Learning to discover: expressive Gaussian mixture models for multi-dimensional simulation and parameter inference in the physical sciences (2021-08-25T00:00:00.000000Z)

Abstract

We show that density models describing multiple observables with (1) hard boundaries and (2) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable spectra are deformed by hypothesis variations, and is made more expressive by projecting data onto a configurable latent space. It may be used as a statistical model for scientific discovery in interpreting experimental observations, for example when constraining the parameters of a physical model or tuning simulation parameters according to calibration data. The model may also be sampled for use within a Monte Carlo simulation chain, or used to estimate likelihood ratios for event classification. The method is demonstrated on simulated high-energy particle physics data considering the anomalous electroweak production of a Z boson in association with a dijet system at the Large Hadron Collider, and the accuracy of inference is tested using a realistic toy example. The developed methods are domain agnostic; they may be used within any field to perform simulation or inference where a dataset consisting of many real-valued observables has conditional dependence on external parameters.

Authors

S. Menary

1 papers

D. Price

1 papers

Abstract

Authors

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iii) In order to deform the PDF downwards

We can numerically estimate the expected distribution of a test-statistic under diﬀerent parameter hypotheses, instead of assuming an asymptotic form

v) Alter the ordering of the observables

The structural features of the PDF, and any deformations induced by variations of θ , must be smooth and wide enough to be modulated by the Gaussian modes

i) Increase the model capacity by using more complicated networks or larger

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Tune the hyperparameter f or the functional form of ˜ q u to create a latent distribution which is well described by a mixture of narrow Gaussians

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