72 citations · 536 across the 51 of their papers we have counts for
54 papers
Natural gradient descent with momentum
Anthony Nouy, Agustín Somacal
We consider the problem of approximating a function by an element of a nonlinear manifold which admits a differentiable parametrization, typical examples being neural networks with…
Surrogate to Poincaré inequalities on manifolds for structured dimension reduction in nonlinear feature spaces
Alexandre Pasco, Anthony Nouy
This paper is concerned with the approximation of continuously differentiable functions with high-dimensional input by a composition of two functions: a feature map that extracts f…
Approximation and learning with compositional tensor trains
Martin Eigel, Charles Miranda, Anthony Nouy +1
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train form…
Surrogate to Poincaré inequalities on manifolds for dimension reduction in nonlinear feature spaces
Anthony Nouy, Alexandre Pasco
We aim to approximate a continuously differentiable function by a composition of functions where $g:\mathbb{R}^d \rightarrow \mat…
Nonlinear manifold approximation using compositional polynomial networks
Antoine Bensalah, Anthony Nouy, Joel Soffo
We consider the problem of approximating a subset of a Hilbert space by a low-dimensional manifold , using samples from . We propose a nonlinear approximation metho…
Optimal sampling for least squares approximation with general dictionaries
Philipp Trunschke, Anthony Nouy
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obt…
Sample-based almost-sure quasi-optimal approximation in reproducing kernel Hilbert spaces
Nando Hegemann, Anthony Nouy, Philipp Trunschke
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size…
Optimal sampling for stochastic and natural gradient descent
Robert Gruhlke, Anthony Nouy, Philipp Trunschke
We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gr…
Weighted least-squares approximation with determinantal point processes and generalized volume sampling
Anthony Nouy, Bertrand Michel
We consider the problem of approximating a function from by an element of a given -dimensional space , associated with some feature map , using evaluati…
Weighted sparsity and sparse tensor networks for least squares approximation
Philipp Trunschke, Anthony Nouy, Martin Eigel
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, c…
A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws
Clément Cardoen, Swann Marx, Anthony Nouy +1
We propose a numerical method to solve parameter-dependent hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous work from Marx et al. (2020)…
A probabilistic reduced basis method for parameter-dependent problems
Marie Billaud-Friess, Arthur Macherey, Anthony Nouy +1
Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we…
Dictionary-based model reduction for state estimation
Anthony Nouy, Alexandre Pasco
We consider the problem of state estimation from a few linear measurements, where the state to recover is an element of the manifold of solutions of a parameter-depen…
Moment-SoS Methods for Optimal Transport Problems
Olga Mula, Anthony Nouy
Most common Optimal Transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is sometimes relevant to work only with…
Active learning of tree tensor networks using optimal least-squares
Cécile Haberstich, Anthony Nouy, Guillaume Perrin
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or arch…
Random sketching of operators with application to learning preconditioners
Oleg Balabanov, Anthony Nouy, Alexandre Pasco
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a lo…
Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions
Mazen Ali, Anthony Nouy
We study the approximation of multivariate functions with tensor networks (TNs), providing some answers to the following two questions: ``what are the approximation capabilities of…
Geometry of tree-based tensor formats in tensor Banach spaces
Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy
In the paper `On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces', we provided a geometrical description of manifolds of tensors in Tucker format with fixed multili…
Approximation of Smoothness Classes by Deep Rectifier Networks
Mazen Ali, Anthony Nouy
We consider approximation rates of sparsely connected deep rectified linear unit (ReLU) and rectified power unit (RePU) neural networks for functions in Besov spaces …
A PAC algorithm in relative precision for bandit problem with costly sampling
Marie Billaud-Friess, Arthur Macherey, Anthony Nouy +1
This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose a naive stochastic bandit algorithm for obt…
Learning with tree tensor networks: complexity estimates and model selection
Bertrand Michel, Anthony Nouy
Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspo…
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part II
Mazen Ali, Anthony Nouy
We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p(…
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
Mazen Ali, Anthony Nouy
We study the approximation of functions by tensor networks (TNs). We show that Lebesgue -spaces in one dimension can be identified with tensor product spaces of arbitrary orde…
A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falcó, Anthony Nouy
In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introdu…