Theoretical Investigation on Inductive Bias of Isolation Forest

TL;DR

This paper provides a theoretical analysis of the inductive bias of Isolation Forest, modeling its growth as a random walk to explain its effectiveness in anomaly detection and its robustness to different anomaly types.

Contribution

It formulates the growth process of iForest as a random walk and derives the expected depth function, offering a theoretical foundation for its success.

Findings

iForest is less sensitive to central anomalies

iForest has greater parameter adaptability than k-NN

Theoretical understanding of iForest's effectiveness

Abstract

Isolation Forest (iForest) stands out as a widely-used unsupervised anomaly detector, primarily owing to its remarkable runtime efficiency and superior performance in large-scale tasks. Despite its widespread adoption, a theoretical foundation explaining iForest's success remains unclear. This paper focuses on the inductive bias of iForest, which theoretically elucidates under what circumstances and to what extent iForest works well. The key is to formulate the growth process of iForest, where the split dimensions and split values are randomly selected. We model the growth process of iForest as a random walk, enabling us to derive the expected depth function, which is the outcome of iForest, using transition probabilities. The case studies reveal key inductive biases: iForest exhibits lower sensitivity to central anomalies while demonstrating greater parameter adaptability compared to $k$-Nearest Neighbor. Our study provides a theoretical understanding of the effectiveness of iForest and establishes a foundation for further theoretical exploration.