# Support Vector Machines and generalisation in HEP

## TL;DR

This paper reviews the use of Support Vector Machines in high energy physics, focusing on hyper-parameter generalisation, implementation in TMVA, and performance benchmarking for background suppression tasks.

## Contribution

It introduces extended SVM functionalities in TMVA, emphasizing improved cross-validation methods to enhance hyper-parameter generalisation in HEP applications.

## Key findings

- Extended TMVA SVM tools for better cross-validation
- Comparison of hold-out and k-fold cross-validation methods
- Demonstrated SVM performance in background suppression for LHC analyses

## Abstract

We review the concept of Support Vector Machines (SVMs) and discuss examples of their use in a number of scenarios. Several SVM implementations have been used in HEP and we exemplify this algorithm using the Toolkit for Multivariate Analysis (TMVA) implementation. We discuss examples relevant to HEP including background suppression for $H\to\tau^+\tau^-$ at the LHC with several different kernel functions. Performance benchmarking leads to the issue of generalisation of hyper-parameter selection. The avoidance of fine tuning (over training or over fitting) in MVA hyper-parameter optimisation, i.e. the ability to ensure generalised performance of an MVA that is independent of the training, validation and test samples, is of utmost importance. We discuss this issue and compare and contrast performance of hold-out and k-fold cross-validation. We have extended the SVM functionality and introduced tools to facilitate cross validation in TMVA and present results based on these improvements.