相关论文: Information Geometry of Wasserstein Statistics on …
Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric…
Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Using the square-root map p-->\sqrt{p} a probability density function p can be represented as a point of the unit sphere S in the Hilbert space of square-integrable functions. If the density function depends smoothly on a set of parameters,…
In this article, we present recent developments of information geometry, namely, geometry of the Fisher metric, dualistic structures and divergences on the space of probability measures, particularly the theory of geodesics of the Fisher…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
The data-aware method of distributions (DA-MD) is a low-dimension data assimilation procedure to forecast the behavior of dynamical systems described by differential equations. It combines sequential Bayesian update with the MD, such that…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
In Wasserstein geometry, one-dimensional location-scale models are flat both intrinsically and extrinsically-that is, they are curvature-free as well as totally geodesic in the space of probability distributions. In this study, we introduce…
We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…
Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in $\mathbb{R}^n$ with an emphasis on affine transformations that have been used in manifold learning of data in Wasserstein space. In…