09:00 to 10:00 Youssef Marzouk (Massachusetts Institute of Technology)tba INI 1 10:00 to 10:30 Mark Girolami (Imperial College London); (The Alan Turing Institute)tba INI 1 10:30 to 11:00 Hugo Maruri-Aguilar (Queen Mary University of London)tba INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:00 Michael Goldstein (Durham University)tba INI 1 12:00 to 13:30 Buffet Lunch at INI 13:30 to 14:30 Andrew Stuart (University of Warwick)Large Graph Limits of Learning Algorithms Many problems in machine learning require the classification of high dimensional data. One methodology to approach such problems is to construct a graph whose vertices are identified with data points, with edges weighted according to some measure of affinity between the data points. Algorithms such as spectral clustering, probit classification and the Bayesian level set method can all be applied in this setting. The goal of the talk is to describe these algorithms for classification, and analyze them in the limit of large data sets. Doing so leads to interesting problems in the calculus of variations, Bayesian inverse problems and in Monte Carlo Markov Chain, all of which will be highlighted in the talk. These limiting problems give insight into the structure of the classification problem, and algorithms for it.     Collaboration with:   Andrea Bertozzi (UCLA) Michael Luo (UCLA) Kostas Zygalakis (Edinburgh) https://arxiv.org/abs/1703.08816   and   Matt Dunlop (Caltech) Dejan Slepcev (CMU) Matt Thorpe (Cambridge) (forthcoming paper) INI 1 14:30 to 15:00 Tim Sullivan (Freie Universität Berlin); (Konrad-Zuse-Zentrum für Informationstechnik Berlin)Bayesian probabilistic numerical methods In this work, numerical computation - such as numerical solution of a PDE - is treated as a statistical inverse problem in its own right. The popular Bayesian approach to inversion is considered, wherein a posterior distribution is induced over the object of interest by conditioning a prior distribution on the same finite information that would be used in a classical numerical method. The main technical consideration is that the data in this context are non-random and thus the standard Bayes' theorem does not hold. General conditions will be presented under which such Bayesian probabilistic numerical methods are well-posed, and a sequential Monte-Carlo method will be shown to provide consistent estimation of the posterior. The paradigm is extended to computational pipelines'', through which a distributional quantification of numerical error can be propagated. A sufficient condition is presented for when such propagation can be endowed with a globally coherent Bayesian interpretation, based on a novel class of probabilistic graphical models designed to represent a computational work-flow. The concepts are illustrated through explicit numerical experiments involving both linear and non-linear PDE models. This is joint work with Jon Cockayne, Chris Oates, and Mark Girolami. Further details are available in the preprint arXiv:1702.03673. INI 1 15:00 to 15:30 Claudia Schillings (University of Warwick)tba INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Poster Session