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Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions
Mathias Niepert · Pasquale Minervini · Luca Franceschi

Wed Dec 08 12:30 AM -- 02:00 AM (PST) @

Combining discrete probability distributions and combinatorial optimization problems with neural network components 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 as 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.

Author Information

Mathias Niepert (University of Stuttgart / NEC Labs Europe)
Pasquale Minervini (University College London)
Luca Franceschi (University College London)

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