Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows

Julien Mairal 1, * Bin Yu 2
* Corresponding author
1 LEAR - Learning and recognition in vision
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or obtain results that are easier to interpret. Regularization or penalty functions for selecting features in graphs have recently been proposed, but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and well-connected subset of features sitting on a directed acyclic graph (DAG). We introduce structured sparsity penalties over paths on a DAG called ''path coding'' penalties. Unlike existing regularization functions that model long-range interactions between features in a graph, path coding penalties are tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs.
Document type :
Journal articles
Complete list of metadatas

Cited literature [60 references]  Display  Hide  Download

https://hal.inria.fr/hal-00806372
Contributor : Julien Mairal <>
Submitted on : Thursday, August 29, 2013 - 2:57:29 PM
Last modification on : Wednesday, August 7, 2019 - 12:19:23 PM
Long-term archiving on : Thursday, April 6, 2017 - 10:34:46 AM

Files

mairal13a.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00806372, version 2

Collections

Citation

Julien Mairal, Bin Yu. Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows. Journal of Machine Learning Research, Microtome Publishing, 2013, 14, pp.2449-2485. ⟨hal-00806372v2⟩

Share

Metrics

Record views

6354

Files downloads

1101