相关论文: Bounded Rank-one Perturbations in Sampling Theory

In many classification settings, the class of primary interest is underrepresented, leading to imbalanced data problems that arise in applications such as rare disease detection and fraud identification. In these contexts, identifying a…

Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…

Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…

We propose a method of quantization based on Hamilton-Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization…

The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…

Learning from imbalanced data is a challenging task. Standard classification algorithms tend to perform poorly when trained on imbalanced data. Some special strategies need to be adopted, either by modifying the data distribution or by…

The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$…

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…

We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

The current theoretical understanding of processes involving many weakly interacting bosons in the Standard Model and in model theories is discussed. In particular, such processes are associated with the baryon and lepton number violation…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

We consider the exact sampling of the first passage of a stable subordinator across a non-increasing regular barrier. First, the sampling is reduced to one from a bivariate distribution parameterized by the index $\alpha$ of the…

Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…

This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…

Surprisal theory links human processing effort to the predictability of an upcoming linguistic unit, but empirical work often leaves the notion of a unit underspecified. In practice, experimental stimuli are segmented into linguistically…

The Boltzmann model for the random generation of "decomposable" combinatorial structures is a set of techniques that allows for efficient random sampling algorithms for a large class of families of discrete objects. The usual requirement of…

In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part,…

We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC.

We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of…