Zobrazeno 1 - 10
of 204
pro vyhledávání: '"Panaretos, Victor"'
We consider the problem of characterizing extreme points of the convex set of positive linear operators on a possibly infinite-dimensional Hilbert space under linear constraints. We show that even perturbations of points in such sets admit what resem
Externí odkaz:
http://arxiv.org/abs/2410.14889
We introduce a novel statistical framework for the analysis of replicated point processes that allows for the study of point pattern variability at a population level. By treating point process realizations as random measures, we adopt a functional a
Externí odkaz:
http://arxiv.org/abs/2404.19661
Autor:
Yun, Ho, Panaretos, Victor M.
The X-ray transform is one of the most fundamental integral operators in image processing and reconstruction. In this article, we revisit the formalism of the X-ray transform by considering it as an operator between Reproducing Kernel Hilbert Spaces
Externí odkaz:
http://arxiv.org/abs/2311.07465
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure of covari
Externí odkaz:
http://arxiv.org/abs/2310.13764
We study the positive-definite completion problem for kernels on a variety of domains and prove results concerning the existence, uniqueness, and characterization of solutions. In particular, we study a special solution called the canonical completio
Externí odkaz:
http://arxiv.org/abs/2309.10143
We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no element i
Externí odkaz:
http://arxiv.org/abs/2306.02347
Autor:
Ghodrati, Laya, Panaretos, Victor M.
We present an optimal transport framework for performing regression when both the covariate and the response are probability distributions on a compact Euclidean subset $\Omega\subset\mathbb{R}^d$, where $d>1$. Extending beyond compactly supported di
Externí odkaz:
http://arxiv.org/abs/2305.17503
We establish a strong law of large numbers and a central limit theorem in the Bures-Wasserstein space of covariance operators -- or equivalently centred Gaussian measures -- over a general separable Hilbert space. Specifically, we show that empirical
Externí odkaz:
http://arxiv.org/abs/2305.15592
Autor:
Ghodrati, Laya, Panaretos, Victor M.
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov chain, where on
Externí odkaz:
http://arxiv.org/abs/2303.09469
We develop a generalisation of Mercer's theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to deduce a Karhunen-Lo\`eve theorem, valid for mean-square continuous Hilbertian functional data, i.e. flows
Externí odkaz:
http://arxiv.org/abs/2303.00702