Selected publications

• pdf The many faces of information geometry, Notices of the AMS 69.1 (2022).

  A short 9-page introduction to the main concepts and results of information geometry for beginners.

• pdf On the Jensen–Shannon symmetrization of distances relying on abstract means, Entropy 21.5 (2019).

  The Jensen-Shannon divergence (JSD) is a symmetrization of the Kullback-Leibler divergence bounded by log 2 (even when supports differs) but is not available in closed-form for Gaussians. Instead of taking the arithmetic mean mixture M(p,q)=(p+q)/2, we consider generic means M and define the M-JSD(p,q)=KL(p:M(p,q))+KL(q:M(p,q)). In particular, the geometric G-JSD between Gaussians or the harmonic H-JSD between Cauchy distributions are available in closed-form. Follow-up work

• pdf On a generalization of the Jensen–Shannon divergence and the Jensen–Shannon centroid, Entropy 22.2 (2020).

  Consider the discrete distributions p=(p1,...,p(n+1)) on the standard simplex (categorical distributions including Bernoulli for n=1) as a mixture family (statistical model of order n). Jensen-Shannon divergence between p and p' rewrites as a Jensen divergence between w=(p1,...,pn) and w'=(p1',...,pn'), and we solve JSD centroid by using the difference of convex algorithm (DCA/CCCP). Allows to cluster robustly histograms with potentially empty bins.

• pdf (updated arxiv) Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models, Handbook of Statistics. Vol. 51. Elsevier, 2024. 67-116.

  Give arbitrary lower and upper bounds for calculating the Fisher-Rao distance between multivariate normal distributions.

• pdf (arxiv) Bregman Voronoi diagrams, Discrete & Computational Geometry 44.2 (2010)

  Voronoi diagrams with respect to Bregman divergences which are asymmetric (except for squared Euclidean distances) are studied: Bregman VDs can be computed by clipping power diagrams or by using the lifting to the Bregman potential function (generalizing the paraboloid lifting transform).

• pdf (arxiv) On the f-divergences between densities of a multivariate location or scale family, Statistics and Computing 34.1 (2024).

  
  

• pdf (arxiv) Revisiting Chernoff information with likelihood ratio exponential families Entropy 24.10 (2022): 1400.

  By building a 1D exponential family for any two probability measures dominated by a given measure, we show that the log-normalizer is the negative of the Bhattacharrya divergence (hence concave). Prove that the best Chernoff parameter is the intersection of an exponential geodesic with a dual mixture bisector.

• pdf (arxiv) q-Paths: Generalizing the geometric annealing path using power means, Uncertainty in Artificial Intelligence (UAI), 2021.

  
  

• pdf (arxiv) Loss factorization, weakly supervised learning and label noise robustness, International conference on machine learning (ICML), 2016.

  
  

• pdf (arxiv) A geometric modeling of Occam's razor in deep learning, Information Geometry 8.Suppl 1 (2025).

  
  

• pdf (arxiv) Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning, International Conference on Machine Learning (ICML), 2023.