Related papers: Pattern recovery by SLOPE
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…
We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO, generalized LASSO, SLOPE, OSCAR, PACS and others. Each of these estimators is…
The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
This paper presents a novel method to make statistical inferences for both the model support and regression coefficients in a high-dimensional logistic regression model. Our method is based on the repro samples framework, in which we…
Sliced inverse regression is one of the most popular sufficient dimension reduction methods. Originally, it was designed for independent and identically distributed data and recently extend to the case of serially and spatially dependent…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Matching pursuit, especially its orthogonal version (OMP) and variations, is a greedy algorithm widely used in signal processing, compressed sensing, and sparse modeling. Inspired by constrained sparse signal recovery, this paper proposes a…
We study sparse principal component analysis in the high-dimensional, sample-limited regime, aiming to recover a leading component supported on a few coordinates. Despite extensive progress, most methods and analyses are tailored to the…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
We introduce a highly expressive class of function approximators called Splat Regression Models. Model outputs are mixtures of heterogeneous and anisotropic bump functions, termed splats, each weighted by an output vector. The power of…
Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an…
In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…
Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems,…
We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood,…
In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method…
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…
Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…
We present a new class of methods for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive…