Related papers: Sparse Estimation with Strongly Correlated Variabl…
The double sparse linear model, which has both group-wise and element-wise sparsity in regression coefficients, has attracted lots of attention recently. This paper establishes the sufficient and necessary relationship between the exact…
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important…
We present a simple and effective algorithm for the problem of \emph{sparse robust linear regression}. In this problem, one would like to estimate a sparse vector $w^* \in \mathbb{R}^n$ from linear measurements corrupted by sparse noise…
When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects…
In $\ell^1$-regularization, which is an important tool in signal and image processing, one usually is concerned with signals and images having a sparse representation in some suitable basis, e.g. in a wavelet basis. Many results on…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters.…
Given full or partial information about a collection of points that lie close to a union of several subspaces, subspace clustering refers to the process of clustering the points according to their subspace and identifying the subspaces. One…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…
The growing availability of large health databases has expanded the use of observational studies for comparative effectiveness research. Unlike randomized trials, observational studies must adjust for systematic differences in patient…
Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…
Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…
The effect of errors in variables in empirical minimization is investigated. Given a loss $l$ and a set of decision rules $\mathcal{G}$, we prove a general upper bound for an empirical minimization based on a deconvolution kernel and a…
We derive the second-order sampling properties of certain autocovariance and autocorrelation estimators for sequences of independent and identically distributed samples. Specifically, the estimators we consider are the classic lag windowed…
Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…
Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to…
Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…