Fisher-Rao metric for Gaussian processes
17 Feb 2025, 16:00 — Room 326, UniGe DIBRIS/DIMA, Via Dodecaneso 35
![Minh.Ha.Quang - [Mento Sopracciglio Fronte]](/media/images/Screenshot_2025-02-17_at_12_jcvreJ9.24.width-800.jpg)
Speaker:
Minh Ha Quang — RIKEN Center for Advanced Intelligence Project (RIKEN-AIP)
Minh Ha Quang — RIKEN Center for Advanced Intelligence Project (RIKEN-AIP)
Abstract:
The Fisher-Rao metric is a central object in Information Geometry and its applications in machine learning and statistics. On the set of zero-mean Gaussian densities on Euclidean space, the Fisher-Rao metric and many of its associated quantities, e.g. Fisher-Rao distance, admit closed form formulas. In this talk, we present their generalization to the infinite-dimensional setting of Gaussian measures on Hilbert space and Gaussian processes. In general, the exact formulation is not generalizable on the set of all Gaussian measures on an infinite-dimensional Hilbert space. Instead, we show that on the set of all Gaussian measures which areequivalent to a fixed one, all finite-dimensional formulas admit direct generalization. By employing regularization, we then have a formulation that is valid for all Gaussian measures on Hilbert space. In the setting of Gaussian processes, by reproducing kernel Hilbert space (RKHS) methodology, we obtain consistent finite-dimensional approximations of the infinite-dimensional quantities that can be practically employed.
The Fisher-Rao metric is a central object in Information Geometry and its applications in machine learning and statistics. On the set of zero-mean Gaussian densities on Euclidean space, the Fisher-Rao metric and many of its associated quantities, e.g. Fisher-Rao distance, admit closed form formulas. In this talk, we present their generalization to the infinite-dimensional setting of Gaussian measures on Hilbert space and Gaussian processes. In general, the exact formulation is not generalizable on the set of all Gaussian measures on an infinite-dimensional Hilbert space. Instead, we show that on the set of all Gaussian measures which areequivalent to a fixed one, all finite-dimensional formulas admit direct generalization. By employing regularization, we then have a formulation that is valid for all Gaussian measures on Hilbert space. In the setting of Gaussian processes, by reproducing kernel Hilbert space (RKHS) methodology, we obtain consistent finite-dimensional approximations of the infinite-dimensional quantities that can be practically employed.
Bio:
Minh Ha Quang received his PhD in Mathematics in 2006 from Brown University (USA). He is currently Team Leader of the Functional Analytic Learning Team at the RIKEN Center for Advanced Intelligence Project (RIKEN-AIP) in Tokyo, Japan. Before joining RIKEN in June 2018, he was a researcher at the Pattern Analysis and Computer Vision (PAVIS) group at the Italian Institute of Technology (IIT) in Genova, Italy. His current research interests are machine learning and statistical methodologies using functional analysis, information geometry, and optimal transport.
Minh Ha Quang received his PhD in Mathematics in 2006 from Brown University (USA). He is currently Team Leader of the Functional Analytic Learning Team at the RIKEN Center for Advanced Intelligence Project (RIKEN-AIP) in Tokyo, Japan. Before joining RIKEN in June 2018, he was a researcher at the Pattern Analysis and Computer Vision (PAVIS) group at the Italian Institute of Technology (IIT) in Genova, Italy. His current research interests are machine learning and statistical methodologies using functional analysis, information geometry, and optimal transport.