Papers › Nuisance hardened data compression for fast likelihood-free inference
Nuisance hardened data compression for fast likelihood-free inference
Justin Alsing, Benjamin Wandelt
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In this paper we show how nuisance parameter marginalized posteriors can be inferred directly from simulations in a likelihood-free setting, without having to jointly infer the higher-dimensional interesting and nuisance parameter posterior first and marginalize a posteriori. The result is that for an inference task with a given number of interesting parameters, the number of simulations required to perform likelihood-free inference can be kept (roughly) the same irrespective of the number of additional nuisances to be marginalized over. To achieve this we introduce two extensions to the standard likelihood-free inference set-up. Firstly we show how nuisance parameters can be re-cast as latent variables and hence automatically marginalized over in the likelihood-free framework. Secondly, we derive an asymptotically optimal compression from N data down to n summaries -- one per interesting parameter -- such that the Fisher information is (asymptotically) preserved, but the summaries are insensitive (to leading order) to the nuisance parameters. This means that the nuisance marginalized inference task involves learning n interesting parameters from n "nuisance hardened" data summaries, regardless of the presence or number of additional nuisance parameters to be marginalized over. We validate our approach on two examples from cosmology: supernovae and weak lensing data analyses with nuisance parameterized systematics. For the supernova problem, high-fidelity posterior inference of Ωₘ and w₀ (marginalized over systematics) can be obtained from just a few hundred data simulations. For the weak lensing problem, six cosmological parameters can be inferred from 𝒪(10³) simulations, irrespective of whether ten additional nuisance parameters are included in the problem or not.
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