# Automatic Bayesian Density Analysis

arXiv: https://arxiv.org/abs/1807.09306 · HTML: https://mlsanity.com/paper/1807.09306/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2018.

## Built on by (most cited first, 10 of 10)

- [Handling Epistemic and Aleatory Uncertainties in Probabilistic Circuits](https://mlsanity.com/paper/2102.10865/) (2021)
- [Characteristic Circuits](https://mlsanity.com/paper/2312.07790/) (2023)
- [Bayesian Structure Scores for Probabilistic Circuits](https://mlsanity.com/paper/2302.12130/) (2023)
- [Tractable Probabilistic Graph Representation Learning with Graph-Induced Sum-Product Networks](https://mlsanity.com/paper/2305.10544/) (2023)
- [Tractable Representation Learning with Probabilistic Circuits](https://mlsanity.com/paper/2507.04385/) (2025)
- [Recursive Bayesian Networks: Generalising and Unifying Probabilistic Context-Free Grammars and Dynamic Bayesian Networks](https://mlsanity.com/paper/2111.01853/) (2021)
- [Probabilistic Circuits with Constraints via Convex Optimization](https://mlsanity.com/paper/2403.13125/) (2024)
- [Soft Learning Probabilistic Circuits](https://mlsanity.com/paper/2403.14504/) (2024)
- [A Sobering Look at Tabular Data Generation via Probabilistic Circuits](https://mlsanity.com/paper/2603.23016/) (2026)
- [Top-Down Bayesian Posterior Sampling for Sum-Product Networks](https://mlsanity.com/paper/2406.12353/) (2024)

## Abstract (arXiv)

Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for {exploratory data analysis} are usually not flexible enough to deal with the uncertainty inherent to real-world data: they are often restricted to fixed latent interaction models and homogeneous likelihoods; they are sensitive to missing, corrupt and anomalous data; moreover, their expressiveness generally comes at the price of intractable inference. As a result, supervision from statisticians is usually needed to find the right model for the data. However, since domain experts are not necessarily also experts in statistics, we propose Automatic Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible at large. Specifically, ABDA allows for automatic and efficient missing value estimation, statistical data type and likelihood discovery, anomaly detection and dependency structure mining, on top of providing accurate density estimation. Extensive empirical evidence shows that ABDA is a suitable tool for automatic exploratory analysis of mixed continuous and discrete tabular data.