Related papers: Mind the duality gap: safer rules for the Lasso
Robust Support Vector Machines (R-SVMs) address feature noise by adopting a worst-case robust formulation that explicitly incorporates uncertainty sets into training. While this robustness improves reliability, it also leads to increased…
Recently, to solve large-scale lasso and group lasso problems, screening rules have been developed, the goal of which is to reduce the problem size by efficiently discarding zero coefficients using simple rules independently of the others.…
The lasso model has been widely used for model selection in data mining, machine learning, and high-dimensional statistical analysis. However, with the ultrahigh-dimensional, large-scale data sets now collected in many real-world…
We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in…
Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some…
In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
Consider a robot operating in an uncertain environment with stochastic, dynamic obstacles. Despite the clear benefits for trajectory optimization, it is often hard to keep track of each obstacle at every time step due to sensing and…
Extracting relevant features from data sets where the number of observations ($n$) is much smaller then the number of predictors ($p$) is a major challenge in modern statistics. Sorted L-One Penalized Estimation (SLOPE), a generalization of…
One way to solve lasso problems when the dictionary does not fit into available memory is to first screen the dictionary to remove unneeded features. Prior research has shown that sequential screening methods offer the greatest promise in…
We propose a new approach to safe variable preselection in high-dimensional penalized regression, such as the lasso. Preselection - to start with a manageable set of covariates - has often been implemented without clear appreciation of its…
Convex estimators such as the Lasso, the matrix Lasso and the group Lasso have been studied extensively in the last two decades, demonstrating great success in both theory and practice. Two quantities are introduced, the noise barrier and…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
This paper introduces a framework that utilizes the Safe Screening technique to accelerate the optimization process of the Unbalanced Optimal Transport (UOT) problem by proactively identifying and eliminating zero elements in the sparse…
We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees. We derive loss functions that produce dual objectives with a sparse solution. We also show how to…
Matrix form data sets arise in many areas, so there are lots of works about the matrix regression models. One special model of these models is the adaptive nuclear norm regularized trace regression, which has been proven have good…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
Typical dimension reduction techniques for nonoverlapping sparse optimization involve screening or sieving strategies based on a dual certificate derived from the first-order optimality condition, approximating the gradients or exploiting…
In this paper we propose a methodology to accelerate the resolution of the so-called "Sorted L-One Penalized Estimation" (SLOPE) problem. Our method leverages the concept of "safe screening", well-studied in the literature for…
We consider the problem of learning a sparse rule model, a prediction model in the form of a sparse linear combination of rules, where a rule is an indicator function defined over a hyper-rectangle in the input space. Since the number of…