DMCA
Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows (2011)
Cached
Download Links
| Citations: | 9 - 3 self |
BibTeX
@MISC{Mairal11supervisedfeature,
author = {Julien Mairal and Bin Yu},
title = {Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows },
year = {2011}
}
Share
 |
 |
 |
 |
||
OpenURL
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 take into account the problem structure, and automatically select a subgraph with a small number of connected components. By exploiting prior knowledge, one can indeed improve the prediction performance and/or obtain better interpretable results. 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, path coding penalties can both model long range interactions between features in the graph and be 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 lead to more connected subgraphs than other regularization functions for graphs.
Keyphrases
network flow supervised feature selection path coding penalty regularization function problem structure penalty function supervised learning problem proximal operator new algorithmic challenge connected subset connected component interpretable result much interest gene expression path selection problem prior knowledge feasible strategy long range interaction small number acyclic graph hard selection problem network flow optimization structured sparsity penalty prediction performance connected subgraphs genomic data gene network
