representation. In particular, we allow an user-friendly specification of sparsity on the groups of features using the L1/L2 measure. Also, we propose a pairwise coordinate descent algorithm to minimize the objective. Experimental evidence of the efficacy of this approach is provided on the ORL faces dataset.

Abstract In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in

Abstract In many applications, data appear with a huge number of instances as well as features. Linear Support Vector Machines (SVM) is one of the most popular tools to deal with such large-scale sparse data. This paper presents a novel dual coordinate descent method for linear SVM with L1-and L2

Abstract. A perceptron is a linear threshold classifier that separates examples with a hyperplane. It is perhaps the simplest learning model that is used standalone. In this paper, we propose a family of random coordinate descent algorithms for perceptron learning on binary classification problems

algorithms for estimating regression coefficients with a lasso penalty. The previously known ℓ2 algorithm is based on cyclic coordinate descent. Our new ℓ1 algorithm is based on greedy coordinate descent and Edgeworth’s algorithm for ordinary ℓ1 regression. Each algorithm relies on a tuning constant that can

We address the problem of sparse selection in linear models. A number of non-convex penalties have been proposed for this purpose, along with a variety of convex-relaxation algorithms for finding good solutions. In this paper we pursue the coordinate-descent approach for optimization, and study its

Abstract not found

objectives are typically solved by performing local block coordinate descent steps. In this work, we show how to perform block coordinate descent on spanning trees of the graphical model. We also show how all of the earlier dual algorithms are related to each other, giving transformations from one type

Abstract. Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in signal processing, statistics, and machine learning. Reasons for this renewed interest include the simplicity, speed, and stability of the method, as well as its competitive per

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L0 norm, however its optimization is NP-hard. Mixed norms, such as L1/L2 measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L1 norm. However, present algorithms designed for optimizing the mixed norm L1/L2 are slow and other formulations for sparse NMF have been proposed such as those based on L1 and L0 norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the- art solvers optimizing the mixed norm and is suitable for large-scale datasets.