research.knit

P. Lezeau, T. Walker, Y. Cao, S. Bhatia, A. Monod. Tropical Expressivity of Neural Networks. arXiv:2405.20174.
R. Talbut, D. Tramontano, Y. Cao, M. Drton, A. Monod. Probability Metrics for Tropical Spaces of Different Dimensions. arXiv:2307.02846.
Y. Cao, A. Monod. A Geometric Condition for Uniqueness of Fréchet Means of Persistence Diagrams. arXiv:2207.03943.
Y. Cao, A. Monod. Approximating Persistent Homology for Large Datasets. arXiv:2204.09155.

Y. Cao, P. Leung, A. Monod, k-Means Clustering for Persistent Homology. Advances in Data Analysis and Classification, 2024.
Y. Cao, A. Vlontzos, L. Schmidtke, B. Kainz, A. Monod. Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures. Information and Inference: A Journal of IMA, 2023.
Y. Cao, D. Li, H. Sun, A. Assadi, S. Zhang. Efficient Weingarten Map and Curvature Estimation on Manifolds. Machine Learning, 2021.
F. Sun, Y. Cao, S. Zhang, H. Sun. The Bayesian Inference of Pareto Models Based on Information Geometry. Entropy, 2021.
Y. Cao, S. Zhang, F. Yan, W. Li, F. Sun, H. Sun. Unsupervised Environmental Sound Classification Based On Topological Persistence. 2019 IEEE International Conference on Signal, Information and Data Processing (ICSIDP), Chongqing, 2019.

Y. Cao. Generalized Multiple Subsampling for Persistent Homology, Applied Topology Seminar, Oxford, 2024. [Invited Talk]
Y. Cao, A. Monod. Computational tropical Abel-Jacobi map for metric graphs, Applied Algebra and Geometry, 19th meeting, Edinburgh, Edinburgh, 2024. [Invited Talk]
S. Bhatia, Y. Cao, P. Lezeau, A. Monod. A Tropical Geometric Perspective on Deep Learning, Geometric Deep Learning workshop, Cambridge, 2024. [Poster]
Y. Cao, A. Monod. A Condition for the Uniqueness of Fréchet Means of Persistence Diagrams, Minisymposium on Applied Algebraic Topology: Theory and Implementation, SIAM Conference on Applied Algebraic Geometry, Eindhoven, 2023. [Invited Talk]
Y. Cao, A. Monod. A Condition for the Uniqueness of Fréchet Means of Persistence Diagrams, Algebraic Topology: Methods, Computation and Science (ATMCS10), Oxford, 2022. [Poster]