Title:
Stochastic (Partial) Differential Equations and Gaussian Processes
Abstract:
Stochastic partial differential equations and stochastic differential equations can be seen as alternatives to kernels in representation of Gaussian processes in machine learning and inverse problems. Linear operator equations correspond to spatial kernels, and temporal kernels are equivalent to linear It^o stochastic differential equations. The differential equation representations allow for the use of differential equation numerical methods on Gaussian processes. For example, finite-differences, finite elements, basis function methods, and Galerkin methods can be used. In temporal and spatio-temporal case we can use linear-time Kalman filter and smoother approaches.
Bio:
Prof. Simo Särkkä received his Master of Science (Tech.) degree (with distinction) in engineering physics and mathematics, and Doctor of Science (Tech.) degree (with distinction) in electrical and communications engineering from Helsinki University of Technology, Espoo, Finland, in 2000 and 2006, respectively. From 2000 to 2010 he worked with Nokia Ltd., Indagon Ltd., and Nalco Company in various industrial research projects related to telecommunications, positioning systems, and industrial process control. From 2010 to 2013 he worked as a Senior Researcher with the Department of Biomedical Engineering and Computational Science (BECS) at Aalto University, Finland.
Currently, Dr. Särkkä is an Associate Professor and Academy Research Fellow with Aalto University, Technical Advisor and Director of IndoorAtlas Ltd., and an Adjunct Professor with Lappeenranta University of Technology. In 2013 he was a Visiting Professor with the Department of Statistics of Oxford University and in 2011 he was a Visiting Scholar with the Department of Engineering at the University of Cambridge, UK. His research interests are in multi-sensor data processing systems with applications in location sensing, health technology, machine learning, inverse problems, and brain imaging. He has authored or coauthored ~80 peer-reviewed scientific articles and has 3 granted patents. His first book “Bayesian Filtering and Smoothing” and its Chinese translation was recently published via the Cambridge University Press. He is a Senior Member of IEEE and serving as an Associate Editor of IEEE Signal Processing Letters from August 2015.