Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective
Anthea Monod, Bo Lin, Ruriko Yoshida, and Qiwen Kang
Vietnam Journal of Mathematics – Special Issue in Memory of Andreas Dress, to appear. [Code]
Confidence Bands for Multiparameter Persistence Landscapes
Inés García-Redondo, Anthea Monod, and Qiquan Wang
Proceedings of the Seventh International Conference on Geometric Science of Information (GSI'25), to appear. [Code]
Tropical Fréchet Means
Bo Lin, Kamillo Ferry, Carlos Améndola, Anthea Monod, and Ruriko Yoshida
Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2025), to appear. [Code]
Tropical Gradient Descent
Roan Talbut and Anthea Monod
Journal of Global Optimization (2025). [arXiv][Code]
https://doi.org/10.1007/s10898-025-01533-1
Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology
Anna Song, Ka Man Yim, and Anthea Monod
Advances in Applied Mathematics, 166:102857 (2025). [arXiv][Code]
https://doi.org/10.1016/j.aam.2025.102857
A Geometric Condition for Uniqueness of Fréchet Means of Persistence Diagrams
Yueqi Cao and Anthea Monod
Computational Geometry, 128:102162 (2024). [arXiv][Code]
https://doi.org/10.1016/j.comgeo.2024.102162
On the Limitations of Fractal Dimension as a Measure of Generalization
Charlie Tan, Inés García-Redondo, Qiquan Wang, Michael M. Bronstein, and Anthea Monod
Advances in Neural Information Processing Systems 38 (NeurIPS 2024). [arXiv][OpenReview][Code]
Stability for Inference with Persistent Homology Rank Functions
Qiquan Wang, Inés García-Redondo, Pierre Faugère, Gregory Henselman-Petrusek, and Anthea Monod
Computer Graphics Forum – Proceedings of the Eurographics Symposium on Geometry Processing 2024, 43(5):e15142 (2024). [arXiv][Code]
https://doi.org/10.1111/cgf.15142
Fast Topological Signal Identification and Persistent Cohomological Cycle Matching
Inés García-Redondo, Anthea Monod, and Anna Song
Journal of Applied and Computational Topology, 8:695–726 (2024). [arXiv][Code]
https://doi.org/10.1007/s41468-024-00179-4
Wavelet-Based Density Estimation for Persistent Homology
Konstantin Häberle, Barbara Bravi, and Anthea Monod
SIAM/ASA Journal on Uncertainty Quantification, 12(2):347–376 (2024). [arXiv][Code]
https://doi.org/10.1137/23M1573811
Topological Community Detection: A Sheaf-Theoretic Approach
Arne Wolf and Anthea Monod
Studies in Computational Intelligence – Complex Networks and Their Applications XII: Proceedings of the 12th International Conference on Complex Networks and Their Applications, 1142:29–42 (2024). [arXiv][Code]
https://doi.org/10.1007/978-3-031-53499-7_3
Rewiring Networks for Graph Neural Network Training Using Discrete Geometry
Jakub Bober, Anthea Monod, Emil Saucan, and Kevin N. Webster
Studies in Computational Intelligence – Complex Networks and Their Applications XII: Proceedings of the 12th International Conference on Complex Networks and Their Applications, 1141:225–236 (2024). [arXiv][Code]
https://doi.org/10.1007/978-3-031-53468-3_19
k-Means Clustering for Persistent Homology
Yueqi Cao, Prudence Leung, and Anthea Monod
Advances in Data Analysis and Classification, https://doi.org/10.1007/s11634-023-00578-y (2024). [arXiv][Code]
An Invitation to Tropical Alexandrov Curvature – Dedicated to Bernd Sturmfels on the occasion of his 60th birthday
Carlos Améndola and Anthea Monod
Algebraic Statistics, 14(2):181–214 (2023). [arXiv][Code]
https://doi.org/10.2140/astat.2023.14.181
Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
Yueqi Cao, Anthea Monod, Athanasios Vlontzos, Luca Schmidtke, and Bernhard Kainz
Information and Inference: A Journal of the IMA, 12(3):1964–1996 (2023). [arXiv][Code]
https://doi.org/10.1093/imaiai/iaad022
Learning Linear Non-Gaussian Polytree Models
Daniele Tramontano, Anthea Monod, and Mathias Drton
Proceedings of the 38th Conference on Uncertainty in Artificial Intelligence (UAI 2022) PMLR, 180:1960–1969 (2022). [arXiv]
Tropical Geometric Variation of Phylogenetic Tree Shapes
Bo Lin, Anthea Monod, and Ruriko Yoshida
Discrete & Computational Geometry, 68:817–849 (2022). [arXiv]
https://doi.org/10.1007/s00454-022-00410-y
Curved Markov Chain Monte Carlo for Network Learning
John Sigbeku, Emil Saucan, and Anthea Monod
Studies in Computational Intelligence – Complex Networks and Their Applications X: Proceedings of The 10th International Conference on Complex Networks and Their Applications, 1073:461–473 (2022). [arXiv]
https://doi.org/10.1007/978-3-030-93413-2_39
Tropical Optimal Transport and Wasserstein Distances
Wonjun Lee, Wuchen Li, Bo Lin, and Anthea Monod
Information Geometry – Special Issue on Optimal Transport, 5:247–287 (2021). [Code][arXiv]
https://doi.org/10.1007/s41884-021-00046-6
Linking transcriptomic and imaging data defines features of a favorable tumor immune microenvironment and identifies a combination biomarker for primary melanoma
Robyn D. Gartrell-Corrado, Andrew X. Chen, Emanuelle M. Rizk, Douglas K. Marks, Margaret H. Bogardus, Thomas D. Hart, Andrew M. Silverman, Claire-Audrey Y. Bayan, Grace G. Finkel, Luke W. Barker, Kimberly M. Komatsubara, Richard D. Carvajal, Basil A. Horst, Rui Chang, Anthea Monod, Raúl Rabadán, and Yvonne M. Saenger
Cancer Research, 80(5):1078–1087 (2020).
https://doi.org/10.1158/0008-5472.CAN-19-2039