866 citations · 1.2k across the 41 of their papers we have counts for
48 papers
Inference for Functional Data under Markov Constraints
Ulysse Naepels, Victor M. Panaretos
Smoothness has long been the dominant form of parsimony in functional data analysis, to the point of occasionally being conflated with the very notion of functional data. However,…
Likelihood Ratio Tests by Kernel Gaussian Embedding
Leonardo V. Santoro, Victor M. Panaretos
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing…
Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity
Ho Yun, Alessia Caponera, Victor M. Panaretos
We consider the problem of nonparametric estimation of the conformational variability in a population of related structures, based on low-dose tomography of a random sample of repr…
Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space
Paul Freulon, Nikitas Georgakis, Victor Panaretos
The Optimal Transport (OT) problem with squared Euclidean cost consists in finding a coupling between two input measures that maximizes correlation. Consequently, the optimal coupl…
Kernel Embeddings and the Separation of Measure Phenomenon
Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish…
Fast and Cheap Krylov-Based Covariance Smoothing
Ho Yun, Victor M. Panaretos
We introduce the Tensorized-and-Restricted Krylov (TReK) method, a simple and efficient algorithm for estimating covariance tensors with large observational sizes. TReK extends the…
Extreme Points of Spectrahedra
Kartik G. Waghmare, Victor M. Panaretos
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. W…
PCA for Point Processes
Franck Picard, Vincent Rivoirard, Angelina Roche +1
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…
Computerized Tomography and Reproducing Kernels
Ho Yun, Victor M. Panaretos
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 co…
Statistical Inference for Bures-Wasserstein Flows
Leonardo V. Santoro, Victor M. Panaretos
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hi…
The Positive-Definite Completion Problem
Kartik G. Waghmare, Victor M. Panaretos
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…
The Functional Graphical Lasso
Kartik G. Waghmare, Tomas Masak, Victor M. Panaretos
We consider the problem of recovering conditional independence relationships between jointly distributed Hilbertian random elements given realizations thereof. We operate i…
Transportation of Measure Regression in Higher Dimensions
Laya Ghodrati, Victor M. Panaretos
We present an optimal transport framework for performing regression when both the covariate and the response are probability distributions on a compact Euclidean subset $Ω\subset\m…
Large Sample Theory for Bures-Wasserstein Barycentres
Leonardo V. Santoro, Victor M. Panaretos
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…
A Karhunen-Loève Theorem for Random Flows in Hilbert spaces
Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos
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-Loève theorem, vali…
Continuously Indexed Graphical Models
Kartik G. Waghmare, Victor M. Panaretos
Let be a real-valued Gaussian process indexed by a set . It can be thought of as an undirected graphical model with every random variable servi…
Transportation-Based Functional ANOVA and PCA for Covariance Operators
Valentina Masarotto, Victor M. Panaretos, Yoav Zemel
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second…
Minimax Rate for Optimal Transport Regression Between Distributions
Laya Ghodrati, Victor M. Panaretos
Distribution-on-distribution regression considers the problem of formulating and estimating a regression relationship where both covariate and response are probability distribution…
On the rate of convergence for the autocorrelation operator in functional autoregression
Alessia Caponera, Victor M. Panaretos
We consider the problem of estimating the autocorrelation operator of an autoregressive Hilbertian process. By means of a Tikhonov approach, we establish a general result that yiel…
Functional Estimation of Anisotropic Covariance and Autocovariance Operators on the Sphere
Alessia Caponera, Julien Fageot, Matthieu Simeoni +1
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a m…
Detecting Whether a Stochastic Process is Finitely Expressed in a Basis
Neda Mohammadi, Victor M. Panaretos
Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the b…
Nonparametric Estimation for SDE with Sparsely Sampled Paths: an FDA Perspective
Neda Mohammadi, Leonardo Santoro, Victor M. Panaretos
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on independent replicates $\left\…
The Completion of Covariance Kernels
Kartik G. Waghmare, Victor M. Panaretos
We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain of a rectangular domain to a covar…
Functional Data Analysis with Rough Sample Paths?
Neda Mohammadi, Victor M. Panaretos
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally…