
Clustering patterns connecting COVID19 dynamics and Human mobility using optimal transport
Social distancing and stayathome are among the few measures that are k...
read it

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...
read it

Hilbert geometry of the Siegel disk: The SiegelKlein disk model
We introduce and study the Hilbert geometry induced by the Siegel disk, ...
read it

A note on Onicescu's informational energy and correlation coefficient in exponential families
The informational energy of Onicescu is a positive quantity that measure...
read it

Cumulantfree closedform formulas for some common (dis)similarities between densities of an exponential family
It is wellknown that the Bhattacharyya, Hellinger, KullbackLeibler, α...
read it

SchoenbergRao distances: Entropybased and geometryaware statistical Hilbert distances
Distances between probability distributions that take into account the g...
read it

The αdivergences associated with a pair of strictly comparable quasiarithmetic means
We generalize the family of αdivergences using a pair of strictly compa...
read it

A generalization of the αdivergences based on comparable and distinct weighted means
We generalize the renown family of αdivergences in information geometry...
read it

On a generalization of the JensenShannon divergence
The JensenShannon divergence is a renown bounded symmetrization of the ...
read it

InformationGeometric Set Embeddings (IGSE): From Sets to Probability Distributions
This letter introduces an abstract learning problem called the “set embe...
read it

On geodesic triangles with right angles in a dually flat space
The dualistic structure of statistical manifolds yields eight types of g...
read it

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...
read it

Planar pcenter problems are solvable in polynomial time when clustering a Pareto Front
This paper is motivated by reallife applications of biobjective optimi...
read it

Lightlike Neuromanifolds, Occam's Razor and Deep Learning
Why do deep neural networks generalize with a very high dimensional para...
read it

A closedform formula for the KullbackLeibler divergence between Cauchy distributions
We report a closedform expression for the KullbackLeibler divergence b...
read it

On the KullbackLeibler divergence between locationscale densities
We show that the KullbackLeibler divergence between two densities of po...
read it

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 ...
read it

On power chi expansions of fdivergences
We consider both finite and infinite power chi expansions of fdivergenc...
read it

The statistical Minkowski distances: Closedform formula for Gaussian Mixture Models
The traditional Minkowski distances are induced by the corresponding Min...
read it

On The Chain Rule Optimal Transport Distance
We define a novel class of distances between statistical multivariate di...
read it

Geometry and clustering with metrics derived from separable Bregman divergences
Separable Bregman divergences induce Riemannian metric spaces that are i...
read it

The Bregman chord divergence
Distances are fundamental primitives whose choice significantly impacts ...
read it

Sinkhorn AutoEncoders
Optimal Transport offers an alternative to maximum likelihood for learni...
read it

An elementary introduction to information geometry
We describe the fundamental differentialgeometric structures of informa...
read it

Guaranteed Deterministic Bounds on the Total Variation Distance between Univariate Mixtures
The total variation distance is a core statistical distance between prob...
read it

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...
read it

qNeurons: Neuron Activations based on Stochastic Jackson's Derivative Operators
We propose a new generic type of stochastic neurons, called qneurons, t...
read it

Monte Carlo Information Geometry: The dually flat case
Exponential families and mixture families are parametric probability mod...
read it

Interactive Music Generation with Positional Constraints using AnticipationRNNs
Recurrent Neural Networks (RNNS) are now widely used on sequence generat...
read it

Deep rankbased transpositioninvariant distances on musical sequences
Distances on symbolic musical sequences are needed for a variety of appl...
read it

GLSRVAE: Geodesic Latent Space Regularization for Variational AutoEncoder Architectures
VAEs (Variational AutoEncoders) have proved to be powerful in the contex...
read it

Clustering in Hilbert simplex geometry
Clustering categorical distributions in the probability simplex is a fun...
read it

On Hölder projective divergences
We describe a framework to build distances by measuring the tightness of...
read it

A series of maximum entropy upper bounds of the differential entropy
We present a series of closedform maximum entropy upper bounds for the ...
read it

DeepBach: a Steerable Model for Bach Chorales Generation
This paper introduces DeepBach, a graphical model aimed at modeling poly...
read it

Exploring and measuring nonlinear correlations: Copulas, Lightspeed Transportation and Clustering
We propose a methodology to explore and measure the pairwise correlation...
read it

Large Margin Nearest Neighbor Classification using Curved Mahalanobis Distances
We consider the supervised classification problem of machine learning in...
read it

Guaranteed bounds on the KullbackLeibler divergence of univariate mixtures using piecewise logsumexp inequalities
Informationtheoretic measures such as the entropy, crossentropy and th...
read it

Optimal Transport vs. FisherRao distance between Copulas for Clustering Multivariate Time Series
We present a methodology for clustering N objects which are described by...
read it

Fast (1+ε)approximation of the Löwner extremal matrices of highdimensional symmetric matrices
Matrix data sets are common nowadays like in biomedical imaging where th...
read it

SSSCAM: A Unified Framework for Video CoSegmentation by Structured Sparse Subspace Clustering with Appearance and Motion Features
Video cosegmentation refers to the task of jointly segmenting common ob...
read it

Clustering Financial Time Series: How Long is Enough?
Researchers have used from 30 days to several years of daily returns as ...
read it

Loss factorization, weakly supervised learning and label noise robustness
We prove that the empirical risk of most wellknown loss functions facto...
read it

Image and Information
A wellknown old adage says that "A picture is worth a thousand words!"...
read it

Optimal Copula Transport for Clustering Multivariate Time Series
This paper presents a new methodology for clustering multivariate time s...
read it

Further heuristics for kmeans: The mergeandsplit heuristic and the (k,l)means
Finding the optimal kmeans clustering is NPhard in general and many he...
read it

Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasiarithmetic means
Bayesian classification labels observations based on given prior informa...
read it

On the symmetrical KullbackLeibler Jeffreys centroids
Due to the success of the bagofword modeling paradigm, clustering hist...
read it

kMLE: A fast algorithm for learning statistical mixture models
We describe kMLE, a fast and efficient local search algorithm for learn...
read it

Chernoff information of exponential families
Chernoff information upper bounds the probability of error of the optima...
read it
Frank Nielsen
verfied profile
Senior Researcher at S. CSL,
Professor at Ecole Polytechnique,