3,901 research outputs found
Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions
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.Comment: NeurIPS 2021 camera-ready; repo:
https://github.com/nec-research/tf-iml
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