Group Sparse Additive Models

By Junming Yin, X. Chen, Eric P. Xing. 2012

43 citations recorded by the source corpus.

We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either study the group sparsity in the parametric setting (e.g., group lasso), or address the problem in the nonparametric setting without exploiting the structural information (e.g., sparse additive models). In this paper, we present a new method, called group sparse additive models (GroupSpAM), which can handle group sparsity in additive models. We generalize the ℓ1/ℓ2 norm to Hilbert spaces as the sparsity-inducing penalty in GroupSpAM. Moreover, we derive a novel thresholding condition for identifying the functional sparsity at the group level, and propose an efficient block coordinate descent algorithm for constructing the estimate. We demonstrate by simulation that GroupSpAM substantially outperforms the competing methods in terms of support recovery and prediction accuracy in additive models, and also conduct a comparative experiment on a real breast cancer dataset.

Subfields: Computational Mechanics, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Junming Yin
2. Ali Shojaie
3. Noah R. Simon
4. Yaoliang Yu
5. Asad Haris

In Statistics and Probability

1. Ali Shojaie
2. Yaoliang Yu
3. Junming Yin
4. Asad Haris
5. Noah R. Simon
6. Matthew F. Dixon

Citations in the corpus

• Generalized Sparse Additive Models (2019, background): “There are also a number of other proposals that do not quite fall in the GSAM framework [Chouldechova and Hastie, 2015, Fan et al., 2012, Yin et al., 2012].”
• Convex-constrained Sparse Additive Modeling and Its Extensions (2017, background): “In the case of additive modeling, it amounts to identifying those few nonzero functional components in (1) based on a set of data samples (Ravikumar et al., 2008; Yin et al., 2012).”