Related papers: A simple LAD-LASSO coordinate descent algorithm fo…

The least absolute shrinkage and selection operator (Lasso) is widely recognized across various fields of mathematics and engineering. Its variant, the generalized Lasso, finds extensive application in the fields of statistics, machine…

Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete…

Coordinate descent (CD) algorithms have become the method of choice for solving a number of optimization problems in machine learning. They are particularly popular for training linear models, including linear support vector machine…

It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…

The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by…

Distributed training algorithms of deep neural networks show impressive convergence speedup properties on very large problems. However, they inherently suffer from communication related slowdowns and communication topology becomes a crucial…

We develop an exact coordinate descent algorithm for high-dimensional regularized Huber regression. In contrast to composite gradient descent methods, our algorithm fully exploits the advantages of coordinate descent when the underlying…

Large-scale non-convex optimization problems are expensive to solve due to computational and memory costs. To reduce the costs, first-order (computationally efficient) and asynchronous-parallel (memory efficient) algorithms are necessary to…

L1 -penalized regression methods such as the Lasso (Tibshirani 1996) that achieve both variable selection and shrinkage have been very popular. An extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which allows for the…

In this work, to facilitate the real-time processing of multi-scan registration error minimization on factor graphs, we devise a point cloud downsampling algorithm based on coreset extraction. This algorithm extracts a subset of the…

We revisit the problem of finding the shortest path between two selected vertices of a graph and formulate this as an $\ell_1$-regularized regression -- Least Absolute Shrinkage and Selection Operator (lasso). We draw connections between a…

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…

A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…

This study proposes sparse estimation methods for the generalized linear models, which run one of least angle regression (LARS) and least absolute shrinkage and selection operator (LASSO) in the tangent space of the manifold of the…

We propose a scalable framework for solving the Maximum Cut (MaxCut) problem in large graphs using projected gradient ascent on quadratic objectives. Our approach is differentiable and leverages GPUs for gradient-based optimization. It is…

The $L_0$-regularized least squares problem (a.k.a. best subsets) is central to sparse statistical learning and has attracted significant attention across the wider statistics, machine learning, and optimization communities. Recent work has…

Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…

Achieving a balance between accuracy and efficiency is a critical challenge in facial landmark detection (FLD). This paper introduces Parallel Optimal Position Search (POPoS), a high-precision encoding-decoding framework designed to address…

The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…

Longitudinal analysis is important in many disciplines, such as the study of behavioral transitions in social science. Only very recently, feature selection has drawn adequate attention in the context of longitudinal modeling. Standard…