Frank NIELSEN / フランク・ニールセン Sony Computer Science Laboratories Inc, Tokyo (contact) Senior Researcher, Fellow (Biography) Publications | Talks | Activities | Events | Software | Blog | @FrnkNlsn | Research cards | Curated book list | Bookmarks

• Research: Geometric Computing for AI/ML and Information Sciences and its Applications: Structures, Dynamics, and Dualities
  
• Main interests:
  • Co-organize the biannual conference on Geometric Science of Information (GSI)
    
    
  • Information Geometry: Elementary survey (40 min. video) or short introduction, pyBregMan natural gradient, information projection, Cramér-Rao lower bound, Deep learning, Bregman nearest neighbor data structures, Bregman clustering/k-MLE mixture family (Cauchy 2-mixtures), Bregman Voronoi diagrams (Bregman Hessian manifolds), Cauchy manifolds [Synonyms]
    
    
  • Distances, divergences, and mutual information:

    f-divergences (elliptical distributions/ Cauchy distributions/ hyperboloid distributions, Taylor expansion, 𝛼-divergences and a generalized 𝛼-divergences), generalized Jensen-Shannon symmetrization KLD discrete normal distributions ), generalized Bhattacharyya and Chernoff distances Fisher-Rao distance (multivariate normal distributions), Birkhoff projective distance, Sharma-Mittal entropies and divergences (Rényi and Tsallis entropies and divergences ), Jeffreys-Bregman divergences, Bregman matrix divergences (portfolio theory), chord/tangent Bregman divergences, comparative convexity Bregman/Jensen divergences duo Bregman/Legendre Fenchel divergences, projective divergences (Cauchy-Schwarz/Hölder divergences, Hilbert simplex distance, γ-divergences), mixture divergence (closed-form, Minkowski distances, MaxEnt upper bounds, bounding total variation bounding f-divergences ), Onicescu's informational energy, curved Mahalanobis distances, chain rule optimal transport, entropic optimal transport (Tsallis regularited OT, sparsity-controlled tempered OT), linear odd loss(LOL), Balanced Convex Surrogates (BCS), variational Jensen-Shannon divergence/variational divergences,

    
    
    
  • Means and centers: inductive means, multivariate quasi-arithmetic means (Bregman centroids), Bregman minimax, Jensen/Burbea-Rao centroids/ Jensen-Bregman centroids, Symmetrized Kullback-Leibler centroid (Jeffreys centroid), Bhattacharyya centroids, Jensen-Shannon centroids, Chernoff Information, conformal centroids (total Jensen/total Bregman), hyperbolic model centroids, Riemannian minimax center, Siegel complex matrices minimax (Hadamard complex manifold), Finsler centers
    

Topics: AI & ML, Information Theory, Data Science, Visual Computing, HPC
Computational Geometry (Geometric Combinatorial Optimization) | Hyperbolic Geometry | Clustering | Image stitching | Systems Biology


• Editor: Information Geometry (INGE, Springer) | Transactions on Information Theory (IEEE) | Entropy (MDPI)
  Book series associate editor: Mathematical Marvels: Texts and Monographs in the Spirit of CR Rao (Springer), Editor

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I program mostly in C/C++/Java, sometimes in Julia and R, and I program maxima scripts for symbolic computing.

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