On the Pitfalls of Nested Monte Carlo
It warns of pitfalls in naive composition of inference and models, which is crucial for researchers and practitioners in probabilistic programming and machine learning.
The paper analyzed nested Monte Carlo (NMC) schemes used in probabilistic programming, establishing conditions for convergence and proving inherent bias in general-purpose nested inference, with empirical data supporting the derived convergence rate.
There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for which classical convergence proofs are insufficient. We give conditions under which NMC will converge, establish a rate of convergence, and provide empirical data that suggests that this rate is observable in practice. Finally, we prove that general-purpose nested inference schemes are inherently biased. Our results serve to warn of the dangers associated with naive composition of inference and models.