Related papers: Lasso-type recovery of sparse representations for …

Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be…

We address the problem of recovering a sparse $n$-vector within a given subspace. This problem is a subtask of some approaches to dictionary learning and sparse principal component analysis. Hence, if we can prove scaling laws for recovery…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the…

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. This study proposes a regression adjustment method based on the least absolute shrinkage…

In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the…

Estimating graphical model structure from high-dimensional and undersampled data is a fundamental problem in many scientific fields. Existing approaches, such as GLASSO, latent variable GLASSO, and latent tree models, suffer from high…

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of…

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…

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 propose a new estimator, the thresholded scaled Lasso, in high dimensional threshold regressions. First, we establish an upper bound on the $\ell_\infty$ estimation error of the scaled Lasso estimator of Lee et al. (2012). This is a…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

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…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

We apply classical and Bayesian lasso regularizations to a family of models with the presence of mixture and process variables. We analyse the performance of these estimates with respect to ordinary least squares estimators by a simulation…

Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…