Solving Marginal MAP Problems with NP Oracles and Parity Constraints

TL;DR

This paper introduces XOR_MMAP, a novel method that approximates Marginal MAP problems by leveraging NP oracles and parity constraints, effectively solving complex inference tasks more efficiently.

Contribution

XOR_MMAP encodes Marginal MAP as a single polynomial-size optimization problem using NP oracles and parity constraints, providing a constant factor approximation.

Findings

Outperforms state-of-the-art Marginal MAP solvers in experiments

Provides a polynomial-size encoding for complex inference problems

Achieves a constant factor approximation for Marginal MAP

Abstract

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.