Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows
This work addresses the challenge of interpretable and efficient feature selection in graph-structured data, which is incremental as it builds on prior regularization methods by improving computational feasibility.
The paper tackles the problem of selecting connected subgraphs of features in supervised learning with graph-embedded features, such as gene networks, by introducing path coding penalties that are computationally tractable and solved via network flow optimization. The result is a scalable approach that produces more connected subgraphs than existing methods, as demonstrated on synthetic, image, and genomic data.
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.