Frank NIELSEN
フランク・ニールセン
PhD'96, HDR'06
Sony CSL, Fellow
Short biography
- "Structure invariance is the only constant in change!"
- "Geometry defines the architecture of spaces"
- What is... an inductive mean?, AMS Notices, to appear.
- Optimal Transport with Tempered Exponential Measures, arxiv:2309.04015
- Fisher-Rao 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) - Non-linear Embeddings in Hilbert Simplex Geometry, 2nd Annual Topology, Algebra, and Geometry in Machine Learning Workshop (ICML TAGML), slides, poster, 2023. 2203.11434
- Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning , ICML'23 (with Wu Lin, Valentin Duruisseaux, Melvin Leok, Mohammad Emtiyaz Khan, Mark Schmidt)
- On the f-divergences between hyperboloid and Poincaré distributions, GSI'23 (2205.13984), Slides video. This work highlights the notion of maximal invariant
- Quasi-arithmetic centers, quasi-arithmetic
mixtures, and the Jensen-Shannon ∇-divergences, GSI'23
(Paper@Springer) Slides video 
A Simple Approximation Method for the Fisher-Rao Distance
between Multivariate Normal Distributions, Entropy 2023, web page
- Product Jacobi-Theta 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 f-divergences between Cauchy distributions, IEEE Transactions on Information Theory, 69(5), 3150 - 3171, 2023 (with Kazuki Okamura)
- Generalizing the Alpha-Divergences and the Oriented Kullback–Leibler Divergences with Quasi-Arithmetic 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 f-divergences between multivariate location-scale 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), 362-376
- 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 Jensen-Shannon Symmetrization of Distances Based on the Information Radius, Entropy 2021
On a Generalization of the Jensen-Shannon 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]
- [Information geometry], [divergences], [natural gradient] and [computational geometry]
- Information theory and mathematical statistics, [clustering]
- [Dissimilarities, distances, divergences, and losses]
- [clustering] (centroids/centers) and generative models, [deep learning] and machine learning
- Visual computing, [image/video stitching] and computational photography
- [Geometric combinatorial optimization]
- Data science for [systems biology]
- Slides and 📹 video
- Software
- Portal Geometric Science of Information (GSI)
- Textbooks:
- Introduction to HPC with MPI for Data Science, Springer, 2016.
- A Concise and Practical Introduction to Programming Algorithms in Java, Springer, 2009.
- Visual Computing: Geometry, Graphics, and Vision, Charles River Media, 2005.
- Journal editorial boards
and conference/workshop/event organizations
- Recent events and activities:
- Geometric Science of Information (GSI), 30 Aug-1st 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 21st-September 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 18-22 2022
- International Conference on Information Geometry for Data Science, Sept. 19-23, Hamburg, Germany. Poster
- Handbook of Statistics (Volume 46). Book home page, July 2022