Publications
I am an editor for the journals Foundations of Data Science and ACM Transactions on Probabilistic Machine Learning. Below you can find my journal and conference papers broken down by research area. You can also see my Google Scholar profile here.
- Large Data Limits of Variational Problems on Graphs
Preprints:
A. Weihs, J. Fadili and M. Thorpe, Discrete-to-Continuum Rates of Convergence for p-Laplacian Regularization, to appear in Information and Inference, preprint, 2023. Arxiv.
A. Weihs and M. Thorpe, Consistency of Fractional Graph-Laplacian Regularization in Semi-Supervised Learning with Finite Labels, preprint, 2023, Arixiv.
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:
N. Garcia Trillos, R. Murray and M. Thorpe, Rates of Convergence for Regression with the Graph Poly-Laplacian, Sampling Theory, Signal Processing, and Data Analysis 21(35), 2023. Arxiv. Journal.
J. Calder, D. Slepcev and M. Thorpe, Rates of Convergence for Laplacian Semi-Supervised Learning with Low Labeling Rates, Research in the Mathematical Sciences 10(1), 2023. Arxiv. Journal.
N. Garcia Trillos, R. Murray and M. Thorpe, From Graph Cuts to Isoperimetric Inequalities: Convergence Rates of Cheeger Cuts on Data Clouds, Archive for Rational Mechanics and Analysis 244(3):541–598, 2022. Arxiv. Journal.
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(2):655–697, 2020. Arxiv. Journal.
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(2):185–231, 2020. Arxiv. Journal.
M. Thorpe and D. Slepcev, Analysis of p-Laplacian Regularization in Semi-Supervised Learning, SIAM Journal on Mathematical Analysis 51(3):2085–2120, 2019. Arxiv. Journal.
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(2):387–427, 2019. Arxiv. Journal.
Conference Papers:
M. Thorpe and B. Wang, Robust Certification for Laplace Learning on Geometric Graphs, Proceedings of Machine Learning Research 107: 1–25, 2021. Arxiv. Conference.
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
Journal Papers:
M. Thorpe and Y. van Gennip, Deep Limits of Residual Neural Networks, Research in the Mathematical Sciences 10(6), 2023. Arxiv. Journal.
Conference Papers:
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:
X. Liu, R. Diaz Martin, Y. Bai, A. Shahbazi, M. Thorpe, A. Aldroubi and S. Kolouri, Expected Sliced Transport Plans, preprint 2024. Arxiv.
K. Hamm, C. Moosmueller, B. Schmitzer and M. Thorpe, Manifold Learning in Wasserstein Space, preprint 2023. Arxiv.
Journal Papers:
O. M. Crook, M. Cucuringu, T. Hurst, C.-B. Schoenlieb, M. Thorpe and K. C. Zygalakis, A Linear Transportation Lp Distance for Pattern Recognition, Pattern Recognition 147, 2024. Arxiv. Journal.
T. Cai, J. Cheng, B. Schmitzer and M. Thorpe, The Linearized Hellinger–Kantorovich Distance, SIAM Journal on Imaging Sciences 15(1):45–83, 2022. Arxiv. Journal.
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(2):187–210, 2017. Arxiv. Journal.
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(4):43–59, 2017. Arxiv. Journal.
Conference Papers:
X. Liu, Y. Bai, H. Tran, Z. Zhu, M. Thorpe and S. Kolouri, PTLp: Partial Transport Lp Distances, 2023. Arxiv. Conference.
Y. Bai, B. Schmitzer, M. Thorpe and S. Kolouri, Sliced Optimal Partial Transport, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 13681–13690, 2023. Arxiv. Conference.
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:
M. C. A. Oliver, M. Graham, I. Manolopoulou, G. F. Medley, L. Pellis, K. B. Pouwels, M. Thorpe and D. Hollingsworth, Uncertainty Quantification in Cost-effectiveness Analysis for Stochastic-based Infectious Disease Models: Insights from Surveillance on Lymphatic Filariasis, preprint, 2024. MedRxiv.
Journal Papers:
I. Fonseca, L. M. Kreusser, C.-B. Schoenlieb and M. Thorpe, Gamma-Convergence of an Ambrosio-Tortorelli Approximation Scheme for Image Segmentation, to appear in the Indiana University Mathematics Journal, 2023. Arxiv.
T. Shadbahr, M. Roberts, J. Stanczuk, J. Gilbey, P. Teare, S. Dittmer, M. Thorpe, R. V. Torne, E. Sala, P. Lio, M. Patel, AIX-COVNET, J. H. F. Rudd, T. Mirtti, A. Rannikko, J. A. D. Aston, J. Tang and C.-B. Schönlieb, The impact of imputation quality on machine learning classifiers for datasets with missing values, Communications Medicine 3(139), 2023. Arxiv. Journal.
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 3:199–217, 2021. Arxiv. Journal.
M. Thorpe and A. M. Johansen, Pointwise Convergence in Probability of General Smoothing Splines, Annals of the Institute of Statistical Mathematics 70(4):717–744, 2018. Arxiv. Journal.
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. Arxiv. Journal.
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(6):2444–2474, 2015. Arxiv. Journal.
Conference Papers:
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:
M. Thorpe, Review of The Plateau Problem from the Perspective of Optimal Transport by Brezis and Mironescu, Mathematical Reviews, 2020.
M. Thorpe, Review of Inverse Optimal Transport by Stuart and Wolfram, Mathematical Reviews, 2020.
Book Reviews:
M. Thorpe, Review of Lectures on Optimal Transport by Ambrosio, Brue and Semola, SIAM Review 64(2):503–513, 2022.