Related papers: Sparse Tensor Additive Regression
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for…
Recent economic events, including the global financial crisis and COVID-19 pandemic, have exposed limitations in linear Factor Augmented Vector Autoregressive (FAVAR) models for forecasting and structural analysis. Nonlinear dimension…
We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either…
Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance and neuroscience. While the problem of sparse modeling based on…
Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…
Support estimation (SE) of a sparse signal refers to finding the location indices of the non-zero elements in a sparse representation. Most of the traditional approaches dealing with SE problem are iterative algorithms based on greedy…
The objectives of this "perspective" paper are to review some recent advances in sparse feature selection for regression and classification, as well as compressed sensing, and to discuss how these might be used to develop tools to advance…
We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
It has recently been shown that ISTA, an unaccelerated optimization method, presents sparse updates for the $\ell_1$-regularized personalized PageRank problem, leading to cheap iteration complexity and providing the same guarantees as the…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
There is currently a large gap in performance between the statistically rigorous methods like linear regression or additive splines and the powerful deep methods using neural networks. Previous works attempting to close this gap have failed…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process,…
Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…
While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…
Nonlinear sparse sensing (NSS) techniques have been adopted for realizing compressive sensing (CS) in many applications such as Radar imaging and sparse channel estimation. Unlike the NSS, in this paper, we propose an adaptive sparse…