Increasing Information Extraction in Low-Signal Regimes via Multiple Instance Learning

TL;DR

This paper presents a new information-theoretic approach to Multiple Instance Learning (MIL), demonstrating its advantage over single-instance methods in low-signal regimes, with applications to particle physics data from the LHC.

Contribution

It introduces an information-theoretic perspective on MIL for parameter estimation and shows MIL's superiority in low-signal scenarios compared to single-instance models.

Findings

MIL can outperform single-instance learners in low-signal regimes.

Pooling instances increases effective Fisher information.

Application to SMEFT parameter constraints at the LHC.

Abstract

In this work, we introduce a new information-theoretic perspective on Multiple Instance Learning (MIL) for parameter estimation with i.i.d. data, and show that MIL can outperform single-instance learners in low-signal regimes. Prior work [Nachman and Thaler, 2021] argued that single-instance methods are often sufficient, but this conclusion presumes enough single-instance signal to train near-optimal classifiers. We demonstrate that even state-of-the-art single-instance models can fail to reach optimal classifier performance in challenging low-signal regimes, whereas MIL can mitigate this sub-optimality. As a concrete application, we constrain Wilson coefficients of the Standard Model Effective Field Theory (SMEFT) using kinematic information from subatomic particle collision events at the Large Hadron Collider (LHC). In experiments, we observe that under specific modeling and weak signal conditions, pooling instances can increase the effective Fisher information compared to single-instance approaches.