Related papers: Complexity Analysis of the Lasso Regularization Pa…
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…
We propose a new method for computing the lasso path, using the fact that the Manhattan norm of the coefficient vector is linear over every orthant of the parameter space. We use simple calculus and present an algorithm in which the lasso…
We consider the exact sampling of the first passage of a stable subordinator across a non-increasing regular barrier. First, the sampling is reduced to one from a bivariate distribution parameterized by the index $\alpha$ of the…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
The lasso and elastic net are popular regularized regression models for supervised learning. Friedman, Hastie, and Tibshirani (2010) introduced a computationally efficient algorithm for computing the elastic net regularization path for…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
In linear regression with fixed design, we propose two procedures that aggregate a data-driven collection of supports. The collection is a subset of the $2^p$ possible supports and both its cardinality and its elements can depend on the…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…
This paper deals with the non-uniqueness of the solutions of an analysis-Lasso regularization. Most of previous works in this area is concerned with the case where the solution set is a singleton, or to derive guarantees to enforce…
The paper revisits the robust $s$-$t$ path problem, one of the most fundamental problems in robust optimization. In the problem, we are given a directed graph with $n$ vertices and $k$ distinct cost functions (scenarios) defined over edges,…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
The paper considers the computation of L1 regularization paths in a state space setting, which includes L1 regularized Kalman smoothing, linear SVM, LASSO, and more. The paper proposes two new algorithms, which are duals of each other; the…
The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…
In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
If the edges of the complete graph $K_n$ are totally ordered, a simple path whose edges are in ascending order is called increasing. The worst-case length of the longest increasing path has remained an open problem for several decades, with…