# Quantile LSTM: A Robust LSTM for Anomaly Detection In Time Series Data

arXiv: https://arxiv.org/abs/2302.08712 · HTML: https://mlsanity.com/paper/2302.08712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 17 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Deep Anomaly Detection with Deviation Networks](https://mlsanity.com/paper/1911.08623/) (2019)
- [Adversarially Learned Anomaly Detection](https://mlsanity.com/paper/1812.02288/) (2018)
- [Anomaly-based Intrusion Detection in Industrial Data with SVM and Random Forests](https://mlsanity.com/paper/1907.10374/) (2019)
- [Estimation and Applications of Quantiles in Deep Binary Classification](https://mlsanity.com/paper/2102.06575/) (2021)
- [A3: Activation Anomaly Analysis](https://mlsanity.com/paper/2003.01801/) (2020)

## Abstract (arXiv)

Anomalies refer to the departure of systems and devices from their normal behaviour in standard operating conditions. An anomaly in an industrial device can indicate an upcoming failure, often in the temporal direction. In this paper, we make two contributions: 1) we estimate conditional quantiles and consider three different ways to define anomalies based on the estimated quantiles. 2) we use a new learnable activation function in the popular Long Short Term Memory networks (LSTM) architecture to model temporal long-range dependency. In particular, we propose Parametric Elliot Function (PEF) as an activation function (AF) inside LSTM, which saturates lately compared to sigmoid and tanh. The proposed algorithms are compared with other well-known anomaly detection algorithms, such as Isolation Forest (iForest), Elliptic Envelope, Autoencoder, and modern Deep Learning models such as Deep Autoencoding Gaussian Mixture Model (DAGMM), Generative Adversarial Networks (GAN). The algorithms are evaluated in terms of various performance metrics, such as Precision and Recall. The algorithms have been tested on multiple industrial time-series datasets such as Yahoo, AWS, GE, and machine sensors. We have found that the LSTM-based quantile algorithms are very effective and outperformed the existing algorithms in identifying anomalies.