# Seminar: Probabilistic Linear Algebra - Treating Approximation as Inference

**Simon Bartels
**

**Date:** October 15, 2019

**Location:** Eurecom - EURECOM

Abstract: At the core of many sophisticated procedures are operations from linear algebra, such as solving linear equation systems Ax=b or evaluating determinants |A|. For large-scale problems (e.g. least-squares in Machine Learning) it is necessary to resort to approximation. However, typical approximation algorithms tend to return only a point estimate of the solution but little information about its quality. This talk will present probabilistic approximation algorithms that aim to provide more information in form of a probability distribution over the solution. The first part is about the design of efficient probabilistic linear solvers, how they are connected to classic solvers and how preconditioning can be seen from an inference perspective. The second part presents a stopping rule for the Cholesky decomposition that gives probably approximately correct estimates for kernel matrix determinants. Bio: Simon Bartels is a PhD student in the Probabilistic Numerics Group led by Philipp Hennig. The group moved from the Max Plank Institute to the University of Tübingen in October 2018. Simon is working on probabilistic numerical methods to solve large linear equation systems.

https://pn.is.tuebingen.mpg.de/person/sbartels

**Permalink:** http://www.eurecom.fr/seminar/91264

*Probabilistic Linear Algebra - Treating Approximation as Inference*