Related papers: Sparse Regularization by Smooth Non-separable Non-…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…
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…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
We study the minimization problem of a non-convex sparsity promoting penalty function, the transformed $l_1$ (TL1), and its application in compressed sensing (CS). The TL1 penalty interpolates $l_0$ and $l_1$ norms through a nonnegative…
We present an efficient mathematical framework based on the linearly-involved Moreau-enhanced-over-subspace (LiMES) model. Two concrete applications are considered: sparse modeling and robust regression. The popular minimax concave (MC)…
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 propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…
This paper investigates quantile regression in the presence of non-convex and non-smooth sparse penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). The non-smooth and non-convex nature of…
We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition…
We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…
This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…
Partial least squares, as a dimension reduction method, has become increasingly important for its ability to deal with problems with a large number of variables. Since noisy variables may weaken the performance of the model, the sparse…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…
We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…