Publication
Positive Definite Completions and Continuous Graphical Models
Related publications (38)
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Mathieu Salzmann, Alexandre Massoud Alahi, Megh Hiren Shukla
Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the challenges associated ...
2024Random matrix methods for high-dimensional machine learning models
In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...
EPFL2024Detecting whether a stochastic process is finitely expressed in a basis
Victor Panaretos, Neda Mohammadi Jouzdani
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 basis of a finite collection of discretely/noisily observed sample paths. We ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2023The two-point correlation function covariance with fewer mocks
We present FITCOV an approach for accurate estimation of the covariance of two-point correlation functions that requires fewer mocks than the standard mock-based covariance. This can be achieved by dividing a set of mocks into jackknife regions and fitting ...
Oxford2023Testing For The Rank Of A Covariance Operator
How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...
INST MATHEMATICAL STATISTICS-IMS2022The Completion Of Covariance Kernels
Victor Panaretos, Kartik Waghmare
We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...
INST MATHEMATICAL STATISTICS-IMS2022CovNet: Covariance networks for functional data on multidimensional domains
Victor Panaretos, Soham Sarkar
Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...
WILEY2022Euclid : Effects of sample covariance on the number counts of galaxy clusters
Georges Meylan, Yi Wang, Richard Massey
Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. Methods. By analysing 1000 Euclid-like light cones, ...
EDP SCIENCES S A2021Sparsely Observed Functional Time Series: Theory and Applications
Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...
EPFL2021Certified And Fast Computations With Shallow Covariance Kernels
Daniel Kressner, Stefano Massei
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...
AMER INST MATHEMATICAL SCIENCES-AIMS2020