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Main Authors: Zheng, Qin-Cheng, Zhang, Shao-Qun, Lyu, Shen-Huan, Jiang, Yuan, Zhou, Zhi-Hua
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2505.12825
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author Zheng, Qin-Cheng
Zhang, Shao-Qun
Lyu, Shen-Huan
Jiang, Yuan
Zhou, Zhi-Hua
author_facet Zheng, Qin-Cheng
Zhang, Shao-Qun
Lyu, Shen-Huan
Jiang, Yuan
Zhou, Zhi-Hua
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_12825
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Theoretical Investigation on Inductive Bias of Isolation Forest
Zheng, Qin-Cheng
Zhang, Shao-Qun
Lyu, Shen-Huan
Jiang, Yuan
Zhou, Zhi-Hua
Machine Learning
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.
title Theoretical Investigation on Inductive Bias of Isolation Forest
topic Machine Learning
url https://arxiv.org/abs/2505.12825