Numerical Analysis Group Internal Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
1 December 2020
14:00
Mario Lezcano
Abstract

In this talk, we will present an approach to constrained optimisation when the set of constraints is a smooth manifold. This setting is of particular interest in data science applications, as many interesting sets of matrices have a manifold structure. We will show how we may couple classic ideas from differential geometry with modern methods such as autodifferentiation to simplify optimisation problems from spaces with a difficult topology (e.g. problems with orthogonal or fixed-rank constraints) to problems on ℝⁿ where we can use any classical optimisation methods to solve them. We will also show how to use these methods to automatically compute quantities such as the Riemannian gradient and Hessian. We will present the library GeoTorch that allows for putting these kind of constraints within models written in PyTorch by adding just one line to the model. We will also comment on some convergence results if time allows.

A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact trefethen@maths.ox.ac.uk.

  • Numerical Analysis Group Internal Seminar
1 December 2020
14:30
Abstract

Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic. Due to the NP-hardness of this problem, most previous attempts rely on heuristic techniques. We formulate the problem as a mixed integer linear program and use a large scale optimisation technique of column generation to solve it without the need of heuristic pattern mining. Our approach focuses on accuracy and on the provision of optimality guarantees. Experimental results on real world datasets demonstrate that our proposed method is effective at producing highly accurate factorisations and improves on the previously available best known results for 16 out of 24 problem instances.

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A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact trefethen@maths.ox.ac.uk.

  • Numerical Analysis Group Internal Seminar
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