b'Frank Nielsen'

research

∙ 09/07/2023

Optimal Transport with Tempered Exponential Measures

In the field of optimal transport, two prominent subfields face each oth...

0 Ehsan Amid, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 03/10/2023

Product Jacobi-Theta Boltzmann machines with score matching

The estimation of probability density functions is a non trivial task th...

0 Andrea Pasquale, et al. ∙

research

∙ 02/20/2023

Simplifying Momentum-based Riemannian Submanifold Optimization

Riemannian submanifold optimization with momentum is computationally cha...

0 Wu Lin, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Nicolas Dupin, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 09/15/2022

Rho-Tau Bregman Information and the Geometry of Annealing Paths

Markov Chain Monte Carlo methods for sampling from complex distributions...

0 Rob Brekelmans, et al. ∙

research

∙ 07/08/2022

Revisiting Chernoff Information with Likelihood Ratio Exponential Families

The Chernoff information between two probability measures is a statistic...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Pascal Mattia Esser, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 03/22/2022

Non-linear Embeddings in Hilbert Simplex Geometry

A key technique of machine learning and computer vision is to embed disc...

0 Frank Nielsen, et al. ∙

research

∙ 02/22/2022

The duo Fenchel-Young divergence

By calculating the Kullback-Leibler divergence between two probability m...

0 Frank Nielsen, et al. ∙

research

∙ 12/07/2021

Towards Modeling and Resolving Singular Parameter Spaces using Stratifolds

When analyzing parametric statistical models, a useful approach consists...

0 Pascal Mattia Esser, et al. ∙

research

∙ 09/30/2021

On the Kullback-Leibler divergence between discrete normal distributions

Discrete normal distributions are defined as the distributions with pres...

0 Frank Nielsen, et al. ∙

research

∙ 07/22/2021

Structured second-order methods via natural gradient descent

In this paper, we propose new structured second-order methods and struct...

0 Wu Lin, et al. ∙

research

∙ 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...

0 Gautier Marti, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 07/01/2021

q-Paths: Generalizing the Geometric Annealing Path using Power Means

Many common machine learning methods involve the geometric annealing pat...

5 Vaden Masrani, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 02/15/2021

Tractable structured natural gradient descent using local parameterizations

Natural-gradient descent on structured parameter spaces (e.g., low-rank ...

0 Wu Lin, et al. ∙

research

∙ 01/29/2021

On f-divergences between Cauchy distributions

We prove that the f-divergences between univariate Cauchy distributions ...

0 Frank Nielsen, et al. ∙

research

∙ 01/11/2021

On information projections between multivariate elliptical and location-scale families

We study information projections with respect to statistical f-divergenc...

0 Frank Nielsen, et al. ∙

research

∙ 12/31/2020

Likelihood Ratio Exponential Families

The exponential family is well known in machine learning and statistical...

12 Rob Brekelmans, et al. ∙

research

∙ 12/14/2020

Annealed Importance Sampling with q-Paths

Annealed importance sampling (AIS) is the gold standard for estimating p...

8 Rob Brekelmans, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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-...

6 Frank Nielsen, et al. ∙

research

∙ 02/19/2020

Schoenberg-Rao distances: Entropy-based and geometry-aware statistical Hilbert distances

Distances between probability distributions that take into account the g...

22 Gaëtan Hadjeres, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 12/02/2019

On a generalization of the Jensen-Shannon divergence

The Jensen-Shannon divergence is a renown bounded symmetrization of the ...

0 Frank Nielsen, et al. ∙

research

∙ 11/27/2019

Information-Geometric Set Embeddings (IGSE): From Sets to Probability Distributions

This letter introduces an abstract learning problem called the “set embe...

16 Ke Sun, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Frank Nielsen, et al. ∙

research

∙ 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...

0 Nicolas Dupin, et al. ∙

research

∙ 05/27/2019

Lightlike Neuromanifolds, Occam's Razor and Deep Learning

Why do deep neural networks generalize with a very high dimensional para...

3 Ke Sun, et al. ∙

research

∙ 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...

0 Frédéric Chyzak, et al. ∙

research

∙ 04/23/2019

On the Kullback-Leibler divergence between location-scale densities

We show that the Kullback-Leibler divergence between two densities of po...

0 Frank Nielsen, et al. ∙

research

∙ 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 ...

0 Frank Nielsen, et al. ∙

research

∙ 03/14/2019

On power chi expansions of f-divergences

We consider both finite and infinite power chi expansions of f-divergenc...

0 Frank Nielsen, et al. ∙

research

∙ 01/09/2019

The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models

The traditional Minkowski distances are induced by the corresponding Min...

6 Frank Nielsen, et al. ∙

research

∙ 12/19/2018

On The Chain Rule Optimal Transport Distance

We define a novel class of distances between statistical multivariate di...

4 Frank Nielsen, et al. ∙

research

∙ 10/25/2018

Geometry and clustering with metrics derived from separable Bregman divergences

Separable Bregman divergences induce Riemannian metric spaces that are i...

6 Erika Gomes-Gonçalves, et al. ∙

research

∙ 10/22/2018

The Bregman chord divergence

Distances are fundamental primitives whose choice significantly impacts ...

4 Frank Nielsen, et al. ∙

Frank Nielsen

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