{Euclidean, metric, and Wasserstein} gradient flows: an overview - Bulletin of Mathematical Sciences
Rethinking statistical learning theory: learning using statistical invariants - Machine Learning
This paper introduces a new learning paradigm, called Learning Using Statistical Invariants (LUSI), which is different from the classical one. In a classical paradigm, the learning machine constructs a classification rule that minimizes the probability of expected error; it is data-driven model of learning. In the LUSI paradigm, in order to construct the desired classification function, a learning
Higher Order Equivalence of Bayes Cross Validation and WAIC
It was proved in the previous paper (Watanabe, J Mach Learn Res, 11:3571–3591, (2010), [16]) that Bayes cross validation is asymptotically equivalent to the widely applicable information criterion (WAIC), even if the posterior distribution can not be approximated by any normal distribution. In the present paper, we prove that they are equivalent to each other according to the second order asymptot
Bayesian Item Response Modeling
The modeling of item response data is governed by item response theory, also referred to as modern test theory. The eld of inquiry of item response theory has become very large and shows the enormous progress that has been made. The mainstream literature is focused on frequentist statistical methods for - timating model parameters and evaluating model t. However, the Bayesian methodology has shown
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Fisher–Rao geometry of equivalent Gaussian measures on infinite-dimensional Hilbert spaces - Information Geometry
Statistical manifold with degenerate metric - Information Geometry
Morse-Smale Decompositions for Modeling Terrain Knowledge
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem - Numerische Mathematik024)
Holographic entanglement negativity and replica symmetry breaking - Journal of High Energy Physics
Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport - Information Geometry
Transport information geometry: Riemannian calculus on probability simplex - Information Geometry
The Banach manifold of measures and the Lagrange multipliers of statistical mechanics - Information Geometry060)
Emergence of AdS geometry in the simulated tempering algorithm - Journal of High Energy Physics
Distance metric learning for graph structured data - Machine Learning
Weak approximation of transformed stochastic gradient MCMC - Machine Learning
Encyclopedia of Algorithms
The Eigenvalues of Mega-dimensional Matrices
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Rapid Prototyping of Digital Systems