Learning to discover: expressive Gaussian mixture models for multi-dimensional simulation and parameter inference in the physical sciences

TL;DR

This paper introduces an auto-regressive Gaussian mixture model that captures complex dependencies and boundaries in multi-dimensional data, enabling improved scientific discovery and parameter inference across various domains.

Contribution

The paper presents a novel expressive Gaussian mixture model with latent space projection for multi-observable data, applicable to simulation and inference in physical sciences.

Findings

Successfully modeled high-energy physics data with the proposed method.

Demonstrated improved parameter inference accuracy in toy examples.

The model is domain-agnostic and adaptable to various scientific fields.

Abstract

We show that density models describing multiple observables with (i) hard boundaries and (ii) 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.