Frank NIELSEN (PhD'96, HDR'06)
Main fields of interest:
- Geometric science of information
- Computational information geometry
- Theory of (dis)similarities and aggregators
- Machine learning and artificial intelligence
- Visual computing and computational photography
- Computational mathematics
- Some introductory and overview papers:
- Cramer-Rao lower bound and information geometry
→ A first read introducing the Fisher information matrix, the CRLB, and the differential-geometrization of statistics
- An elementary introduction to information geometry
→ Learn what is the fundamental theorem of information geometry!
- Introduction to Bregman manifolds
→ Learn the dually flat spaces of exponential families and mixture families, and the dual generalized Pythagorean theorems
- What is... an information projection?
→ Projection along geodesics, projection as divergence minimization, cases where we have uniqueness of projections
- Five selected publications:
- Bregman Voronoi diagrams, Discrete and Computational Geometry, 2010.
- The Burbea-Rao and Bhattacharyya centroids, IEEE Transactions on Information Theory, 2011.
- An information-geometric characterization of Chernoff information, IEEE Signal Processing Letters, 2013.
- On the chi square and higher-order chi distances for approximating f-divergences, IEEE Signal Processing Letters, 2013.
- Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means, Pattern Recognition Letters, 2014.
- Five selected collaborative publications tackling various applications:
- Some research cards
- Textbooks (AMZ book author web page):