# LEAN-DMKDE: Quantum Latent Density Estimation for Anomaly Detection

arXiv: https://arxiv.org/abs/2211.08525 · HTML: https://mlsanity.com/paper/2211.08525/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Anomaly Detection With Conditional Variational Autoencoders](https://mlsanity.com/paper/2010.05531/) (2020)
- [Anomaly Detection in Medical Imaging -- A Mini Review](https://mlsanity.com/paper/2108.11986/) (2021)
- [Robust Unsupervised Video Anomaly Detection by Multi-Path Frame Prediction](https://mlsanity.com/paper/2011.02763/) (2020)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [Quantum Adaptive Fourier Features for Neural Density Estimation](https://mlsanity.com/paper/2208.00564/) (2022)
- [AD-DMKDE: Anomaly Detection through Density Matrices and Fourier Features](https://mlsanity.com/paper/2210.14796/) (2022)

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

- [MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design](https://mlsanity.com/paper/2406.08591/) (2024)

## Abstract (arXiv)

This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deep-learning models. The method combines an autoencoder, for learning a low-dimensional representation of the data, with a density-estimation model based on random Fourier features and density matrices in an end-to-end architecture that can be trained using gradient-based optimization techniques. The method predicts a degree of normality for new samples based on the estimated density. A systematic experimental evaluation was performed on different benchmark datasets. The experimental results show that the method performs on par with or outperforms other state-of-the-art methods.