TY - GEN

T1 - Optimal Variance Control of the Score-Function Gradient Estimator for Importance Weighted Bounds

AU - Liévin, Valentin

AU - Dittadi, Andrea

AU - Christensen, Anders

AU - Winther, Ole

N1 - Publisher Copyright: © 2020 Neural information processing systems foundation. All rights reserved.

PY - 2020

Y1 - 2020

N2 - This paper introduces novel results for the score function gradient estimator of the importance weighted variational bound (IWAE). We prove that in the limit of large K (number of importance samples) one can choose the control variate such that the Signal-to-Noise ratio (SNR) of the estimator grows as pK. This is in contrast to the standard pathwise gradient estimator where the SNR decreases as 1/pK. Based on our theoretical findings we develop a novel control variate that extends on VIMCO. Empirically, for the training of both continuous and discrete generative models, the proposed method yields superior variance reduction, resulting in an SNR for IWAE that increases with K without relying on the reparameterization trick. The novel estimator is competitive with state-of-the-art reparameterization-free gradient estimators such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective (TVO) when training generative models.

AB - This paper introduces novel results for the score function gradient estimator of the importance weighted variational bound (IWAE). We prove that in the limit of large K (number of importance samples) one can choose the control variate such that the Signal-to-Noise ratio (SNR) of the estimator grows as pK. This is in contrast to the standard pathwise gradient estimator where the SNR decreases as 1/pK. Based on our theoretical findings we develop a novel control variate that extends on VIMCO. Empirically, for the training of both continuous and discrete generative models, the proposed method yields superior variance reduction, resulting in an SNR for IWAE that increases with K without relying on the reparameterization trick. The novel estimator is competitive with state-of-the-art reparameterization-free gradient estimators such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective (TVO) when training generative models.

UR - http://www.scopus.com/inward/record.url?scp=85100493425&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85100493425

VL - 2020-December

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

SN - 1049-5258

T2 - 34th Conference on Neural Information Processing Systems, NeurIPS 2020

Y2 - 6 December 2020 through 12 December 2020

ER -