Thanks to all my coauthors!
Publications
[Books]
[DBLP]
[Google Scholar] [Books]
[ResearchGate]
[arXiv preprints]
Recent publications (PDF)
Selected Preprints
2024
-
Information measures and
geometry of the hyperbolic
exponential families of Poincaré and hyperboloid distributions,
Information Geometry, November 2024.
(2205.13984)
- Hyperbolic
Embeddings of Supervised Models, NeurIPS 2024
(with Richard Nock, Ehsan Amid, Alexander Soen and Manfred K. Warmuth)
- Approximation and bounding techniques for the Fisher-Rao distances
between parametric statistical models, Handbook of Statistics: Probability models, vol. 51, Elsevier, 2024 (2403.10089)
- A Rate-Distortion View of Uncertainty Quantification, ICML'24
(with Ifigeneia Apostolopoulou, Benjamin Eysenbach and Artur Dubrawski), 2406.10775
[Paper]
[Code]
[Poster]
[Tweet thread]
- Divergences Induced by the Cumulant and Partition Functions of Exponential Families
and Their Deformations Induced by Comparative Convexity, Entropy 26(3), 2024.
2312.12849
- Home page of pyBregMan:
A Python package for Bregman Manifolds
pyBregMan: A Python library for Bregman Manifolds (arXiv:2408.04175)
Colab:
Data Representations on the Bregman Manifold, tutorial for the GRaM workshop at ICML 2024 (with Alexander Soen).
- On the f-divergences between densities of a multivariate location or scale family,
Statistics and Computing (Springer), 34(60), 2024.
2204.10952 (with Kazuki Okamura)
- Optimal Transport with
Tempered Exponential Measures, Proceedings of AAAI'24.
2309.04015 (with Ehsan Amid, Richard Nock and Manfred Warmuth)
- Variational representations of annealing paths: Bregman information under monotonic embedding,
Information geometry, 2024.
2209.07481 (with Rob Brekelmans)
2023
-
What is... an inductive mean?,
Notices of the American Mathematical Society, 2023
web page,
extended paper 2410.15717 (fixed typos, include more references and background).
- Fisher-Rao and pullback Hilbert cone distances on the multivariate Gaussian manifold with applications to simplification and
quantization of mixtures,
2nd Annual Topology,
Algebra, and Geometry in Machine Learning Workshop (ICML TAGML'23)
poster,
Slides
video
- Non-linear Embeddings in Hilbert Simplex Geometry, 2nd Annual Topology,
Algebra, and Geometry in Machine Learning Workshop (ICML TAGML)' 23
slides,
poster, 2023.
2203.11434
- Simplifying Momentum-based Positive-definite
Submanifold Optimization with Applications to Deep Learning, ICML'23
2302.09738
(with Wu Lin, Valentin Duruisseaux, Melvin Leok, Mohammad Emtiyaz Khan, Mark Schmidt)
- On the f-divergences between hyperboloid and
Poincaré distributions, GSI'23
2205.13984,
Slides
video.
This work highlights the notion of maximal invariant
- Quasi-arithmetic centers, quasi-arithmetic
mixtures, and the Jensen-Shannon ∇-divergences, GSI'23
(Paper@Springer),
Slides,
video.
2301.10980
- A Simple Approximation Method
for the Fisher-Rao Distance
between Multivariate Normal Distributions,
Entropy 25(4), 654, 2023
web page
-
On f-divergences between Cauchy distributions,
IEEE Transactions on Information Theory, 69(5), 3150 - 3171, 2023.
2101.12459 (with Kazuki Okamura)
- Proceedings of 6th International Conference on Geometric Science of Information, GSI 2023,
LNCS (Springer), Part I
and Part II
(with Frédéric Barbaresco)
- Proceedings of the 41st International Workshop
on Bayesian Inference and Maximum Entropy Methods in Science and Engineering,
MaxEnt 2022, Phys. Sci. Forum, 2023.
(with Frédéric Barbaresco, Ali Mohammad-Djafari and Martino Trassinelli)
2022
- pdf Generalizing the Alpha-Divergences and the Oriented Kullback–Leibler Divergences
with Quasi-Arithmetic Means, Algorithms 15 (11), 435, 2022.
(2001.09660)
- pdf Comparing the Zeta distributions with the Pareto
distributions from the viewpoint of information theory and information geometry: Discrete versus
continuous exponential families of power laws, Physical Sciences Forum 5 (1), 2, 2022.
(2104.10548),
web page
- pdf
Revisiting Chernoff information with likelihood ratio exponential families, Entropy 24 (10), 1400, 2022.
(2207.03745)
-
Handbook of Statistics: Geometry and statistics, Volume 46, F Nielsen, ASRS Rao, CR Rao, Elsevier, 2022.
web page
- pdf
Onicescu’s informational energy and correlation coefficient in exponential families, Foundations 2 (2), 362-376,
2022. (2003.13199)
- pdf
Statistical divergences between densities of truncated exponential families with nested supports: Duo Bregman and duo Jensen divergences
Entropy 24 (3), 421, 2022.
(2202.10726)
- pdf
Practical Structured Riemannian Optimization with Momentum by using Generalized Normal Coordinates,
NeurIPS 2022 Workshop on Symmetry and Geometry in Neural Representations, 2022.
- pdf
The Kullback–Leibler
Divergence Between Lattice Gaussian Distributions,
Journal of the Indian Institute of Science, 2022.
(2109.14920)
slides
- The analytic dually
flat space of the mixture family of two prescribed distinct Cauchy distributions,
Handbook of Statistics 46, 225-256, 2022.
(2104.13801)
- pdf The many faces of information geometry,
Notices of the American Mathematical Society 69 (1), 36-45, 2022
2021
- A review of two decades of
correlations, hierarchies, networks and clustering in financial markets,
Progress in information geometry: Theory and applications (2021): 245-274.
(1703.00485)
- On a variational definition for the Jensen-Shannon symmetrization of distances based
on the information radius, Entropy 23.4 (2021): 464.
(2102.09728)
- Tractable structured natural-gradient descent using local parameterizations. ICML 2021.
- Fast approximations of the Jeffreys divergence between univariate
Gaussian mixtures via mixture conversions to exponential-polynomial distributions, Entropy 23.11 (2021): 1417.
(2107.05901)
- Unified polynomial dynamic programming algorithms for p-center
variants in a 2D Pareto Front, Mathematics 9.4 (2021): 453. (with Nicolas Dupin and Talbi El-Ghazali)
- q-paths: Generalizing the geometric
annealing path using power means, UAI 2021.
(2107.00745)
- On geodesic
triangles with right angles in a dually flat space,
Progress in Information Geometry: Theory and Applications. Cham: Springer International Publishing, 2021. 153-190.
(1910.03935)
- Classification in the Siegel Space for Vectorial Autoregressive Data, GSI'21.
(with Yann Cabanes)
- Structured second-order methods via natural gradient descent,
ICML'21 workshop: Beyond first-order methods in machine learning systems.
(2107.10884)
Marti, Gautier, Victor Goubet, and Frank Nielsen.
"." International Conference on Geometric Science of Information. Cham: Springer International Publishing, 2021.
- cCorrGAN:
Conditional correlation GAN for learning empirical conditional distributions in the elliptope, GSI'21.
(2107.10606)
- Geometric structures of statistical physics, information geometry, and learning,
Springer International Publishing, 2021.
- Chain Rule Optimal Transport, Progress in Information Geometry: Theory and Applications. Cham: Springer International Publishing, 2021. 191-217.
(1812.08113)
- Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Vol. 12829. Springer Nature, 2021.
- Computing statistical divergences with sigma points, GSI'21.
- q-Neurons: Neuron Activations Based on Stochastic Jackson's Derivative Operators,
IEEE Trans. Neural Networks Learn. Syst. 32(6): 2782-2789 (2021)
- On f-divergences Between Cauchy Distributions, GSI'21. (with Kazuki Okamura)
Before 2021
AMS papers with local PDFs for fast previewing:
- pdf What is... an Inductive Mean?
Notices of the American Mathematical Society 70.11 (2023): 1851-1855.
- pdf The many faces of information geometry,
Notices of the American Mathematical Society 69.1 (2022): 36-45.
- pdf What is... an information projection?
Notices of the American Mathematical Society 65.3 (2018): 321-324.
Entropy papers with local PDFs for fast previewing:
- pdf Divergences Induced by the Cumulant and Partition Functions of Exponential Families and Their Deformations Induced by Comparative Convexity. Entropy 26(3): 193 (2024)
- pdf A Simple Approximation Method for the Fisher-Rao Distance between Multivariate Normal Distributions. Entropy 25(4): 654 (2023)
- pdf Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences. Entropy 24(3): 421 (2022)
- pdf Revisiting Chernoff Information with Likelihood Ratio Exponential Families. Entropy 24(10): 1400 (2022)
- pdf On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius. Entropy 23(4): 464 (2021)
- pdf Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions. Entropy 23(11): 1417 (2021)
- pdf On a Generalization of the Jensen-Shannon Divergence and the Jensen-Shannon Centroid. Entropy 22(2): 221 (2020)
- pdf On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds. Entropy 22(7): 713 (2020)
- pdf The Siegel-Klein Disk: Hilbert Geometry of the Siegel Disk Domain. Entropy 22(9): 1019 (2020)
- pdf An Elementary Introduction to Information Geometry. Entropy 22(10): 1100 (2020)
- pdf On the Jensen-Shannon Symmetrization of Distances Relying on Abstract Means. Entropy 21(5): 485 (2019)
- pdf Computational Information Geometry for Binary Classification of High-Dimensional Random Tensors. Entropy 20(3): 203 (2018)
- pdf On Holder Projective Divergences. Entropy 19(3): 122 (2017)
- pdf Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities. Entropy 18(12): 442 (2016)
- pdf On Clustering Histograms with k-Means by Using Mixed α-Divergences. Entropy 16(6): 3273-3301 (2014)
Machine learning
- pdf
project
Hyperbolic Embeddings of Supervised Models,
NeurIPS 2024.
(arXiv)
- pdf
project
A Rate-Distortion View of Uncertainty Quantification,
ICML 2024.
(arXiv)
-
colab
Data Representations on the Bregman Manifold,
GRaM workshop, ICML 2024.
(arXiv)
- pdf
project
Optimal Transport with Tempered Exponential Measures,
AAAI 2024.
(arXiv)
- pdf
project
Simplifying Momentum-based
Positive-definite Submanifold Optimization with Applications to Deep Learning,
ICML 2023.
(arXiv)
- pdf
project
Non-linear Embeddings in Hilbert Simplex Geometry, TAG-ML 2023.
(arXiv)
- pdf
project
Fisher-Rao and pullback Hilbert cone distances on the multivariate
Gaussian manifold with applications to simplification and quantization of mixtures, TAG-ML 2023.
(arXiv)
- pdf
project
Tractable structured natural-gradient descent using local parameterizations, ICML 2021.
(arXiv)
- pdf
project
q-Paths: Generalizing the geometric annealing path using power means, UAI 2021.
(arXiv)
- pdf
project
Sinkhorn AutoEncoders, UAI 2020.
(arXiv)
- pdf
project
DeepBach: a Steerable Model for Bach Chorales Generation, ICML 2017.
(arXiv)
- pdf
project
Relative Fisher Information and Natural Gradient for Learning Large Modular Models, ICML 2017.
(arXiv)
- pdf
project
Tsallis Regularized Optimal Transport and Ecological Inference, AAAI 2017.
(arXiv)
- pdf
project
k-variates++: more pluses in the k-means++, ICML 2016.
(arXiv)
- pdf
project
Loss factorization, weakly supervised learning and label noise robustness, ICML 2016.
(arXiv)
- pdf
Clustering Financial Time Series: How Long Is Enough?, IJCAI 2016.
(arXiv)
- pdf
project
Exploring and measuring non-linear correlations: Copulas, Lightspeed Transportation and Clustering,
NeurIPS Time Series Workshop 2016.
(arXiv)
- pdf
Boosting Nearest Neighbors for the Efficient Estimation of Posteriors, ECML/PKDD 2012.
(hal)
- pdf
On tracking portfolios with certainty equivalents on a generalization of Markowitz model:
the Fool, the Wise and the Adaptive, ICML 11.
(arXiv)
- pdf
Boosting Bayesian MAP Classification, ICPR 2010.
- pdf
On the efficient minimization of convex surrogates in supervised learning, ICPR 2008.
- pdf
Real Boosting a la Carte with an Application to Boosting Oblique Decision Tree, IJCAI 2007.
- pdf
journal
A Real Generalization of Discrete AdaBoost, ECAI 2006, Artificial Intelligence 2007.
- pdf
Soft Uncoupling of Markov Chains for Permeable Language Distinction: A New Algorithm, ECAI 2006.
(arXiv)
- pdf
Fitting the Smallest Enclosing Bregman Ball, ECML 2005.
Computer vision and pattern recognition (CVPR)
- Closed-form information-theoretic divergences for statistical mixtures. ICPR 2012
- k-MLE for mixtures of generalized Gaussians. ICPR 2012: 2825-2828
- Jensen divergence based SPD matrix means and applications. ICPR 2012: 2841-2844
- Interactive Pinpoint Image Object Removal. CVPR (2) 2005: 1191
- Total Bregman divergence and its applications to shape retrieval. CVPR 2010: 3463-3468
- Texture Regimes for Entropy-Based Multiscale Image Analysis. ECCV (3) 2010: 692-705
- Boosting Bayesian MAP Classification. ICPR 2010: 661-665
- Bhattacharyya Clustering with Applications to Mixture Simplifications. ICPR 2010: 1437-1440
- Bregman sided and symmetrized centroids. ICPR 2008: 1-4
- On the efficient minimization of convex surrogates in supervised learning. ICPR 2008: 1-4
- Improving Clustering Algorithms through Constrained Convex Optimization. ICPR (4) 2004: 557-560
- Grouping with Bias Revisited. CVPR (2) 2004: 460-465
- On Region Merging: The Statistical Soundness of Fast Sorting, with Applications. CVPR (2) 2003: 19-26
- pdf Hierarchical clustering,
Introduction to HPC with MPI for Data Science (2016): 195-211.
Overview of some contributions on computational geometry on various geometric structures beyond the Euclidean structure
Books
