11 papers
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…
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,…
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…
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…
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…
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…