Related papers: The Poisson tensor completion parametric estimator

Let $M$ be an $n$-dimensional Hadamard manifold of pinched negative curvature $-b^2 \leq K_M \leq -a^2$. The solution of the Dirichlet problem at infinity for $M$ leads to the construction of a family of mutually absolutely continuous…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

Compressive sensing (CS) has triggered enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact…

While Bernoulli sampling is extensively studied in tensor completion, t-CUR sampling approximates low-tubal-rank tensors via lateral and horizontal subtensors. However, both methods lack sufficient flexibility for diverse practical…

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

The Poisson probability distribution is frequently encountered in physical science measurements. In spite of the simplicity and familiarity of this distribution, there is considerable confusion among physicists concerning the description of…

In this paper, we study the problem of computing a Principal Component Analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principle components of a fixed…

We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the…

Estimating a binary vector from noisy linear measurements is a prototypical problem for MIMO systems. A popular algorithm, called the box-relaxation decoder, estimates the target signal by solving a least squares problem with convex…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…

Stochastic finite automata arise naturally in many language and speech processing tasks. They include stochastic acceptors, which represent certain probability distributions over random strings. We consider the problem of efficient…

In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…

A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…

Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity transmitted through a slab of random material. Our approach is based on the modeling of forward…

We present sparse topical coding (STC), a non-probabilistic formulation of topic models for discovering latent representations of large collections of data. Unlike probabilistic topic models, STC relaxes the normalization constraint of…

This note aims at presenting several new theoretical results for the compound Poisson point process, which follows the work of Zhang \emph{et al.} [Insurance~Math.~Econom.~59(2014), 325-336]. The first part provides a new characterization…