# Dr Matthew Thorpe

## Career

**2017-current:**Research Fellow, Cantab Capital Institute for the Mathematics of Information, Department of Applied Mathematics and Theoretical Physics, University of Cambridge**2015-2017:**Postdoctoral Associate, Department of Mathematical Sciences, Carnegie Mellon University**2012-2015:**PhD Student, Mathematics Institute, University of Warwick

## Research

Matthew is a research fellow in the Cantab Capital Institute for the Mathematics of Information. His research interests are in discrete-to-continuum limits in graphical problems, particularly variational problems that arise from applications in machine learning, and optimal transport distances and their applications to signal and image analysis.

Before joining Cambridge Matthew was a postdoctoral associate at Carnegie Mellon University working with Dejan Slepčev on optimal transport problems (NSF grant number 1421502). Prior to that Matthew was a PhD student in the maths and statistics doctoral training centre (MASDOC) at Warwick under the supervision of Florian Theil and Adam Johansen. The focus of the PhD was on applying variational methods to statistical inference problems.

More information on his research is given below under research projects.

## Publications

### Preprints

- M. Thorpe and D. Slepčev,
*Analysis of p-Laplacian Regularization in Semi-Supervised Learning*, 2017. Arxiv. - M. Thorpe and D. Slepčev,
*Transportation L*, 2017. Arxiv.^{p}Distances: Properties and Extensions

### Accepted

- M. Thorpe and F. Theil,
*Asymptotic Analysis of the Ginzburg-Landau Functional on Point Clouds*, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2017. Arxiv. - M. Thorpe and A. M. Johansen,
*Pointwise Convergence in Probability of**General Smoothing Splines*, the Annals of the Institute of Statistical Mathematics, 2017. Article. Arxiv.

### Published

- M. Thorpe, S. Park, S. Kolouri, G. K. Rohde and D. Slepčev,
*A Transportation Lp Distance for Signal Analysis*, Journal of Mathematical Imaging and Vision, 59(2):187-210, 2017. Article. Arxiv. - S. Kolouri, S. Park, M. Thorpe, D. Slepčev and G. K. Rohde,
*Optimal Mass Transport: Signal Processing and Machine-Learning Applications*, IEEE Signal Processing Magazine, 34(4):43-59, 2017. Article. Arxiv. - M. Thorpe and A. M. Johansen,
*Convergence and Rates for Fixed-Interval Multiple-Track Smoothing Using k-Means Type Optimization*, Electronic Journal of Statistics, 10(2):3693-3722, 2016. Article. Arxiv. - M. Thorpe,
*Variational Methods for Geometric Statistical Inference*, PhD Thesis, 2015. - M. Thorpe, F. Theil, A. M. Johansen and N. Cade,
*Convergence of the k-Means Minimization Problem Using Gamma-Convergence*, SIAM Journal on Applied Mathematics, 75(6): 2444-2474, 2015. Article. Arxiv. - A. Gkiokas, A. Cristea and M. Thorpe,
*Self-Reinforced Meta Learning for Belief Generation*, Research and Development in Intelligent Systems XXXI, Springer International Publishing, 185-190, 2014. Article.

## Links to Colloborators

- Luca Calatroni
- Riccardo Cristoferi
- Matthew Dunlop
- Nicolas Garcia Trillos
- Yves van Gennip
- Adam Johansen
- Filip Rindler
- Gustavo Rohde
- Carola-Bibiane Schönlieb
- Dejan Slepčev
- Andrew Stuart
- He Sun
- Daniel Tenbrinck
- Florian Theil
- Kostas Zygalakis

## Other Links

- Maths and Statistics Doctoral Training Centre at the University of Warwick, MASDOC.
- Centre for Nonlinear Anaysis at Carnegie Mellon University, CNA.
- Cantab Capital Institute for the Mathematics of Information at the University of Cambridge, CCIMI.
- Cambridge Image Analysis, CIA.
- Isaac Newton Institute, INI.
- Turing Gateway to Mathematics, TGM.
- The Alan Turing Institute.
- The Smith Institute.

## Research Projects

### Large Data Limits in Graphical Modelling

*** Under construction ***

### Optimal Transport Distances for Image and Signal Analysis

*** Under construction ***

### Large Data Limits in Data Association-Smoothing Problems

*** Under construction ***