Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions

• URL: http://arxiv.org/abs/2106.01798v1
• Date: Thu, 3 Jun 2021 12:42:21 GMT
• Title: Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions
• Authors: Mathias Niepert and Pasquale Minervini and Luca Franceschi
• Abstract summary: Implicit Maximum Likelihood Estimation is a framework for end-to-end learning of models combining discrete exponential family distributions and differentiable neural components. We show that I-MLE is competitive with and often outperforms existing approaches which rely on problem-specific relaxations.
• Score: 24.389388509299543
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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