Solving Marginal MAP Problems with NP Oracles and Parity Constraints
This addresses a high-complexity inference problem in machine learning and decision making, offering a novel solution with practical improvements.
The paper tackles the Marginal MAP problem, which combines optimization and counting inference, by proposing XOR_MMAP, a method that uses NP oracles and parity constraints to provide a constant factor approximation, outperforming state-of-the-art solvers in evaluations.
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 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.