Related papers: Optimization for L1-Norm Error Fitting via Data Ag…
We address the issue of recovering the structure of large sparse directed acyclic graphs from noisy observations of the system. We propose a novel procedure based on a specific formulation of the l1-norm regularized maximum likelihood,…
Fitting parametric models of human bodies, hands or faces to sparse input signals in an accurate, robust, and fast manner has the promise of significantly improving immersion in AR and VR scenarios. A common first step in systems that…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
We propose a fast proximal Newton-type algorithm for minimizing regularized finite sums that returns an $\epsilon$-suboptimal point in $\tilde{\mathcal{O}}(d(n + \sqrt{\kappa d})\log(\frac{1}{\epsilon}))$ FLOPS, where $n$ is number of…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision,…
We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…
We propose Shotgun, a parallel coordinate descent algorithm for minimizing L1-regularized losses. Though coordinate descent seems inherently sequential, we prove convergence bounds for Shotgun which predict linear speedups, up to a…
Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that…
In many statistical learning problems, it is desired that the optimal solution conforms to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires…