University of Edinburgh

TBD

TBA

Deep Gaussian processes have proved remarkably successful as a tool for various statistical inference tasks. This success relates in part to the flexibility of these processes and their ability to capture complex, non-stationary behaviours. 

In this talk, we will introduce the general framework of deep Gaussian processes, in which many examples can be constructed, and demonstrate their superiority in inverse problems including computational imaging and regression.

 We will discuss recent algorithmic developments for efficient sampling, as well as recent theoretical results which give crucial insight into the behaviour of the methodology.

 

I will discuss certain dynamics of interacting particles in interlacing arrays with inhomogeneous, in space and time, jump probabilities and their relations to conditioned random walks and random tilings of the Aztec diamond.

In this talk, we will present a loop expansion for lattice gauge theories and its application to prove ultraviolet stability in the Abelian Higgs model. We will first describe this loop expansion and how it relates to earlier works of Brydges-Frohlich-Seiler. We will then show how the expansion leads to a quantitative diamagnetic inequality, which in turn implies moment estimates, uniform in the lattice spacing, on the Holder-Besov norm of the gauge field marginal of the Abelian Higgs lattice model. Based on Gauge field marginal of an Abelian Higgs model, which is joint work with Ajay Chandra.

The study of cohomology of infinite-dimensional Lie algebras was started by Gel'fand and Fuchs in the late 1960s. Since then, significant progress has been made, mainly focusing on the Witt algebra (the Lie algebra of vector fields on the punctured affine line) and some of its subalgebras. In this talk, I will explain the basics of Lie algebra cohomology and sketch the computation of the first cohomology group of certain subalgebras of the Witt algebra known as submodule-subalgebras. Interestingly, these cohomology groups are, in some sense, controlled by the cohomology of the Witt algebra. This can be explained by the fact that the Witt algebra can be abstractly reconstructed from any of its submodule-subalgebras, which can be described as a universal property satisfied by the Witt algebra.

HiGHS is open-source optimization software for linear programming, mixed-integer programming, and quadratic programming. Created initially from research solvers written by Edinburgh PhD students, HiGHS attracted industrial funding that allowed further development, and saw it contribute to a REF 2021 Impact Case Study. Having been identified as a game-changer by the open-source energy systems planning community, the resulting crowdfunding campaign has received large donations that will allow the HiGHS project to expand and create further Impact.

This talk will give an insight into the state-of-the-art techniques underlying the linear programming solvers in HiGHS, with a particular focus on the challenge of solving sequences of linear systems of equations with remarkable properties. The means by which "gradware" created by PhD students has been transformed into software, generating income and Impact, will also be described. Independent benchmark results will be given to demonstrate that HiGHS is the world’s best open-source linear optimization software.

 

 We develop a probabilistic framework for analysing model-based reinforcement learning in the episodic setting. We then apply it to study finite-time horizon stochastic control problems with linear dynamics but unknown coefficients and convex, but possibly irregular, objective function. Using probabilistic representations, we study regularity of the associated cost functions and establish precise estimates for the performance gap between applying optimal feedback control derived from estimated and true model parameters. We identify conditions under which this performance gap is quadratic, improving the linear performance gap in recent work [X. Guo, A. Hu, and Y. Zhang, arXiv preprint, arXiv:2104.09311, (2021)], which matches the results obtained for stochastic linear-quadratic problems. Next, we propose a phase-based learning algorithm for which we show how to optimise exploration-exploitation trade-off and achieve sublinear regrets in high probability and expectation. When assumptions needed for the quadratic performance gap hold, the algorithm achieves an order (N‾‾√lnN) high probability regret, in the general case, and an order ((lnN)2) expected regret, in self-exploration case, over N episodes, matching the best possible results from the literature. The analysis requires novel concentration inequalities for correlated continuous-time observations, which we derive.

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Dr Lukasz Szpruch