256 citations · 2.3k across the 100 of their papers we have counts for
8 papers · 1 filter
On The Chain Rule Optimal Transport Distance
Frank Nielsen, Ke Sun
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance de…
Geometry and clustering with metrics derived from separable Bregman divergences
Erika Gomes-Gonçalves, Henryk Gzyl, Frank Nielsen
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its co…
The Bregman chord divergence
Frank Nielsen, Richard Nock
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropr…
An elementary introduction to information geometry
Frank Nielsen
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some u…
Guaranteed Deterministic Bounds on the Total Variation Distance between Univariate Mixtures
Frank Nielsen, Ke Sun
The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in . This distance plays…
q-Neurons: Neuron Activations based on Stochastic Jackson's Derivative Operators
Frank Nielsen, Ke Sun
We propose a new generic type of stochastic neurons, called -neurons, that considers activation functions based on Jackson's -derivatives with stochastic parameters . Our…
k-medoids and p-median clustering are solvable in polynomial time for a 2d Pareto front
Nicolas Dupin, Frank Nielsen, El-Ghazali Talbi
This paper examines a common extension of k-medoids and k-median clustering in the case of a two-dimensional Pareto front, as generated by bi-objective optimization approaches. A c…
Monte Carlo Information Geometry: The dually flat case
Frank Nielsen, Gaëtan Hadjeres
Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical diverg…