# LSTM-Based Anomaly Detection: Detection Rules from Extreme Value Theory

arXiv: https://arxiv.org/abs/1909.06041 · HTML: https://mlsanity.com/paper/1909.06041/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2019.

## Built on by (most cited first, 1 of 1)

- [Spliced Binned-Pareto Distribution for Robust Modeling of Heavy-tailed Time Series](https://mlsanity.com/paper/2106.10952/) (2021)

## Abstract (arXiv)

In this paper, we explore various statistical techniques for anomaly detection in conjunction with the popular Long Short-Term Memory (LSTM) deep learning model for transportation networks. We obtain the prediction errors from an LSTM model, and then apply three statistical models based on (i) the Gaussian distribution, (ii) Extreme Value Theory (EVT), and (iii) the Tukey's method. Using statistical tests and numerical studies, we find strong evidence against the widely employed Gaussian distribution based detection rule on the prediction errors. Next, motivated by fundamental results from Extreme Value Theory, we propose a detection technique that does not assume any parent distribution on the prediction errors. Through numerical experiments conducted on several real-world traffic data sets, we show that the EVT-based detection rule is superior to other detection rules, and is supported by statistical evidence.