# Anomaly Detection with Variance Stabilized Density Estimation

arXiv: https://arxiv.org/abs/2306.00582 · HTML: https://mlsanity.com/paper/2306.00582/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 56 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 28 of 28)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Deep Anomaly Detection with Deviation Networks](https://mlsanity.com/paper/1911.08623/) (2019)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Deep Learning for Medical Anomaly Detection -- A Survey](https://mlsanity.com/paper/2012.02364/) (2020)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [Anomaly Detection using One-Class Neural Networks](https://mlsanity.com/paper/1802.06360/) (2018)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [RNADE: The real-valued neural autoregressive density-estimator](https://mlsanity.com/paper/1306.0186/) (2013)
- [Latent Outlier Exposure for Anomaly Detection with Contaminated Data](https://mlsanity.com/paper/2202.08088/) (2022)
- [Perfect density models cannot guarantee anomaly detection](https://mlsanity.com/paper/2012.03808/) (2020)
- [Noise Regularization for Conditional Density Estimation](https://mlsanity.com/paper/1907.08982/) (2019)
- [Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications](https://mlsanity.com/paper/1904.00176/) (2019)
- [Estimating the Accuracies of Multiple Classifiers Without Labeled Data](https://mlsanity.com/paper/1407.7644/) (2014)
- [Entropic Issues in Likelihood-Based OOD Detection](https://mlsanity.com/paper/2109.10794/) (2021)
- [ButterflyFlow: Building Invertible Layers with Butterfly Matrices](https://mlsanity.com/paper/2209.13774/) (2022)
- [Probabilistic Robust Autoencoders for Outlier Detection](https://mlsanity.com/paper/2110.00494/) (2021)
- [Neural Inverse Transform Sampler](https://mlsanity.com/paper/2206.11172/) (2022)

## Built on by (most cited first, 8 of 8)

- [Representation Learning for Tabular Data: A Comprehensive Survey](https://mlsanity.com/paper/2504.16109/) (2025)
- [TabADM: Unsupervised Tabular Anomaly Detection with Diffusion Models](https://mlsanity.com/paper/2307.12336/) (2023)
- [Unveiling Multiple Descents in Unsupervised Autoencoders](https://mlsanity.com/paper/2406.11703/) (2024)
- [Hybrid Autoencoders for Tabular Data: Leveraging Model-Based Augmentation in Low-Label Settings](https://mlsanity.com/paper/2511.06961/) (2025)
- [Multivariate Latent Recalibration for Conditional Normalizing Flows](https://mlsanity.com/paper/2505.16636/) (2025)
- [Detect and Correct: A Selective Noise Correction Method for Learning with Noisy Labels](https://mlsanity.com/paper/2505.13342/) (2025)
- [UniOD: A Universal Model for Outlier Detection across Diverse Domains](https://mlsanity.com/paper/2507.06624/) (2025)
- [When Identical Rows Disagree: From Benchmark Identifiability to Replication-Robust Anomaly Detection](https://mlsanity.com/paper/2609.29580/) (2026)

## Abstract (arXiv)

We propose a modified density estimation problem that is highly effective for detecting anomalies in tabular data. Our approach assumes that the density function is relatively stable (with lower variance) around normal samples. We have verified this hypothesis empirically using a wide range of real-world data. Then, we present a variance-stabilized density estimation problem for maximizing the likelihood of the observed samples while minimizing the variance of the density around normal samples. To obtain a reliable anomaly detector, we introduce a spectral ensemble of autoregressive models for learning the variance-stabilized distribution. We have conducted an extensive benchmark with 52 datasets, demonstrating that our method leads to state-of-the-art results while alleviating the need for data-specific hyperparameter tuning. Finally, we have used an ablation study to demonstrate the importance of each of the proposed components, followed by a stability analysis evaluating the robustness of our model.