Publications

I am an editor for the journal Foundations of Data Science. Below you can find my journal and conference papers broken down by research area. You can also see my Google Scholar profile here.

  1. Large Data Limits of Variational Problems on Graphs

Preprints:

  1. J. Calder, D. Slepcev and M. Thorpe, Rates of Convergence for Laplacian Semi-Supervised Learning with Low Labeling Rates, preprint, 2020. Arxiv.

  2. O. M. Crook, T. Hurst, C.-B. Schoenlieb, M. Thorpe and K. C. Zygalakis, PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds, preprint, 2019. Arxiv.

Journal Papers:

  1. N. Garcia Trillos, R. Murray and M. Thorpe, From Graph Cuts to Isoperimetric Inequalities: Convergence Rates of Cheeger Cuts on Data Clouds, to appear in the Archive for Rational Mechanics and Analysis, 2022. Arxiv. Journal.

  2. M. M. Dunlop, D. Slepcev, A. M. Stuart and M. Thorpe, Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms, Journal of Applied and Computational Harmonic Analysis, 49 no. 2, pp 655–697, 2020. Arxiv. Journal.

  3. R. Cristoferi and M. Thorpe, Large Data Limit for a Phase Transition Model with the p-Laplacian on Point Clouds, the European Journal of Applied Mathematics, 31 no. 2, pp. 185–231, 2020. Arxiv. Journal.

  4. M. Thorpe and D. Slepcev, Analysis of p-Laplacian Regularization in Semi-Supervised Learning, SIAM Journal on Mathematical Analysis, 51 no. 3, pp. 2085–2120, 2019. Arxiv. Journal.

  5. 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, 149 no. 2, pp. 387–427, 2019. Arxiv. Journal.

Conference Papers:

  1. M. Thorpe and B. Wang, Robust Certification for Laplace Learning on Geometric Graphs, Proceedings of Machine Learning Research, 107, pp. 1-25, 2021. Arxiv. Conference.

  2. J. Calder, B. Cook, M. Thorpe and D. Slepcev, Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates, proceedings of the International Conference on Machine Learning, pp. 1306–1316, 2020. Arxiv. Conference.

2. From PDE's to Neural Networks

Preprints:

  1. M. Thorpe and Y. van Gennip, Deep Limits of Residual Neural Networks, preprint, 2018. Arxiv.

Conference Papers:

  1. M. Thorpe, T. M. Nguyen, H. Xia, T. Strohmer, A. Bertozzi, S. Osher and B. Wang, GRAND++: Graph Neural Diffusion with A Source Term, proceedings of the International Conference on Learning Representations, 2022. Conference.

3. Applications of Optimal Transport Distances

Preprints:

  1. O .M. Crook, M. Cucuringu, T. Hurst, C.-B. Schoenlieb, M. Thorpe and K. C. Zygalakis, A Linear Transportation Lp Distance for Pattern Recognition, 2020. Arxiv.

Journal Papers:

  1. T. Cai, J. Cheng, B. Schmitzer and M. Thorpe, The Linearized Hellinger–Kantorovich Distance, SIAM Journal on Imaging Sciences, 15 no. 1, pp 45-83, 2022. Arxiv. Journal.

  2. M. Thorpe, S. Park, S. Kolouri, G. Rohde and D. Slepcev, A Transportation Lp Distance for Signal Analysis, Journal of Mathematical Imaging and Vision, 59 no. 2, pp. 187–210, 2017. Arxiv. Journal.

  3. S. Kolouri, S. Park, M. Thorpe, D. Slepcev and G. Rohde, Optimal Mass Transport: Signal Processing and Machine Learning Applications, IEEE Signal Processing Magazine, 34 no. 4, pp. 43– 59, 2017. Arxiv. Journal.

Conference Papers:

  1. S. Park and M. Thorpe, Representing and Learning High Dimensional Data with the Optimal Transport Map from a Probabilistic Viewpoint, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7864–7872, 2018. Conference.

4. Miscellaneous

Preprints:

  1. I. Fonseca, L. M. Kreusser, C.-B. Schoenlieb and M. Thorpe, Gamma-Convergence of an Ambrosio-Tortorelli Approximation Scheme for Image Segmentation, preprint, 2022. Arxiv.

Journal Papers:

  1. M. Roberts, D. Driggs, M. Thorpe, J. Gilbey, M. Yeung, S. Ursprung, A. I. Aviles-Rivero, C. Etmann, C. McCague, L. Beer, J. R. Weir-McCall, Z. Teng, E. Gkrania-Klotsas, AIX-COVNET, J. H. F. Rudd, E. Sala and C.-B. Schoenlieb, Common Pitfalls and Recommendations for Using Machine Learning to Detect and Prognosticate for COVID-19 Using Chest Radiographs and CT Scans, Nature Machine Intelligence 3, pp 199–217, 2021. Arxiv. Journal.

  2. M. Thorpe and A. M. Johansen, Pointwise Convergence in Probability of General Smoothing Splines, Annals of the Institute of Statistical Mathematics, 70 no. 4, pp. 717–744, 2018. Arxiv. Journal.

  3. 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 no. 2, pp. 3693–3722, 2016. Arxiv. Journal.

  4. M. Thorpe, F. Theil, A. M. Johansen and N. Cade, Convergence of the k-Means Minimization Problem Using Γ-Convergence, SIAM Journal on Applied Mathematics, 75 no. 6, pp. 2444–2474, 2015. Arxiv. Journal.

Conference Papers:

  1. A. Gkiokas, A. Cristea and M. Thorpe, Self-Reinforced Meta Learning for Belief Generation, Research and Development, Research and Development in Intelligent Systems XXXI, Springer International Publishing, pp. 185–190, 2014. Conference.

5. Reviews

Paper Reviews:

  1. M. Thorpe, Review of The Plateau Problem from the Perspective of Optimal Transport by Brezis and Mironescu, Mathematical Reviews, 2020.

  2. M. Thorpe,Review of Inverse optimal transport by Stuart and Wolfram, Mathematical Reviews, 2020.

Book Reviews:

  1. M. Thorpe, Review of Lectures on Optimal Transport by Ambrosio, Brue and Semola, to appear in SIAM Review 2022.