Related papers: Improved $\ell_{p}$ Regression via Iteratively Rew…
We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an…
In this paper we study the performance of the Projected Gradient Descent(PGD) algorithm for $\ell_{p}$-constrained least squares problems that arise in the framework of Compressed Sensing. Relying on the Restricted Isometry Property, we…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
In this paper, we propose a support driven reweighted $\ell_1$ minimization algorithm (SDRL1) that solves a sequence of weighted $\ell_1$ problems and relies on the support estimate accuracy. Our SDRL1 algorithm is related to the IRL1…
It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…
In this paper, we consider the problem of $\ell_{p}$ norm linear regression, which has several applications such as in sparse recovery, data clustering, and semi-supervised learning. The problem, even though convex, does not enjoy a…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…
The recursive least-squares (RLS) algorithm is one of the most well-known algorithms used in adaptive filtering, system identification and adaptive control. Its popularity is mainly due to its fast convergence speed, which is considered to…
Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very…
Addressing large-scale indefinite least squares (ILS) problem poses notable computational bottlenecks in the field of numerical linear algebra. State-of-the-art iterative schemes for such problems are predominantly constructed upon the…
We present a parallel algorithm for the undirected $s,t$-mincut problem with floating-point valued weights. Our overarching algorithm uses an iteratively reweighted least squares framework. This generates a sequence of Laplacian linear…
Dimensionality reduction plays an important role in computer vision problems since it reduces computational cost and is often capable of yielding more discriminative data representation. In this context, Partial Least Squares (PLS) has…
Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted $\ell_1$ algorithms for solving $\ell_p$ regularization problems, which are widely applied for inducing sparse solutions. We show that if…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
We study the $\ell_p$ regression problem, which requires finding $\mathbf{x}\in\mathbb R^{d}$ that minimizes $\|\mathbf{A}\mathbf{x}-\mathbf{b}\|_p$ for a matrix $\mathbf{A}\in\mathbb R^{n \times d}$ and response vector…
We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…
In this paper, the recursive least squares (RLS) algorithm is considered in the sparse system identification setting. The cost function of RLS algorithm is regularized by a $p$-norm-like ($0 \leq p \leq 1$) constraint of the estimated…
For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori…