Related papers: Variable selection in convex quantile regression: …

For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called…

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…

Variable selection is an old and pervasive problem in regression analysis. One solution is to impose a lasso penalty to shrink parameter estimates toward zero and perform continuous model selection. The lasso-penalized mixture of linear…

Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this…

Feature selection in learning to rank has recently emerged as a crucial issue. Whereas several preprocessing approaches have been proposed, only a few works have been focused on integrating the feature selection into the learning process.…

We consider the problem of learning the underlying graph of a sparse Ising model with $p$ nodes from $n$ i.i.d. samples. The most recent and best performing approaches combine an empirical loss (the logistic regression loss or the…

Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…

We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…

In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the…

Penalized likelihood methods are fundamental to ultra-high dimensional variable selection. How high dimensionality such methods can handle remains largely unknown. In this paper, we show that in the context of generalized linear models,…

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…

Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…

High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…

We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean…

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…