Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard even under many common structural constraints and approximation schemes. We introduce $\mathit{probably\ approximately\ correct}$ (PAC) algorithms for MAP inference that provide provably optimal solutions under variable and fixed computational budgets. We characterize tractability conditions for PAC-MAP using information theoretic measures that can be estimated from finite samples. Our PAC-MAP solvers are efficiently implemented using probabilistic circuits with appropriate architectures. The randomization strategies we develop can be used either as standalone MAP inference techniques or to improve on popular heuristics, fortifying their solutions with rigorous guarantees. Experiments confirm the benefits of our method in a range of benchmarks.

翻译：计算分布的条件众数，即$\mathit{最大后验}$（MAP）赋值，是概率推断中的一项基础任务。然而，MAP估计通常难以精确求解，即使在许多常见的结构约束和近似方案下仍具有较高计算复杂度。本文提出用于MAP推断的$\mathit{概率近似正确}$（PAC）算法，该算法能在可变与固定计算预算下提供可证明的最优解。我们通过可从有限样本估计的信息论度量来刻画PAC-MAP的可处理性条件。所提出的PAC-MAP求解器通过具有适当架构的概率电路实现高效计算。我们开发的随机化策略既可作为独立的MAP推断方法使用，也可用于改进常见启发式算法，从而为其解提供严格的理论保证。实验在一系列基准测试中验证了本方法的优势。