相关论文: Optimality of Operator-Like Wavelets for Represent…
This work offers a new prospective on asymptotic perturbation theory for varying self-adjoint extensions of symmetric operators. Employing symplectic formulation of self-adjointness we obtain a new version of Krein formula for resolvent…
The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…
We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on…
A signature result in compressed sensing is that Gaussian random sampling achieves stable and robust recovery of sparse vectors under optimal conditions on the number of measurements. However, in the context of image reconstruction, it has…
We consider the sample efficient estimation of failure probabilities from expensive oracle evaluations of a limit state function via importance sampling (IS). In contrast to conventional ``two stage'' approaches, which first train a…
We adopt an operator-theoretic perspective to study convergence of linear fixed-point iterations and discrete- time linear systems. We mainly focus on the so-called Krasnoselskij-Mann iteration x(k+1) = ( 1 - \alpha(k) ) x(k) + \alpha(k) A…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a…
The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of…
We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr\"obner bases. If successful, a push forward Gaussian…
We consider the high-dimensional linear regression model $Y = X \beta^0 + \epsilon$ with Gaussian noise $\epsilon$ and Gaussian random design $X$. We assume that $\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\Theta :=…
Channel state information (CSI) acquisition and feedback overhead grows with the number of antennas, users, and reported subbands. This growth becomes a bottleneck for many antenna and reconfigurable intelligent surface (RIS) systems as…
Synchrosqueezed transforms are non-linear processes for a sharpened time-frequency representation of wave-like components. They are efficient tools for identifying and analyzing wave-like components from their superposition. This paper is…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…
We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…
We have presented a new and alternative algorithm for noise reduction using the methods of discrete wavelet transform and numerical differentiation of the data. In our method the threshold for reducing noise comes out automatically. The…
The Karhunen-Lo\`eve transform (KLT) stands as a well-established discrete transform, demonstrating optimal characteristics in data decorrelation and dimensionality reduction. Its ability to condense energy compression into a select few…
This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets…
Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes…
We develop machinery to design efficiently computable and consistent estimators, achieving estimation error approaching zero as the number of observations grows, when facing an oblivious adversary that may corrupt responses in all but an…