Amortized Rejection Sampling in Universal Probabilistic Programming
This work addresses a specific bottleneck in probabilistic programming for researchers and practitioners, offering an incremental improvement in inference reliability.
The paper tackles the problem of infinite variance in amortized inference for probabilistic programs with unbounded loops, particularly those using rejection sampling, by developing a new amortized importance sampling estimator that ensures finite variance and demonstrates efficiency compared to existing methods.
Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection sampling as part of the user-programmed generative procedure. In this paper we develop a new and efficient amortized importance sampling estimator. We prove finite variance of our estimator and empirically demonstrate our method's correctness and efficiency compared to existing alternatives on generative programs containing rejection sampling loops and discuss how to implement our method in a generic probabilistic programming framework.