# Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations

arXiv: https://arxiv.org/abs/2403.20313 · HTML: https://mlsanity.com/paper/2403.20313/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Exact and Approximate MCMC for Doubly-intractable Probabilistic Graphical Models Leveraging the Underlying Independence Model](https://mlsanity.com/paper/2510.03587/) (2025)

## Abstract (arXiv)

Given a smooth function f, we develop a general approach to turn Monte Carlo samples with expectation m into an unbiased estimate of f(m). Specifically, we develop estimators that are based on randomly truncating the Taylor series expansion of f and estimating the coefficients of the truncated series. We derive their properties and propose a strategy to set their tuning parameters -- which depend on m -- automatically, with a view to make the whole approach simple to use. We develop our methods for the specific functions f(x)=log x and f(x)=1/x, as they arise in several statistical applications such as maximum likelihood estimation of latent variable models and Bayesian inference for un-normalised models. Detailed numerical studies are performed for a range of applications to determine how competitive and reliable the proposed approach is.