# Why the Counterintuitive Phenomenon of Likelihood Rarely Appears in Tabular Anomaly Detection with Deep Generative Models?

arXiv: https://arxiv.org/abs/2602.09593 · HTML: https://mlsanity.com/paper/2602.09593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 77 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 30 of 36)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (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)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
- [Density of States Estimation for Out-of-Distribution Detection](https://mlsanity.com/paper/2006.09273/) (2020)
- [Understanding Anomaly Detection with Deep Invertible Networks through Hierarchies of Distributions and Features](https://mlsanity.com/paper/2006.10848/) (2020)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Perfect density models cannot guarantee anomaly detection](https://mlsanity.com/paper/2012.03808/) (2020)
- [Benchmarking Unsupervised Outlier Detection with Realistic Synthetic Data](https://mlsanity.com/paper/2004.06947/) (2020)

## Abstract (arXiv)

Deep generative models with tractable and analytically computable likelihoods, exemplified by normalizing flows, offer an effective basis for anomaly detection through likelihood-based scoring. We demonstrate that, unlike in the image domain where deep generative models frequently assign higher likelihoods to anomalous data, such counterintuitive behavior occurs far less often in tabular settings. We first introduce a domain-agnostic formulation that enables consistent detection and evaluation of the counterintuitive phenomenon, addressing the absence of precise definition. Through extensive experiments on 47 tabular datasets and 10 CV/NLP embedding datasets in ADBench, benchmarked against 13 baseline models, we demonstrate that the phenomenon, as defined, is consistently rare in general tabular data. We further investigate this phenomenon from both theoretical and empirical perspectives, focusing on the roles of data dimensionality and difference in feature correlation. Our results suggest that likelihood-only detection with normalizing flows offers a practical and reliable approach for anomaly detection in tabular domains.