Papers

Preprints:

• On the Limitations of Fractal Dimension as a Measure of Generalization
  Joint with Charlie Tan, Inés García-Redondo, Qiquan Wang, and Michael Bronstein (17 pages)

• Tropical Expressivity of Neural Networks
  Joint with Shiv Bhatia, Yueqi Cao, and Paul Lezeau (17 pages)

• Tropical Gradient Descent
  Joint with Roan Talbut (26 pages)

• Computable Stability for Persistence Rank Function Machine Learning
  Joint with Qiquan Wang, Inés García-Redondo, Pierre Faugère, and Gregory Henselman-Petrusek (45 pages)

• Probability Metrics for Tropical Spaces of Different Dimensions
  Joint with Roan Talbut, Daniele Tramontano, Yueqi Cao, and Mathias Drton (17 pages)

• Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology
  Joint with Anna Song and Ka Man (Ambrose) Yim (65 pages)

• A Geometric Condition for Uniqueness of Fréchet Means of Persistence Diagrams
  Joint with Yueqi Cao (15 pages)

• Approximating Persistent Homology for Large Datasets
  Joint with Yueqi Cao (25 pages)

• Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective
  Joint with Bo Lin, Ruriko Yoshida, and Qiwen Kang (26 pages)

Completed/Published:

• 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 Symposium on Geometry Processing 2024, to appear

• Fast Topological Signal Identification and Persistent Cohomological Cycle Matching
  Inés García-Redondo, Anthea Monod, and Anna Song
  Journal of Applied and Computational Topology, to appear

• 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 (2024). [arXiv][Code]

• 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]

• 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]

• 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]

• 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]

• Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
  Yueqi Cao, Athanasios Vlontzos, Luca Schmidtke, Bernhard Kainz, and Anthea Monod
  Information and Inference: A Journal of the IMA, 12(3):1964–1996 (2023). [arXiv][Code]

• 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]

• 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]

• 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]

• 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).

• Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis
  Lorin Crawford, Anthea Monod, Andrew X. Chen, Sayan Mukherjee, and Raúl Rabadán
  Journal of  the American Statistical Association, 115(531):1139–1150 (2020). [Code][arXiv]

• Tropical Sufficient Statistics for Persistent Homology
  Anthea Monod, Sara Kališnik, Juan Ángel Patiño-Galindo, and Lorin Crawford
  SIAM Journal on Applied Algebra and Geometry, 3(2):337–371 (2019). [Code][arXiv]

• Linking Transcriptomic Features of the Melanoma Tumor Environment
  Andrew X. Chen, Robyn D. Gartrell, Douglas K. Marks, Thomas D. Hart, Emanuelle M. Rizk, Anthea Monod, Raúl Rabadán, and Yvonne M. Saenger
  Cancer Immunology Research, 7(2):B005 (2019).

• Quantitative Compositional and Spatial Analysis of Tumor Microenvironment (TME) in Primary Melanoma
  Robyn D. Gartrell, Andrew X. Chen, Douglas K. Marks, Thomas D. Hart, Gen Li, Alan Wu, Yan Lu, Camden L. Esancy, Zoë Blake, Bret Taback, Raúl Rabadán, Howard L. Kaufman, Charles G. Drake, Basil Horst, Anthea Monod, and Yvonne M. Saenger
  Cancer Research, 78(13):2091 (2018).

• Quantitative Analysis of Immune Infiltrates in Primary Melanoma
  Robyn D. Gartrell, Douglas K. Marks, Thomas D. Hart, Gen Li, Danielle R. Davari, Alan Wu, Zoë Blake, Yan Lu, Kayleigh N. Askin, Anthea Monod, Camden L. Esancy, Edward C. Stack, Dan Tong Jia, Paul M. Armenta, Yichun Fu, Daisuke Izaki, Bret Taback, Raúl Rabadán, Howard L. Kaufman, Charles G. Drake, Basil A. Horst, and Yvonne M. Saenger
  Cancer Immunolology Research, 6(4): 481–493 (2018).

• Estimating Thresholding Levels for Random Fields via Euler Characteristics
  Robert J. Adler, Kevin Bartz, Samuel C. Kou, and Anthea Monod
  arXiv:1704.08562 (2017).

• Random Effects Modeling and the Zero-Inflated Poisson Distribution
  Anthea Monod
  Communications in Statistics: Theory & Methods, 43(4): 664–680 (2014). [Code]

• Modeling Count Panel Data with a Zero-Inflated Poisson Model
  Anthea Monod
  Quaderni di Statistica, 14: 173–176 (2012).

• Generalized Estimating Equations for Zero-Inflated Spatial Count Data
  Anthea Monod
  Procedia Environmental Sciences, 7: 281–286 (2011).

Theses

• PhD Dissertation: A Quasi-Likelihood Approach to Zero-Inflated Spatial Count Data. EPFL Thesis No. 5442 (2012)

• MSc Thesis: An Analysis on Count Panel Data Using a Zero-Inflated Poisson Model. University of Neuchâtel, Institute of Statistics (2007)