Pierre Nyquist

KTH Royal Institute of Technology

Title: Piecewise deterministic Markov processes for MCMC - A large deviations analysis of the zig-zag sampler

Abstract:

Over the last decade piecewise deterministic Markov processes (PDMPs) have emerged as a new tool for MCMC simulation, potentially mitigating the problems of slow convergence and heavy computational cost exhibited by many other methods. The two main examples of such processes are the bouncy particle sampler and the zig-zag sampler. The idea of using PDMPs extends the ubiquitous discrete time MCMC methodology towards a new continuous time approach, having several advantageous aspects, for example non-reversibility and the possibility to reduce the computational effort per iteration by using subsampling techniques.

In order to employ this new PDMP methodology a solid understanding of mathematical properties of these methods is necessary. Whereas the theoretical

properties of PDMPs have been an active research area in recent years, our understanding of the performance of the corresponding MCMC methods is still incomplete. In particular knowledge of the speed of convergence of time averages is essential in choosing the most suitable sampling technology for a particular problem and in tuning the parameters of the chosen method.

In this talk I will discuss recent work on using large deviation results for empirical measures to study and compare the performance of PDMPs. We will start with a general discussion of non-reversible MCMC methods and the use of empirical measure large deviations in the simulation setting. We then focus on PDMPs, in particular the zig-zag sampler, and a large deviations analysis based on the Feng-Krutz approach; no previous knowledge of either PDMPs or large deviations will be necessary. This is based on joint work with Joris Bierkens and Mikola Schlottke.

Bio:

Pierre Nyquist is associate professor in the Department of Mathematics at KTH Royal Institute of Technology in Stockholm. He received his PhD in Applied and Computational Mathematics from the same institution in 2014. Before moving back to KTH in 2018 he spent time as a postdoc in the Division of Applied Mathematics at Brown University and as assistant professor at Eindhoven University of Technology. His research interests lie broadly at the intersection of analysis and probability and include large deviations, stochastic control, interacting particle systems and design and analysis of Monte Carlo methods. Recent work has focused on the mathematical foundation of methods in machine learning.

Title: Piecewise deterministic Markov processes for MCMC - A large deviations analysis of the zig-zag sampler

Abstract:

Over the last decade piecewise deterministic Markov processes (PDMPs) have emerged as a new tool for MCMC simulation, potentially mitigating the problems of slow convergence and heavy computational cost exhibited by many other methods. The two main examples of such processes are the bouncy particle sampler and the zig-zag sampler. The idea of using PDMPs extends the ubiquitous discrete time MCMC methodology towards a new continuous time approach, having several advantageous aspects, for example non-reversibility and the possibility to reduce the computational effort per iteration by using subsampling techniques.

In order to employ this new PDMP methodology a solid understanding of mathematical properties of these methods is necessary. Whereas the theoretical

properties of PDMPs have been an active research area in recent years, our understanding of the performance of the corresponding MCMC methods is still incomplete. In particular knowledge of the speed of convergence of time averages is essential in choosing the most suitable sampling technology for a particular problem and in tuning the parameters of the chosen method.

In this talk I will discuss recent work on using large deviation results for empirical measures to study and compare the performance of PDMPs. We will start with a general discussion of non-reversible MCMC methods and the use of empirical measure large deviations in the simulation setting. We then focus on PDMPs, in particular the zig-zag sampler, and a large deviations analysis based on the Feng-Krutz approach; no previous knowledge of either PDMPs or large deviations will be necessary. This is based on joint work with Joris Bierkens and Mikola Schlottke.

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Bio:

Pierre Nyquist is associate professor in the Department of Mathematics at KTH Royal Institute of Technology in Stockholm. He received his PhD in Applied and Computational Mathematics from the same institution in 2014. Before moving back to KTH in 2018 he spent time as a postdoc in the Division of Applied Mathematics at Brown University and as assistant professor at Eindhoven University of Technology. His research interests lie broadly at the intersection of analysis and probability and include large deviations, stochastic control, interacting particle systems and design and analysis of Monte Carlo methods. Recent work has focused on the mathematical foundation of methods in machine learning.