Bayesian networks are among the most prominent graphical models for probability distributions.

Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their expressive power. In this work, we propose a new GNN architecture - the Neural Tree. The neural tree architecture does not perform message passing on the input graph, but on a tree-structured graph, called the H-tree, that is constructed from the input graph. Nodes in the H-tree correspond to subgraphs in the input graph, and they are reorganized in a hierarchical manner such that the parent of a node in the H-tree always corresponds to a larger subgraph in the input graph.

Parviainen et al. (2014) adopted an anytime integer linear programming (ILP) Otherwise it returns a sub-optimal DAG with bounded treewidth. Nie et al. (2014) proposed an efficient anytime ILP approach with a polynomial number of constraints Nie et al. (2015) proposed the method S2.

Numerical results demonstrate the efficacy of the new penalties.

Neural Information Processing Systems http://nips.cc/

The world of deep learning is moving toward bigger model architectures.

Learning algorithms must consider complex relationships between variables to provide useful predictions in many structured prediction problems.

Neural Information Processing Systems http://nips.cc/