  The goal in network state prediction (NSP) is to classify the global state
(label) associated with features embedded in a graph. This graph structure
encoding feature relationships is the key distinctive aspect of NSP compared to
classical supervised learning. NSP arises in various applications: gene
expression samples embedded in a protein-protein interaction (PPI) network,
temporal snapshots of infrastructure or sensor networks, and fMRI coherence
network samples from multiple subjects to name a few. Instances from these
domains are typically ``wide'' (more features than samples), and thus, feature
sub-selection is required for robust and generalizable prediction. How to best
employ the network structure in order to learn succinct connected subgraphs
encompassing the most discriminative features becomes a central challenge in
NSP. Prior work employs connected subgraph sampling or graph smoothing within
optimization frameworks, resulting in either large variance of quality or weak
control over the connectivity of selected subgraphs.
  In this work we propose an optimization framework for discriminative subgraph
learning (DSL) which simultaneously enforces (i) sparsity, (ii) connectivity
and (iii) high discriminative power of the resulting subgraphs of features. Our
optimization algorithm is a single-step solution for the NSP and the associated
feature selection problem. It is rooted in the rich literature on
maximal-margin optimization, spectral graph methods and sparse subspace
self-representation. DSL simultaneously ensures solution interpretability and
superior predictive power (up to 16% improvement in challenging instances
compared to baselines), with execution times up to an hour for large instances.
