Frank Nielsen
@FrnkNlsn
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Information Geometry, Information Theory, and Geometric Science of Information (GSI) for machine learning and AI, visual computing, HPC, pyBregMan lib @SonyCSL
Tokyo 東京
Joined February 2010
New preprint: . "Two tales for a geometric Jensen--Shannon divergence" . Both types can be interpreted as regularized Jensen-Shannon divergence.
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Survey on clustering financial time series: . "A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets". @GautierMarti1
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Paradigm shifts. 1970's: Algorithms + Data Structures = Programs. 2020's: Architecture + Learning = Intelligence
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New book in town!. "The Philosophy and Physics of Duality". with preprint on arxiv (601 pages):.
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🎉A book on the geometry of ∞-dimensional statistical models by Richard Nickl and Evarist Giné,.Cambridge University Press (2016). 👉Nonparametric and high-dimensional statistical models. PDF draft:.
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Bregman divergences require the calculation of the gradient of the Bregman generator. We can approximate the BDs without using the gradient by either the scaled skew Jensen divergences or the Bregman chord divergences.
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Must books on artificial neural networks in the 1960's:. Principles of Neurodynamics (1962).Perceptrons and the Theory of Brain Mechanisms. Learning machines（1965）.foundations of trainable pattern-classifying systems. Perceptrons (1969).An Introduction to Computational Geometry
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Forthcoming talk at Mathematics of Machine Learning 2025:. "Recent perspectives on Bregman divergences".
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Symmetrized Bregman divergences (SBDs) not Bregman div. except for generalized quadratic divergences. Obtain SBD by doubling dimension with parameter (θ,η) and using convex conjugates. However, double parameter space is not convex because of η= ∇F (θ). 👉
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Jensen-Shannon centroid of discrete distributions: . ➊ Categorical distributions = *mixture family*.➋ JSD centroid ≡ Jensen centroid on mixture parameters .➌ ConCave-Convex Procedure (CCCP)
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Game theory is becoming increasingly important in machine learning and AI. → Some books on "Game Theory"
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IEEE Transactions on Information Theory:. "On f-divergences between Cauchy distributions". Chi square divergence = maximal invariant . ➔ f-divergences between Cauchy distributions = functions of their chi2. arXiv version.
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computation as a first principle. This highlighted portion of Chapter 16 on "Number systems" of Roger Penrose master book on ."Road to Reality" .is indeed inspiring! . Imho, Computability shall have deeper relevance in future physical and AI theories.
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