3-14-1 Kouhoku-ku, Hiyoshi, Yokohama 223-8522, JAPAN
Speaker: Isao Ishikawa
Title: Metrics on random dynamical systems via vector-valued reproducing kernel Hilbert spaces
Abstract: The development of a metric on structural data-generating mechanisms is fundamental in machine learning and the related fields. In this talk, we introduce a general framework to construct metrics on random nonlinear dynamical systems, which are defined with the Perron-Frobenius operators in vector-valued reproducing kernel Hilbert spaces (vvRKHSs). Here, vvRKHSs are employed to design mathematically manageable metrics and also to introduce $L^2(\Omega)$-valued kernels, which are necessary to handle the randomness in systems.
Our metric is a natural extension of existing metrics for deterministic systems, and can give a specification of the kernel maximal mean discrepancy of random processes.
Moreover, by considering the time-wise independence of random processes, we discuss the connection between our metric and the independence criteria with kernels such as Hilbert-Schmidt independence criteria.
We empirically illustrate our metric with synthetic data, and evaluate it in the context of the independence test for random processes. This is a joint works with Akinori Tanaka, Masahiro Ikeda, and Yoshinobu Kawahara.
time: 13:00 - 14:00 + 30 min
place: Keio Univ. Yagami-campus Bldg.14th, 6F
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