Related papers: Sampling formulas involving differences in shift-i…
We consider weak-star closed invariant subspaces of the shift operator in the classical Bloch space. We prove that any bounded analytic function decomposes into two factors, one which is cyclic and another one generating a proper shift…
Unsupervised approaches for learning representations invariant to common transformations are used quite often for object recognition. Learning invariances makes models more robust and practical to use in real-world scenarios. Since data…
The purpose of this paper is to develop some methods to study Riesz type inequalities, Hardy-Littlewood type theorems and smooth moduli of holomorphic, pluriharmonic and harmonic functions in high-dimensional cases. Initially, we prove some…
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…
We introduce a new, simple metric method of sampling metric measure spaces, based on a well-known "snowflakeing operator" and we show that, as a consequence of a classical result of Assouad, the sampling of doubling metric spaces is…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
Estimating spatially distributed information through the interpolation of scattered observation datasets often overlooks the critical role of domain knowledge in understanding spatial dependencies. Additionally, the features of these data…
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…
Rapid progress in representation learning has led to a proliferation of embedding models, and to associated challenges of model selection and practical application. It is non-trivial to assess a model's generalizability to new, candidate…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and…
Image-to-Image (I2I) multi-domain translation models are usually evaluated also using the quality of their semantic interpolation results. However, state-of-the-art models frequently show abrupt changes in the image appearance during…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…
Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…
This study examines a modified Kantorovich approach applied to generalized sampling series. The paper establishes that the approximation order to a function using these modified operators is atleast as good as that achieved by classical…
In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…
Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…