Coupled Gradient Estimators for Discrete Latent Variables

• URL: http://arxiv.org/abs/2106.08056v1
• Date: Tue, 15 Jun 2021 11:28:44 GMT
• Title: Coupled Gradient Estimators for Discrete Latent Variables
• Authors: Zhe Dong, Andriy Mnih, George Tucker
• Abstract summary: Training models with discrete latent variables is challenging due to the high variance of unbiased gradient estimators. We introduce a novel derivation of their estimator based on importance sampling and statistical couplings. We show that our proposed categorical gradient estimators provide state-of-the-art performance.
• Score: 41.428359609999326
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Training models with discrete latent variables is challenging due to the high variance of unbiased gradient estimators. While low-variance reparameterization gradients of a continuous relaxation can provide an effective solution, a continuous relaxation is not always available or tractable. Dong et al. (2020) and Yin et al. (2020) introduced a performant estimator that does not rely on continuous relaxations; however, it is limited to binary random variables. We introduce a novel derivation of their estimator based on importance sampling and statistical couplings, which we extend to the categorical setting. Motivated by the construction of a stick-breaking coupling, we introduce gradient estimators based on reparameterizing categorical variables as sequences of binary variables and Rao-Blackwellization. In systematic experiments, we show that our proposed categorical gradient estimators provide state-of-the-art performance, whereas even with additional Rao-Blackwellization, previous estimators (Yin et al., 2019) underperform a simpler REINFORCE with a leave-one-out-baseline estimator (Kool et al., 2019).

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