Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Takatsu, Asuka"'
We identify the optimal protocols to achieve the minimal entropy production in finite-time information exchange processes in Langevin systems, on the basis of optimal transport theory. Our general results hold even for non-Gaussian cases, while we de
Externí odkaz:
http://arxiv.org/abs/2410.11603
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an open inter
Externí odkaz:
http://arxiv.org/abs/2408.16435
Autor:
Bao, Han, Takatsu, Asuka
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 for estimators. Proper losses are commonly chosen, ensuring minimizer
Externí odkaz:
http://arxiv.org/abs/2407.10417
Autor:
Kitagawa, Jun, Takatsu, Asuka
We define a new two-parameter family of metrics on a subspace of Borel probability measures on a metric fiber bundle, called the disintegrated Monge--Kantorovich metrics. We then prove the disintegrated Monge--Kantorovich metrics are complete, separa
Externí odkaz:
http://arxiv.org/abs/2407.01879
We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain.
Comment: 18 pages. Comments welcome!
Comment: 18 pages. Comments welcome!
Externí odkaz:
http://arxiv.org/abs/2405.03982
Autor:
Kitagawa, Jun, Takatsu, Asuka
We introduce a one-parameter family of metrics on the space of Borel probability measures on Euclidean space with finite $p$th moment for $1\leq p <\infty$, called the $\textit{sliced Monge--Kantorovich metrics}$, which include the sliced Wasserstein
Externí odkaz:
http://arxiv.org/abs/2311.15874
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the required
Externí odkaz:
http://arxiv.org/abs/2309.11666
Autor:
Kitagawa, Jun, Takatsu, Asuka
We prove existence of equal area partitions of the unit sphere via optimal transport methods, accompanied by diameter bounds written in terms of Monge--Kantorovich distances. This can be used to obtain bounds on the expectation of the maximum diamete
Externí odkaz:
http://arxiv.org/abs/2306.16239
$F$-concavity is a generalization of power concavity and, actually, the largest available generalization of the notion of concavity. We characterize the $F$-concavities preserved by the Dirichlet heat flow in convex domains on ${\mathbb R}^n$, and co
Externí odkaz:
http://arxiv.org/abs/2207.13449
Autor:
Takatsu, Asuka
We prove that the spectral structure on the $N$-dimensional standard sphere of radius $(N-1)^{1/2}$ compatible with a projection onto the first $n$-coordinates converges to the spectral structure on the $n$-dimensional Gaussian space with variance $1
Externí odkaz:
http://arxiv.org/abs/2106.09452