Publications associées à Statistique exhaustive

A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

Daniel Kuhn, Viet Anh Nguyen, Yves Rychener

The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either chosen heuristically ...

2024

Detecting 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 SCIENCE2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

Learning Linearized Degradation of Health Indicators using Deep Koopman Operator Approach

Olga Fink, Sergei Garmaev

With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a crucial criterion fo ...

Research Publishing2023

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan

In this paper, we set the mathematical foundations of the Dynamical Low Rank Approximation (DLRA) method for high-dimensional stochastic differential equations. DLRA aims at approximating the solution as a linear combination of a small number of basis vect ...

2023

Testing For The Rank Of A Covariance Operator

Victor Panaretos

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-IMS2022

Data-Driven Unknown-Input Observers and State Estimation

Giancarlo Ferrari Trecate, Mustafa Sahin Turan

Unknown-input observers (UIOs) allow for estimation of the states of an LTI system without knowledge of all inputs. In this letter, we provide a novel data-driven UIO based on behavioral system theory and the result known as Fundamental Lemma proposed by J ...

2022

The 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-IMS2022

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Statistique exhaustive

A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

Detecting whether a stochastic process is finitely expressed in a basis

Positive Definite Completions and Continuous Graphical Models

Stable parameterization of continuous and piecewise-linear functions

Learning Linearized Degradation of Health Indicators using Deep Koopman Operator Approach

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Testing For The Rank Of A Covariance Operator

Data-Driven Unknown-Input Observers and State Estimation

The Completion Of Covariance Kernels

Data-driven and Safe Networked Control with Applications to Microgrids

Graph Chatbot

Chattez avec Graph Search

A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

Detecting whether a stochastic process is finitely expressed in a basis

Positive Definite Completions and Continuous Graphical Models

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Stable parameterization of continuous and piecewise-linear functions

Testing For The Rank Of A Covariance Operator

The Completion Of Covariance Kernels

Data-driven and Safe Networked Control with Applications to Microgrids

Learning Linearized Degradation of Health Indicators using Deep Koopman Operator Approach

Data-Driven Unknown-Input Observers and State Estimation