Calibration of One-Class SVM for MV set estimation

TL;DR

This paper introduces a new method for calibrating One-Class SVMs to improve the estimation of high-density regions and MV sets, addressing hyperparameter sensitivity and overfitting issues.

Contribution

It proposes a novel calibration approach that adjusts the OCSVM offset on test data and aggregates models to enhance hyperparameter tuning and set estimation accuracy.

Findings

Outperforms standard OCSVM in experiments

Less affected by curse of dimensionality than kernel density estimates

Enables automatic hyperparameter tuning and nested set estimation

Abstract

A general approach for anomaly detection or novelty detection consists in estimating high density regions or Minimum Volume (MV) sets. The One-Class Support Vector Machine (OCSVM) is a state-of-the-art algorithm for estimating such regions from high dimensional data. Yet it suffers from practical limitations. When applied to a limited number of samples it can lead to poor performance even when picking the best hyperparameters. Moreover the solution of OCSVM is very sensitive to the selection of hyperparameters which makes it hard to optimize in an unsupervised setting. We present a new approach to estimate MV sets using the OCSVM with a different choice of the parameter controlling the proportion of outliers. The solution function of the OCSVM is learnt on a training set and the desired probability mass is obtained by adjusting the offset on a test set to prevent overfitting. Models learnt on different train/test splits are then aggregated to reduce the variance induced by such random splits. Our approach makes it possible to tune the hyperparameters automatically and obtain nested set estimates. Experimental results show that our approach outperforms the standard OCSVM formulation while suffering less from the curse of dimensionality than kernel density estimates. Results on actual data sets are also presented.