Integrating discrete probability distributions and combinatorial optimization problems into neural networks has numerous applications but poses several challenges. We propose Implicit Maximum Likelihood Estimation (I-MLE), a framework for end-to-end learning of models combining discrete exponential family distributions and differentiable neural components. I-MLE is widely applicable: it only requires the ability to compute the most probable states; and does not rely on smooth relaxations. The framework encompasses several approaches, such as perturbation-based implicit differentiation and recent methods to differentiate through black-box combinatorial solvers. We introduce a novel class of noise distributions for approximating marginals via perturb-and-MAP. Moreover, we show that I-MLE simplifies to maximum likelihood estimation when used in some recently studied learning settings that involve combinatorial solvers. Experiments on several datasets suggest that I-MLE is competitive with and often outperforms existing approaches which rely on problem-specific relaxations.

该论文提出了一种基于离散指数族分布和可微神经组件相结合的模型的端到端学习框架Implicit Maximum Likelihood Estimation（I-MLE），并介绍了一种新型的噪声分布perturb-and-MAP，该框架在几个数据集上表现良好，并且与依赖于特定问题松弛的现有方法相比竞争力强。

隐式最大似然估计：通过离散指数族分布反向传播