# Neural Bayesian Network Understudy

arXiv: https://arxiv.org/abs/2211.08243 · HTML: https://mlsanity.com/paper/2211.08243/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [Causal Learning and Explanation of Deep Neural Networks via Autoencoded Activations](https://mlsanity.com/paper/1802.00541/) (2018)
- [A Comprehensive Scoping Review of Bayesian Networks in Healthcare: Past, Present and Future](https://mlsanity.com/paper/2002.08627/) (2020)
- [Constructing Deep Neural Networks by Bayesian Network Structure Learning](https://mlsanity.com/paper/1806.09141/) (2018)
- [Causal Inference with Deep Causal Graphs](https://mlsanity.com/paper/2006.08380/) (2020)
- [Medical idioms for clinical Bayesian network development](https://mlsanity.com/paper/2007.00364/) (2020)

## Abstract (arXiv)

Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do not have this limitation, they are not interpretable and are inherently unable to deal with causal structure in the input space. Our goal is to build neural networks that combine the advantages of both approaches. Motivated by the perspective to inject causal knowledge while training such neural networks, this work presents initial steps in that direction. We demonstrate how a neural network can be trained to output conditional probabilities, providing approximately the same functionality as a Bayesian Network. Additionally, we propose two training strategies that allow encoding the independence relations inferred from a given causal structure into the neural network. We present initial results in a proof-of-concept setting, showing that the neural model acts as an understudy to its Bayesian Network counterpart, approximating its probabilistic and causal properties.