Improving Group Lasso for High-Dimensional Categorical Data

Nowakowski, Szymon; Pokarowski, Piotr; Rejchel, Wojciech; Sołtys, Agnieszka

doi:10.1007/978-3-031-36021-3_47

Cited by 3 publications

(1 citation statement)

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“…where λ ≥ 0 is a tuning parameter which controls the amount of penalization, ω l = |G l | is used to normalize across groups of different sizes and ∥ • ∥ 2 denotes the L 2 norm of a vector. Meier et al [13] established the asymptotic consistency theory of Group Lasso for logistic regression, Wang et al [14] analyzed the rates of convergence, Blazere et al [15] stated oracle inequalities and Kwemou [16] and Nowakowski [17] studied non-asymptotic oracle inequalities. Furthermore, Zhang et al [18] studied the L p,q regularization penalty estimates for logistic regression.…”

Section: Introductionmentioning

confidence: 99%

Variable Selection for Sparse Logistic Regression with Grouped Variables

Zhong,

Yin,

Wang

2023

Preprint

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We present a new penalized method for estimation in sparse logistic regression models with group structure. Group sparsity suggests us to consider the Group Lasso penalty. Being different from penalized log-likelihood estimation, our method can be viewed as a penalized weighted score function method. Under some mild conditions, we provide non-asymptotic oracle inequalities promoting group sparsity of predictors. A modified block coordinate descent algorithm based on a weighted score function is also employed. The net advantage of our algorithm over the existing Group Lasso-type procedures is that the tuning parameter can be pre-specified. The simulations show that this algorithm is considerably faster and more stable than competing methods. Finally, we illustrate our methodology with two real data sets.

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