed approach improves the learning efficiency by keeping the mixing time of the Markov chains short. In particular, we propose a method of temporal-difference learning for estimating the gradient of the hitting time. Numerical experiments show that the proposed method outperforms conventional methods of PGRL.. |

11. | Naoto Miyoshi, Tomoyuki Shirai, Downlink coverage probability in a cellular network with Ginibre deployed base stations and Nakagami-m fading channels, 2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2015, 2015.07, Recently, spatial stochastic models based on deter-minantal point processes (DPP) are studied as promising models for analysis of cellular wireless networks. Indeed, the DPPs can express the repulsive nature of the macro base station (BS) configuration observed in a real cellular network and have many desirable mathematical properties to analyze the network performance. However, almost all the prior works on the DPP based models assume the Rayleigh fading while the spatial models based on Poisson point processes have been developed to allow arbitrary distributions of fading/shadowing propagation effects. In order for the DPP based model to be more promising, it is essential to extend it to allow non-Rayleigh propagation effects. In the present paper, we propose the downlink cellular network model where the BSs are deployed according to the Ginibre point process, which is one of the main examples of the DPPs, over Nakagami-m fading. For the proposed model, we derive a numerically computable form of the coverage probability and reveal some properties of it numerically and theoretically.. |

12. | Naoto Miyoshi, Tomoyuki Shirai, A sufficient condition for tail asymptotics of SIR distribution in downlink cellular networks, 14th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2016, 2016.06, We consider the spatial stochastic model of single-tier downlink cellular networks, where the wireless base stations are deployed according to a general stationary point process on the Euclidean plane with general i.i.d. propagation effects. Recently, Ganti & Haenggi (2016) consider the same general cellular network model and, as one of many significant results, derive the tail asymptotics of the signal-to-interference ratio (SIR) distribution. However, they do not mention any conditions under which the result holds. In this paper, we compensate their result for the lack of the condition and expose a sufficient condition for the asymptotic result to be valid. We further illustrate some examples satisfying such a sufficient condition and indicate the corresponding asymptotic results for the example models. We give also a simple counterexample violating the sufficient condition.. |

13. | 白井 朋之, Probabilistic apsects of persistent homology, La Trobe-Kyushu Joint Seminar on Mathematics for Industry, 2016.06. |

14. | 白井 朋之, Persistent homology and minimum spanning acycle for certain random complexes, Workshop on "High-Dimensional Expanders 2016", 2016.06. |

15. | 白井 朋之, Lifetime Sum of Persistent Homology and Minimum Spanning Acycles in Random Simplicial Complexes, Topological Data Analysis on Materials Science, 2015.02. |

16. | 白井 朋之, Persistent homology of certain random simplicial complexes, 13thSALSIS The 13th workshop on "Stochastic Analysis on Large Scale Interacting Systems", 2014.11. |

17. | 白井 朋之, Absolute continuity and singularity for the Ginibre point process and its Palm measures, UK-Japan Stochastic Analysis School , 2014.09. |

18. | 白井 朋之, Persistent homology for certain random simplicial complexes, International Conference on "Stochastic Processes, Analysis and Mathematical Physics, 2014.08. |

19. | Tomoyuki Shirai, Correlation functions for zeros of a Gaussian power series and Pfaffians, Seminars on determinantal processes and related topics, 2013.03. |

20. | Tomoyuki Shirai, On the zeros of random analytic functions, Markov processes and stochastic analysis, 2013.01. |

21. | Random analytic functions and their zeros. |

22. | , [URL]. |

23. | , [URL]. |

Unauthorized reprint of the contents of this database is prohibited.