Neural models operating over structured spaces such as knowledge graphs require a continuous embedding of the discrete elements of this space (such as entities) as well as the relationships between them. Relational embeddings with high expressivity, however, have high model complexity, making them computationally difficult to train.

Arising from many applications at the intersection of decision-making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) problems unify the two main classes of inference, namely maximization (optimization) and marginal inference (counting), and are believed to have higher complexity than both of them. We propose XOR_MMAP, a novel approach to solve the Marginal MAP problem, which represents the intractable counting subproblem with queries to NP oracles, subject to additional parity constraints. XOR_MMAP provides a constant factor approximation to the Marginal MAP problem, by encoding it as a single optimization in a polynomial size of the original problem. We evaluate our approach in several machine learning and decision-making applications, and show that our approach outperforms several state-of-the-art Marginal MAP solvers.

Neural models operating over structured spaces such as knowledge graphs require a continuous embedding of the discrete elements of this space (such as entities) as well as the relationships between them. Relational embeddings with high expressivity, however, have high model complexity, making them computationally difficult to train.