相关论文: Sparse domination of sharp variational truncations

In this paper we establish sharp weighted bounds (Buckley type theorems) for one{sided maximal and fractional integral operators in terms of one{sided $A_p$ characteristics. Appropriate sharp bounds for strong maximal functions, multiple…

In a variety of application areas, there is a growing interest in analyzing high dimensional sparse count data, with sparsity exhibited by an over-abundance of zeros and small non-zero counts. Existing approaches for analyzing multivariate…

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

Structural damage due to excessive loading or environmental degradation typically occurs in localized areas in the absence of collapse. This prior information about the spatial sparseness of structural damage is exploited here by a…

In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators. We deduce the strong unique continuation property in the presence of subcritical and…

We consider local weak solutions of the Poisson equation for the p--Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…

In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…

Dense embeddings deliver strong retrieval performance but often lack interpretability and controllability. This paper introduces a novel approach using sparse autoencoders (SAE) to interpret and control dense embeddings via the learned…

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…

We prove sharp L^2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on…

Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity)…

Sparse optimization receives increasing attention in many applications such as compressed sensing, variable selection in regression problems, and recently neural network compression in machine learning. For example, the problem of…

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by…

When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative…

The observations in many applications consist of counts of discrete events, such as photons hitting a dector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model.…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…