Frank NIELSEN フランク・ニールセン PhD'96, HDR'06
Sony CSL, Fellow
Short biography
My motto:
 "Structure invariance is the only constant in change!"
 "Geometry defines the architecture of spaces"
Blog
Tweets
Research cards (510+)
Curated book lists

 What is... an inductive mean?, AMS Notices, to appear.
 Optimal Transport with Tempered Exponential Measures, arxiv:2309.04015
 FisherRao and pullback Hilbert cone distances on the multivariate Gaussian manifold with applications to simplification and
quantization of mixtures,
2nd Annual Topology,
Algebra, and Geometry in Machine Learning Workshop (ICML TAGML),
poster
2023
Slides (GSI'23)
video (GSI'23)
 Nonlinear Embeddings in Hilbert Simplex Geometry, 2nd Annual Topology,
Algebra, and Geometry in Machine Learning Workshop (ICML TAGML),
slides,
poster, 2023.
2203.11434
 Simplifying Momentumbased Positivedefinite Submanifold Optimization with Applications to Deep Learning
, ICML'23 (with Wu Lin, Valentin Duruisseaux, Melvin Leok, Mohammad Emtiyaz Khan, Mark Schmidt)
 On the fdivergences between hyperboloid and
Poincaré distributions, GSI'23
(2205.13984),
Slides
video.
This work highlights the notion of maximal invariant
 Quasiarithmetic centers, quasiarithmetic
mixtures, and the JensenShannon ∇divergences, GSI'23
(Paper@Springer)
Slides
video
 A Simple Approximation Method for the FisherRao Distance
between Multivariate Normal Distributions, Entropy 2023, web page
 Product JacobiTheta Boltzmann machines with score matching,
Proceedings of 21st International Workshop on Advanced Computing and Analysis Techniques in Physics Research
(ACAT22), IOP Press, 2023. talk video

On fdivergences between Cauchy distributions,
IEEE Transactions on Information Theory, 69(5), 3150  3171, 2023 (with Kazuki Okamura)
 Generalizing the AlphaDivergences
and the Oriented Kullback–Leibler Divergences with QuasiArithmetic Means, Algorithms 2022, 15(11), 435
 Practical Structured Riemannian Optimization with Momentum by using
Generalized Normal Coordinates, NeurReps Workshop of NeurIPS 2022,
(with Wu Lin, Valentin Duruisseaux, Melvin Leok Mohammad Emtiyaz Khan, Mark Schmidt)
 Introduction
to Information Geometry, MaxEnt'22 tutorial
 Information measures and information geometry of the Zeta distributions (MaxEnt'22)
 Revisiting Chernoff Information with Likelihood Ratio Exponential Families, Entropy 2022, 24(10), 1400
 A note on the fdivergences between multivariate locationscale families with either prescribed scale matrices or location parameters, submitted
 The analytic dually flat space of the mixture family
of two prescribed distinct Cauchy distributions, Handbook of Statistics (Elsevier), Volume 46, 2022

Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman
and Duo Jensen Divergences, Entropy 2022, 24(3)

Onicescu’s Informational Energy and Correlation Coefficient in Exponential Families, Foundations 2022, 2(2), 362376
 The
Kullback–Leibler Divergence Between Lattice Gaussian Distributions,
Journal of the Indian Institute of Science (2022),
[2109.14920]
 The Many Faces of Information Geometry,
AMS Notices, 2022

On a Variational Definition for the JensenShannon Symmetrization of Distances Based
on the Information Radius, Entropy 2021

On a Generalization of the JensenShannon Divergence and the Jensen–Shannon Centroid, Entropy 2020
 Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences,
Geometric Structures of Statistical Physics, Information Geometry, and Learning, Springer 2021
[Publications by reverse
chronological order] [pdf]
 📖 Publications sorted by research interest: [Google Scholar] [DBLP] [Books]
 Slides and 📹 video
 Software
 Portal Geometric Science of Information (GSI)
 Textbooks:
 Journal editorial boards
and conference/workshop/event organizations
 Recent events and activities:
 Geometric Science of Information (GSI), 30 Aug1st Sept 2023, Saint Malo, France.
 Introduction to Information Geometry, Recent Advances and Applications
School and workshop on
Where: Baltic Institute of Mathematics (hybrid format: Gothenburg, Sweden and online)
When: August 21stSeptember 1st 2023
 Special Issue of Information Geometry journal:
Half a Century of Information Geometry
 Symmetry
and Geometry in Neural Representations, NeurIPS workshop 2022 (Dec., New Orleans)
 International Conference on Bayesian and Maximum Entropy
methods in Science and Engineering (MaxEnt’22) at
Institut Henri Poincaré, July 1822 2022
 International Conference
on Information Geometry for Data Science, Sept. 1923, Hamburg, Germany.
Poster
 Handbook of Statistics (Volume 46).
Book home page, July 2022
