# Tractable Uncertainty for Structure Learning

arXiv: https://arxiv.org/abs/2204.14170 · HTML: https://mlsanity.com/paper/2204.14170/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 29 Apr 2022.

## Builds on (most cited first, 14 of 14)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [On the Latent Variable Interpretation in Sum-Product Networks](https://mlsanity.com/paper/1601.06180/) (2016)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [Partition MCMC for inference on acyclic digraphs](https://mlsanity.com/paper/1504.05006/) (2015)
- [Towards Scalable Bayesian Learning of Causal DAGs](https://mlsanity.com/paper/2010.00684/) (2020)
- [Efficient Sampling and Structure Learning of Bayesian Networks](https://mlsanity.com/paper/1803.07859/) (2018)
- [Probabilistic Circuits for Variational Inference in Discrete Graphical Models](https://mlsanity.com/paper/2010.11446/) (2020)
- [Visualizing and Understanding Sum-Product Networks](https://mlsanity.com/paper/1608.08266/) (2016)
- [On Relaxing Determinism in Arithmetic Circuits](https://mlsanity.com/paper/1708.06846/) (2017)
- [Minimal I-MAP MCMC for Scalable Structure Discovery in Causal DAG Models](https://mlsanity.com/paper/1803.05554/) (2018)

## Built on by (most cited first, 15 of 15)

- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [Subtractive Mixture Models via Squaring: Representation and Learning](https://mlsanity.com/paper/2310.00724/) (2023)
- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [A Compositional Atlas for Algebraic Circuits](https://mlsanity.com/paper/2412.05481/) (2024)
- [Scaling Probabilistic Circuits via Monarch Matrices](https://mlsanity.com/paper/2506.12383/) (2025)
- [Characteristic Circuits](https://mlsanity.com/paper/2312.07790/) (2023)
- [Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challenges](https://mlsanity.com/paper/2405.05025/) (2024)
- [Learning Latent Structural Causal Models](https://mlsanity.com/paper/2210.13583/) (2022)
- [Permutation-based Inference for Variational Learning of Directed Acyclic Graphs](https://mlsanity.com/paper/2402.02644/) (2024)
- [ProDAG: Projected Variational Inference for Directed Acyclic Graphs](https://mlsanity.com/paper/2405.15167/) (2024)
- [Toward a Graph-Theoretic Model of Belief: Confidence, Credibility, and Structural Coherence](https://mlsanity.com/paper/2508.03465/) (2025)
- [Belief Graphs with Reasoning Zones: Structure, Dynamics, and Epistemic Activation](https://mlsanity.com/paper/2510.10042/) (2025)
- [SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2608.04930/) (2026)
- [Interpretable Causal Discovery via Causal-Effect Constraints](https://mlsanity.com/paper/2608.12640/) (2026)

## Abstract (arXiv)

Bayesian structure learning allows one to capture uncertainty over the causal directed acyclic graph (DAG) responsible for generating given data. In this work, we present Tractable Uncertainty for STructure learning (TRUST), a framework for approximate posterior inference that relies on probabilistic circuits as the representation of our posterior belief. In contrast to sample-based posterior approximations, our representation can capture a much richer space of DAGs, while also being able to tractably reason about the uncertainty through a range of useful inference queries. We empirically show how probabilistic circuits can be used as an augmented representation for structure learning methods, leading to improvement in both the quality of inferred structures and posterior uncertainty. Experimental results on conditional query answering further demonstrate the practical utility of the representational capacity of TRUST.