Optimal transport aligns samples across distributions by minimizing the transportation cost
between them, eg, the geometric distances. Yet, it ignores coherence structure in the data …

A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol
that drives a nonequilibrium system between two thermodynamic states in the slow-driving …

Abstract Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based
deterministic sampling algorithm. Despite its wide usage, understanding the theoretical …

We propose a geometric theory of non-equilibrium thermodynamics, namely geometric
thermodynamics, using our recent developments of differential-geometric aspects of entropy …

Extracting physical parameters that cannot be directly measured from an observed data set
remains a great challenge in several fields of science and physics. In many of these …

Consider the Monge-Kantorovich optimal transport problem where the cost function is given
by a Bregman divergence. The associated transport cost, which we call the Bregman …

We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is
defined as the pullback of the full Wasserstein metric on the space of smooth probability …

Information geometry is a study of statistical manifolds, that is, spaces of probability
distributions from a geometric perspective. Its classical information-theoretic applications …

When there are no constraints upon the solutions of the equation 𝑨⁢ 𝝃= 𝒚, where 𝑨 is a K×
N-matrix, 𝝃∈ ℝ N and 𝒚∈ ℝ K a given vector, the description of the set of solutions as 𝒚 …

Forecasting stochastic nonlinear dynamical systems under the influence of conditioning
variables is a fundamental challenge repeatedly encountered across the biological and …