Jeffrey, Niall;
Wandelt, Benjamin Dan;
(2024)
Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison.
Machine Learning: Science and Technology
, 5
(1)
, Article 015008. 10.1088/2632-2153/ad1a4d.
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Abstract
Evidence Networks can enable Bayesian model comparison when state-of-the-art methods (e.g. nested sampling) fail and even when likelihoods or priors are intractable or unknown. Bayesian model comparison, i.e. the computation of Bayes factors or evidence ratios, can be cast as an optimization problem. Though the Bayesian interpretation of optimal classification is well-known, here we change perspective and present classes of loss functions that result in fast, amortized neural estimators that directly estimate convenient functions of the Bayes factor. This mitigates numerical inaccuracies associated with estimating individual model probabilities. We introduce the leaky parity-odd power (l-POP) transform, leading to the novel ``l-POP-Exponential'' loss function. We explore neural density estimation for data probability in different models, showing it to be less accurate and scalable than Evidence Networks. Multiple real-world and synthetic examples illustrate that Evidence Networks are explicitly independent of dimensionality of the parameter space and scale mildly with the complexity of the posterior probability density function. This simple yet powerful approach has broad implications for model inference tasks. As an application of Evidence Networks to real-world data we compute the Bayes factor for two models with gravitational lensing data of the Dark Energy Survey. We briefly discuss applications of our methods to other, related problems of model comparison and evaluation in implicit inference settings.
| Type: | Article |
|---|---|
| Title: | Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/2632-2153/ad1a4d |
| Publisher version: | http://dx.doi.org/10.1088/2632-2153/ad1a4d |
| Language: | English |
| Additional information: | Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10185683 |
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