Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Jiayi Kang

Thursday, November 3, 2022 8:30 PM - 9:00 PM

Online

I will introduce a work considered data fusion for the purpose of smoothing and interpolation based on observation records with missing data. Stochastic processes are generated by linear stochastic models. The paper begins by drawing a connection between time reversal in stochastic systems and all-pass extensions. A particular normalization (choice of basis) between the two time-directions allows the two to share the same orthonormalized state process and simplifies the mathematics of data fusion. In this framework, they derive symmetric and balanced Mayne–Fraser-like formulas that apply simultaneously to continuous-time smoothing and interpolation, providing a definitive unification of these concepts. The absence of data over subintervals requires in general a hybrid filtering approach involving both continuous-time and discrete-time filtering steps.

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025. His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.