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

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• Francesca Romana Crucinio (King's College London)
• Friday 19 July 2024, 13:30-14:30
• External.

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DMLW01 - International workshop on diffusions in machine learning: foundations, generative models, and optimisation

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.    

This talk is part of the Isaac Newton Institute Seminar Series series.

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