Related papers: Optimal rates for density and mode estimation with…
Linear prediction (LP) is an ubiquitous analysis method in speech processing. Various studies have focused on sparse LP algorithms by introducing sparsity constraints into the LP framework. Sparse LP has been shown to be effective in…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions…
A deep generative model yields an implicit estimator for the unknown distribution or density function of the observation. This paper investigates some statistical properties of the implicit density estimator pursued by VAE-type methods from…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
We study a non-parametric approach to multivariate density estimation. The estimators are piecewise constant density functions supported by binary partitions. The partition of the sample space is learned by maximizing the likelihood of the…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…
The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a…
In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…
Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
A new approximation format for solutions of partial differential equations depending on infinitely many parameters is introduced. By combining low-rank tensor approximation in a selected subset of variables with a sparse polynomial…
Learned sparse and dense representations capture different successful approaches to text retrieval and the fusion of their results has proven to be more effective and robust. Prior work combines dense and sparse retrievers by fusing their…
Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…