相关论文: Exhaustive search for sparse variable selection in…
In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…
While inference-time scaling has significantly enhanced generative quality in large language and diffusion models, its application to vector-quantized (VQ) visual autoregressive modeling (VAR) remains unexplored. We introduce VAR-Scaling,…
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
We present a technique using data depth functions and resampling to perform best subset variable selection for a wide range of statistical models. We do this by assigning a score, called an $e$-value, to a candidate model, and use a fast…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
We consider the problem of sparse variable selection on high dimension heterogeneous data sets, which has been taking on renewed interest recently due to the growth of biological and medical data sets with complex, non-i.i.d. structures and…
We discuss a strategy of sparse approximation that is based on the use of an overcomplete basis, and evaluate its performance when a random matrix is used as this basis. A small combination of basis vectors is chosen from a given…
We present the novel adaptive hierarchical sensing algorithm K-AHS, which samples sparse or compressible signals with a measurement complexity equal to that of Compressed Sensing (CS). In contrast to CS, K-AHS is adaptive as sensing vectors…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…
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 consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column…
Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
There exist endless examples of dynamical systems with vast available data and unsatisfying mathematical descriptions. Sparse regression applied to symbolic libraries has quickly emerged as a powerful tool for learning governing equations…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
The model interpretation is essential in many application scenarios and to build a classification model with a ease of model interpretation may provide useful information for further studies and improvement. It is common to encounter with a…
The randomized sparse Kaczmarz method, designed for seeking the sparse solutions of the linear systems $Ax=b$, selects the $i$-th projection hyperplane with likelihood proportional to $\|a_{i}\|_2^2$, where $a_{i}^T$ is $i$-th row of $A$.…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…