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09/07/2023
Optimal Transport with Tempered Exponential Measures
In the field of optimal transport, two prominent subfields face each oth...
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07/20/2023
Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributions
Data sets of multivariate normal distributions abound in many scientific...
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03/10/2023
Product Jacobi-Theta Boltzmann machines with score matching
The estimation of probability density functions is a non trivial task th...
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02/20/2023
Simplifying Momentum-based Riemannian Submanifold Optimization
Riemannian submanifold optimization with momentum is computationally cha...
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02/16/2023
A numerical approximation method for the Fisher-Rao distance between multivariate normal distributions
We present a simple method to approximate Rao's distance between multiva...
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02/11/2023
Partial k-means to avoid outliers, mathematical programming formulations, complexity results
A well-known bottleneck of Min-Sum-of-Square Clustering (MSSC, the celeb...
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01/26/2023
Beyond scalar quasi-arithmetic means: Quasi-arithmetic averages and quasi-arithmetic mixtures in information geometry
We generalize quasi-arithmetic means beyond scalars by considering the g...
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09/15/2022
Rho-Tau Bregman Information and the Geometry of Annealing Paths
Markov Chain Monte Carlo methods for sampling from complex distributions...
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07/08/2022
Revisiting Chernoff Information with Likelihood Ratio Exponential Families
The Chernoff information between two probability measures is a statistic...
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06/17/2022
On the Influence of Enforcing Model Identifiability on Learning dynamics of Gaussian Mixture Models
A common way to learn and analyze statistical models is to consider oper...
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05/27/2022
Information geometry of the Tojo-Yoshino's exponential family on the Poincaré upper plane
We study the dually flat information geometry of the Tojo-Yoshino expone...
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04/22/2022
A note on the f-divergences between multivariate location-scale families with either prescribed scale matrices or location parameters
We first extend the result of Ali and Silvey [Journal of the Royal Stati...
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03/22/2022
Non-linear Embeddings in Hilbert Simplex Geometry
A key technique of machine learning and computer vision is to embed disc...
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02/22/2022
The duo Fenchel-Young divergence
By calculating the Kullback-Leibler divergence between two probability m...
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12/07/2021
Towards Modeling and Resolving Singular Parameter Spaces using Stratifolds
When analyzing parametric statistical models, a useful approach consists...
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09/30/2021
On the Kullback-Leibler divergence between discrete normal distributions
Discrete normal distributions are defined as the distributions with pres...
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07/22/2021
Structured second-order methods via natural gradient descent
In this paper, we propose new structured second-order methods and struct...
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07/22/2021
cCorrGAN: Conditional Correlation GAN for Learning Empirical Conditional Distributions in the Elliptope
We propose a methodology to approximate conditional distributions in the...
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07/13/2021
Fast approximations of the Jeffreys divergence between univariate Gaussian mixture models via exponential polynomial densities
The Jeffreys divergence is a renown symmetrization of the statistical Ku...
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07/01/2021
q-Paths: Generalizing the Geometric Annealing Path using Power Means
Many common machine learning methods involve the geometric annealing pat...
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04/28/2021
The dually flat information geometry of the mixture family of two prescribed Cauchy components
In information geometry, a strictly convex and smooth function induces a...
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04/21/2021
A note on some information-theoretic divergences between Zeta distributions
In this short communication, we first report a closed-form formula for c...
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02/19/2021
On a Variational Definition for the Jensen-Shannon Symmetrization of Distances based on the Information Radius
We generalize the Jensen-Shannon divergence by considering a variational...
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02/15/2021
Tractable structured natural gradient descent using local parameterizations
Natural-gradient descent on structured parameter spaces (e.g., low-rank ...
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01/29/2021
On f-divergences between Cauchy distributions
We prove that the f-divergences between univariate Cauchy distributions ...
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01/11/2021
On information projections between multivariate elliptical and location-scale families
We study information projections with respect to statistical f-divergenc...
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12/31/2020
Likelihood Ratio Exponential Families
The exponential family is well known in machine learning and statistical...
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12/14/2020
Annealed Importance Sampling with q-Paths
Annealed importance sampling (AIS) is the gold standard for estimating p...
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07/21/2020
Clustering patterns connecting COVID-19 dynamics and Human mobility using optimal transport
Social distancing and stay-at-home are among the few measures that are k...
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06/12/2020
On Voronoi diagrams and dual Delaunay complexes on the information-geometric Cauchy manifolds
We study the Voronoi diagrams of a finite set of Cauchy distributions an...
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04/17/2020
Hilbert geometry of the Siegel disk: The Siegel-Klein disk model
We study the Hilbert geometry induced by the Siegel disk domain, an open...
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03/30/2020
A note on Onicescu's informational energy and correlation coefficient in exponential families
The informational energy of Onicescu is a positive quantity that measure...
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03/05/2020
Cumulant-free closed-form formulas for some common (dis)similarities between densities of an exponential family
It is well-known that the Bhattacharyya, Hellinger, Kullback-Leibler, α-...
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02/19/2020
Schoenberg-Rao distances: Entropy-based and geometry-aware statistical Hilbert distances
Distances between probability distributions that take into account the g...
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01/27/2020
The α-divergences associated with a pair of strictly comparable quasi-arithmetic means
We generalize the family of α-divergences using a pair of strictly compa...
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01/27/2020
A generalization of the α-divergences based on comparable and distinct weighted means
We generalize the renown family of α-divergences in information geometry...
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12/02/2019
On a generalization of the Jensen-Shannon divergence
The Jensen-Shannon divergence is a renown bounded symmetrization of the ...
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11/27/2019
Information-Geometric Set Embeddings (IGSE): From Sets to Probability Distributions
This letter introduces an abstract learning problem called the “set embe...
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10/09/2019
On geodesic triangles with right angles in a dually flat space
The dualistic structure of statistical manifolds yields eight types of g...
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09/19/2019
A note on the quasiconvex Jensen divergences and the quasiconvex Bregman divergences derived thereof
We first introduce the class of quasiconvex and quasiconcave Jensen dive...
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08/19/2019
Planar p-center problems are solvable in polynomial time when clustering a Pareto Front
This paper is motivated by real-life applications of bi-objective optimi...
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05/27/2019
Lightlike Neuromanifolds, Occam's Razor and Deep Learning
Why do deep neural networks generalize with a very high dimensional para...
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05/27/2019
A closed-form formula for the Kullback-Leibler divergence between Cauchy distributions
We report a closed-form expression for the Kullback-Leibler divergence b...
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04/23/2019
On the Kullback-Leibler divergence between location-scale densities
We show that the Kullback-Leibler divergence between two densities of po...
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04/08/2019
On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means
The Jensen-Shannon divergence is a renown bounded symmetrization of the ...
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03/14/2019
On power chi expansions of f-divergences
We consider both finite and infinite power chi expansions of f-divergenc...
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01/09/2019
The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models
The traditional Minkowski distances are induced by the corresponding Min...
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12/19/2018
On The Chain Rule Optimal Transport Distance
We define a novel class of distances between statistical multivariate di...
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10/25/2018
Geometry and clustering with metrics derived from separable Bregman divergences
Separable Bregman divergences induce Riemannian metric spaces that are i...
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10/22/2018