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

This manuscript presents a convergence analysis, generalized from a study of boosting [1], of unregularized linear prediction. Here the empirical risk — incorporating strictly convex penalties composed with a linear term — may fail to be strongly convex, or even attain a minimizer. This analysis

Abstract not found

or Basis Pursuit Denoising has been shown to perform reasonably well in some situations. However, it was also proved that non-convex penalties like the pseudo ℓq-norm with q < 1 or SCAD penalty are able to recover sparsity in a more efficient way than the Lasso. Several algorithms have been proposed

Abstract not found

We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, twoclass logistic regression, and multinomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the

as penalized regression with grouping pursuit. In addition to the novel use of a non-convex group penalty and its associated unique operating characteristics in the proposed clustering method, a main advantage of this formulation is its allowing borrowing some well established results in classification

Survival analysis is a commonly-used method for the analysis of time to event data. This kind of data arises in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. A common feature of these data sets is they contain either censored of truncated observations. Censored data arises when an individual’s life length is

are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems

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 ℓ1-norm penalty term. The problem as formulated is convex