Best-Choice Edge Grafting for Efficient Structure Learning of Markov Random Fields

Incremental methods for structure learning of pairwise Markov random fields (MRFs), such as grafting, improve scalability by avoiding inference over the entire feature space in each optimization step. Instead, inference is performed over an incrementally grown active set of features. In this paper, we address key computational bottlenecks that current incremental techniques still suffer by introducing best-choice edge grafting, an incremental, structured method that activates edges as groups of features in a streaming setting. The method uses a reservoir of edges that satisfy an activation condition, approximating the search for the optimal edge to activate. It also reorganizes the search space using search-history and structure heuristics. Experiments show a significant speedup for structure learning and a controllable trade-off between the speed and quality of learning

Block Belief Propagation for Parameter Learning in Markov Random Fields

Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models. In this paper, we propose \emph{block belief propagation learning} (BBPL), which uses block-coordinate updates of approximate marginals to compute approximate gradients, removing the need to compute inference on the entire graphical model. Thus, the iteration complexity of BBPL does not scale with the size of the graphs. We prove that the method converges to the same solution as that obtained by using full inference per iteration, despite these approximations, and we empirically demonstrate its scalability improvements over standard training methods.Comment: Accepted to AAAI 201

Litigation Finance: What Do Judges Need to Know?

In our classic image of an American lawsuit, including class actions, the plaintiffs lawyer pays the upfront costs and then hopes to recoup them from a share of the winnings. But today, this picture is incomplete. It is no longer only the law firm\u27s own war chest that finances a case – so can outside investors and lenders. As Judge Hellerstein has just reminded us, the 9/11 cases he presided over involved such third-party financing. The Ecuadorian plaintiffs\u27 environmental case against Chevron, now pending in the Southern District of New York, is another prominent example in the news