Related papers: Lower bounds for invariant statistical models with…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We propose a method for obtaining rigorous and accurate upper and lower bounds on the eigenvalues of ordinary and partial differential operators in bounded regions of Euclidean space. It uses a boundary condition homotopy method starting…
The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present…
We study decaying half-line Schr\"odinger operators and the local eigenvalue spacing of their Dirichlet restrictions. While absolutely continuous spectrum is strongly associated with bulk universality and clock behavior, singular spectral…
We consider the Stokes eigenvalue problem in a bounded domain of R3 with Dirich- let boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the boundary perturbations of…
The theorem on the existence of maximal nonnegative invariant subspaces for a special class of dissipative operators in Hilbert space with indefinite inner product is proved in the paper. It is shown in addition that the spectra of the…
This is mostly a survey paper, where we collect results concerning the spectral bounds of deterministic and random Schr\"odinger operators with complex potentials, both on \(\mathbb{R}^d\) and on compact manifolds. The survey part is…
The estimation of regression parameters in spatially referenced data plays a crucial role across various scientific domains. A common approach involves employing an additive regression model to capture the relationship between observations…
Let $Y$ be a $d$-dimensional random vector with unknown mean $\mu$ and covariance matrix $\Sigma$. This paper is motivated by the problem of designing an estimator of $\Sigma$ that admits tight deviation bounds in the operator norm under…
We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The…
We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains the best possible estimate on the rate of decay, that is to…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and P\'ech\'e. We…
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…
A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from…
We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…