On May 8th the CCIMI held its first Colloquium featuring a talk by Andrew Stuart, Bren Professor of Computing and Mathematical Sciences at Caltech Univeristy, presenting on ‘Reconciling Bayesian Regularization And Total Variation Regularization’.
Andrew presented joint work with Matt Dunlop (Caltech), Charlie Elliott (Warwick), and Viet Ha Haong (NTU): A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization, for example via total variation penalization. On the other hand, sparse or noisy data often demands a probabilistic approach to the reconstruction of images, to enable uncertainty quantification; the Bayesian approach to inversion is a natural framework in which to carry this out. The link between Bayesian inversion methods and perimeter regularization, however, is not fully understood. In this talk two links were studied: (i) the MAP objective function of a suitably chosen phase-field Bayesian approach is shown to be closely related to a least squares plus perimeter regularization objective; (ii) sample paths of a suitably chosen Bayesian level set formulation are shown to possess finite perimeter and to have the ability to learn about the true perimeter. Furthermore, the level set approach was shown to lead to faster algorithms for uncertainty quantification than the phase field approach.
Speaker: Andrew Stuart has research interests in applied and computational mathematics, and is interested in particular in the question of how to optimally combine complex mechanistic models with data. He joined Caltech in 2016 as Bren Professor of Computing and Mathematical Sciences, after 17 years as Professor of Mathematics at the University of Warwick (1999—2016). Prior to that he was on the faculty in The Departments of Computer Science and Mechanical Engineering at Stanford University (1992—1999), and in the Mathematics Department at Bath University (1989—1992). He obtained his PhD from the Oxford University Computing Laboratory in 1986, and held postdoctoral positions in Mathematics at Oxford University and at MIT in the period 1986—1989
The event was followed by a drinks and networking reception.