Related papers: Nonparametric Information Geometry
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite-dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also…
The purpose of this article is to study the existence of a coincidence point for two mappings defined on a nonempty set and taking values on a Banach space using the fixed point theory for nonexpansive mappings. Moreover, this type of…
We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…
Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of…
These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach…
For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms…
Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…
Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of a…
We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…
In this article, we apply the approach of relative algebraic geometry towards analytic geometry to the category of bornological and Ind-Banach spaces (non-Archimedean or not). We are able to recast the theory of Grosse-Kl\"onne dagger…
High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures…
We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the…
In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James' space. Further, we show that the averaging…
A quantum system can be entirely described by the K\"ahler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we…
The main result of this article is a rigidity result pertaining to the spreading model structure for Banach spaces coarsely embeddable into Tsirelson's original space $T^*$. Every Banach space that is coarsely embeddable into $T^*$ must be…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
The Fisher information metric or the Fisher-Rao metric corresponds to a natural Riemannian metric defined on a parameterized family of probability density functions. As in the case of Riemannian geometry, we can define a distance in terms…
Conjectures have historically played an important role in the development of pure mathematics. We propose a systematic approach to finding abstract patterns in mathematical data, in order to generate conjectures about mathematical…
We introduce a new transformation called \emph{relative differential-escort}, which extends the usual differential-escort transformation by relating the change of variable to a reference probability density. As an application of it, we…
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…