Mon, 29 Apr 2024

11:00 - 12:00
Lecture Room 3

Deep Gaussian processes: theory and applications

Aretha Teckentrup
(University of Edinburgh)
Further Information

Please note that this seminar starts at 11am and finishes at 12pm. 

Abstract

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.

 

Tue, 27 Feb 2024
16:00
L6

Dynamics in interlacing arrays, conditioned walks and the Aztec diamond

Theodoros Assiotis
(University of Edinburgh)
Abstract

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.

Mon, 13 Nov 2023
15:30
Lecture Theatre 3, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

Loop expansions for lattice gauge theories

Dr Ilya Chevyrev
(University of Edinburgh)
Abstract

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.

Fri, 19 May 2023

12:00 - 13:00
N3.12

The first cohomology of submodule-subalgebras of the Witt algebra

Lucas Buzaglo
(University of Edinburgh)
Abstract

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.

Tue, 01 Nov 2022

14:00 - 15:00
L3

HiGHS: From gradware to software and Impact

Dr Julian Hall
(University of Edinburgh)
Abstract

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.

 

Mon, 09 May 2022

15:30 - 16:30
L3

Exploration-exploitation trade-off for continuous-time episodic reinforcement learning with linear-convex models

LUKASZ SZPRUCH
(University of Edinburgh)
Abstract

 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

Mon, 14 Mar 2022

15:30 - 16:30
L3

TBC

GONCALO DOS REIS
(University of Edinburgh)
Abstract

TBC

Tue, 07 Dec 2021

14:00 - 15:00
Virtual

FFTA: Directed Network Laplacians and Random Graph Models

Xue Gong
(University of Edinburgh)
Abstract

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph model. We focus on two existing spectral approaches that build and analyse Laplacian-style matrices via the minimization of frustration and trophic incoherence. These algorithms aim to reveal directed periodic and linear hierarchies, respectively. We show that reordering nodes using the two algorithms, or mapping them onto a specified lattice, is associated with new classes of directed random graph models. Using this random graph setting, we are able to compare the two algorithms on a given network and quantify which structure is more likely to be present. We illustrate the approach on synthetic and real networks, and discuss practical implementation issues. This talk is based on a joint work with Desmond Higham and Konstantinos Zygalakis. 

Article link: https://royalsocietypublishing.org/doi/10.1098/rsos.211144

Mon, 10 May 2021

16:00 - 17:00

 Superdiffusive limits for deterministic fast-slow dynamical systems

ILYA CHEVYREV
(University of Edinburgh)
Abstract

In this talk, we will consider multidimensional fast-slow dynamical systems in discrete-time with random initial conditions but otherwise completely deterministic dynamics. The question we will investigate is whether the slow variable converges in law to a stochastic process under a suitable scaling limit. We will be particularly interested in the case when the limiting dynamic is superdiffusive, i.e. it coincides in law with the solution of a Marcus SDE driven by a discontinuous stable Lévy process. Under certain assumptions, we will show that generically convergence does not hold in any Skorokhod topology but does hold in a generalisation of the Skorokhod strong M1 topology which we define using so-called path functions. Our methods are based on a combination of ergodic theory and ideas arising from (but not using) rough paths. We will finally show that our assumptions are satisfied for a class of intermittent maps of Pomeau-Manneville type. 

 

Tue, 10 Nov 2020

15:30 - 16:30
Virtual

On the joint moments of characteristic polynomials of random unitary matrices

Theo Assiotis
(University of Edinburgh)
Further Information

This seminar will be held via zoom. Meeting link will be sent to members of our mailing list (https://lists.maths.ox.ac.uk/mailman/listinfo/random-matrix-theory-anno…) in our weekly announcement on Monday.

Abstract

I will talk about the joint moments of characteristic polynomials of random unitary matrices and their derivatives. In joint work with Jon Keating and Jon Warren we establish the asymptotics of these quantities for general real values of the exponents as the size N of the matrix goes to infinity. This proves a conjecture of Hughes from 2001. In subsequent joint work with Benjamin Bedert, Mustafa Alper Gunes and Arun Soor we focus on the leading order coefficient in the asymptotics, we connect this to Painleve equations for general values of the exponents and obtain explicit expressions corresponding to the so-called classical solutions of these equations.

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