
Structured secondorder methods via natural gradient descent
In this paper, we propose new structured secondorder methods and struct...
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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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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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qPaths: Generalizing the Geometric Annealing Path using Power Means
Many common machine learning methods involve the geometric annealing pat...
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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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A note on some informationtheoretic divergences between Zeta distributions
In this short communication, we first report a closedform formula for c...
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On a Variational Definition for the JensenShannon Symmetrization of Distances based on the Information Radius
We generalize the JensenShannon divergence by considering a variational...
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Tractable structured natural gradient descent using local parameterizations
Naturalgradient descent on structured parameter spaces (e.g., lowrank ...
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On fdivergences between Cauchy distributions
We prove that the fdivergences between univariate Cauchy distributions ...
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On information projections between multivariate elliptical and locationscale families
We study information projections with respect to statistical fdivergenc...
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Likelihood Ratio Exponential Families
The exponential family is well known in machine learning and statistical...
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Annealed Importance Sampling with qPaths
Annealed importance sampling (AIS) is the gold standard for estimating p...
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Clustering patterns connecting COVID19 dynamics and Human mobility using optimal transport
Social distancing and stayathome are among the few measures that are k...
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On Voronoi diagrams and dual Delaunay complexes on the informationgeometric Cauchy manifolds
We study the Voronoi diagrams of a finite set of Cauchy distributions an...
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Hilbert geometry of the Siegel disk: The SiegelKlein disk model
We study the Hilbert geometry induced by the Siegel disk domain, an open...
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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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Cumulantfree closedform formulas for some common (dis)similarities between densities of an exponential family
It is wellknown that the Bhattacharyya, Hellinger, KullbackLeibler, α...
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SchoenbergRao distances: Entropybased and geometryaware statistical Hilbert distances
Distances between probability distributions that take into account the g...
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The αdivergences associated with a pair of strictly comparable quasiarithmetic means
We generalize the family of αdivergences using a pair of strictly compa...
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A generalization of the αdivergences based on comparable and distinct weighted means
We generalize the renown family of αdivergences in information geometry...
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On a generalization of the JensenShannon divergence
The JensenShannon divergence is a renown bounded symmetrization of the ...
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InformationGeometric Set Embeddings (IGSE): From Sets to Probability Distributions
This letter introduces an abstract learning problem called the “set embe...
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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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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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Planar pcenter problems are solvable in polynomial time when clustering a Pareto Front
This paper is motivated by reallife applications of biobjective optimi...
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Lightlike Neuromanifolds, Occam's Razor and Deep Learning
Why do deep neural networks generalize with a very high dimensional para...
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A closedform formula for the KullbackLeibler divergence between Cauchy distributions
We report a closedform expression for the KullbackLeibler divergence b...
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On the KullbackLeibler divergence between locationscale densities
We show that the KullbackLeibler divergence between two densities of po...
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On a generalization of the JensenShannon divergence and the JSsymmetrization of distances relying on abstract means
The JensenShannon divergence is a renown bounded symmetrization of the ...
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On power chi expansions of fdivergences
We consider both finite and infinite power chi expansions of fdivergenc...
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The statistical Minkowski distances: Closedform formula for Gaussian Mixture Models
The traditional Minkowski distances are induced by the corresponding Min...
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On The Chain Rule Optimal Transport Distance
We define a novel class of distances between statistical multivariate di...
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Geometry and clustering with metrics derived from separable Bregman divergences
Separable Bregman divergences induce Riemannian metric spaces that are i...
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The Bregman chord divergence
Distances are fundamental primitives whose choice significantly impacts ...
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Sinkhorn AutoEncoders
Optimal Transport offers an alternative to maximum likelihood for learni...
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An elementary introduction to information geometry
We describe the fundamental differentialgeometric structures of informa...
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Guaranteed Deterministic Bounds on the Total Variation Distance between Univariate Mixtures
The total variation distance is a core statistical distance between prob...
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Clustering in a 2d Pareto Front: pmedian and pcenter are solvable in polynomial time
This paper is motivated by a real life application of multiobjective op...
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qNeurons: Neuron Activations based on Stochastic Jackson's Derivative Operators
We propose a new generic type of stochastic neurons, called qneurons, t...
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Monte Carlo Information Geometry: The dually flat case
Exponential families and mixture families are parametric probability mod...
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Interactive Music Generation with Positional Constraints using AnticipationRNNs
Recurrent Neural Networks (RNNS) are now widely used on sequence generat...
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Deep rankbased transpositioninvariant distances on musical sequences
Distances on symbolic musical sequences are needed for a variety of appl...
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GLSRVAE: Geodesic Latent Space Regularization for Variational AutoEncoder Architectures
VAEs (Variational AutoEncoders) have proved to be powerful in the contex...
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Clustering in Hilbert simplex geometry
Clustering categorical distributions in the probability simplex is a fun...
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On Hölder projective divergences
We describe a framework to build distances by measuring the tightness of...
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A series of maximum entropy upper bounds of the differential entropy
We present a series of closedform maximum entropy upper bounds for the ...
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DeepBach: a Steerable Model for Bach Chorales Generation
This paper introduces DeepBach, a graphical model aimed at modeling poly...
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Exploring and measuring nonlinear correlations: Copulas, Lightspeed Transportation and Clustering
We propose a methodology to explore and measure the pairwise correlation...
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Large Margin Nearest Neighbor Classification using Curved Mahalanobis Distances
We consider the supervised classification problem of machine learning in...
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Guaranteed bounds on the KullbackLeibler divergence of univariate mixtures using piecewise logsumexp inequalities
Informationtheoretic measures such as the entropy, crossentropy and th...
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Frank Nielsen
verfied profile
Senior Researcher at S. CSL,
Professor at Ecole Polytechnique,