8 papers
An example of an optimal transport map on a sphere
Asuka Takatsu
We construct an optimal transport map between uniform distributions on two antipodal annuli of a sphere.
Stochastic Thermodynamics on Time-Evolving Curved Spaces
Rihito Nagase, Shoki Sugimoto, Asuka Takatsu +1
We construct stochastic thermodynamics of overdamped Langevin systems on nonrelaticvistic curved spaces with time-dependent metrics. The time dependence of the metric contributes t…
Proper losses regret at least 1/2-order
Han Bao, Asuka Takatsu
A fundamental challenge in machine learning is the choice of a loss as it characterizes our learning task, is minimized in the training phase, and serves as an evaluation criterion…
Disintegrated optimal transport for metric fiber bundles
Jun Kitagawa, Asuka Takatsu
We define a new two-parameter family of metrics on subsets of Borel probability measures on general metric fiber bundles, called the $ \textit{disintegrated Monge--Kantorovich metr…
Barycenters in Disintegrated optimal transport
Jun Kitagawa, Asuka Takatsu
We prove existence and duality on a wide class of metric spaces, and uniqueness results on any connected, complete Riemannian manifold, with or without boundary, for classical Mong…
Divergence and Deformed Exponential Family
Hiroshi Matsuzoe, Asuka Takatsu
The Kullback--Leibler divergence together with exponential families establishes the foundation of information geometry and is widely generalized. Among the generalization, we focus…