Related papers: Exponential Screening and optimal rates of sparse …
We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
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…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
Forecasting revenues by aggregating analyst forecasts is a fundamental problem in financial research and practice. A key objective in this context is to improve the accuracy of the forecast by optimizing two performance metrics: the hit…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\ell_1$-regularized…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search…