Personal profile

Research interests

My current research is in the area of machine learning, including both mathematical foundations and applications. Prediction with expert advice and topological data analysis are my main topics of interest. 

Prediction with expert advice is a paradigm for sequential forecasting that studies how one can merge predictions from different sources when reliability of these sources needs to be inferred from the predictions themselves. This paradigm is close to online bandits and related to many other machine learning techniques, from ridge regression to boosting. I am particularly interested in direct applications for prediction with expert advice algorithms.

Topological data analysis is a relatively recent but already mature area of machine learning that tries to apply notions from topology, a highly abstract branch of pure mathematics, to finding patterns in point clouds. Currently, I am working mostly on expressing topological data analysis ideas in the form of kernels inducing a reproducing kernel Hilbert space structure on data.

I am also remaining interested in the developments in both of my original research areas: algorithmic information theory / Kolmogorov complexity and constructive logical semantics.

Approach to teaching

I have taught a range of mathematical and statistical courses for both undergraduate and postgraduate students. My ideal teaching includes a rigorous but concise mathematical presentation of the main ideas illustrated by a few carefully selected examples and extensive computer simulations where possible. However, I believe that the only way to learn something is to do it, and hence I aim at providing students with a wide range of exercises, from simple modifications of lecture examples to real-world (or quasi real-world) problems that require combining and synthesising knowledge from different sources.

Scholarly biography

I studied mathematics at Moscow State University and completed a PhD in algorithmic information theory and non-classical logics in 2003. Then my research interests shifted to machine learning and I held research positions in IDSIA (Lugano, Switzerland), LIFM (Marseille, France), Royal Holloway University of London and Durham University. Finally, after a lectureship at University of Bedfordshire, I joined University of Brighton in 2015.

Supervisory Interests

I am interested in supervising postgraduate research projects related to mathematically intensive methods of machine learning. My main area is sequential online forecasting, particularly prediction with expert advice. I am also interested in reinforcement learning (especially as a generalisation of online forecasting), kernel methods and topological data analysis.


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