# Explaining Deep Tractable Probabilistic Models: The sum-product network case

arXiv: https://arxiv.org/abs/2110.09778 · HTML: https://mlsanity.com/paper/2110.09778/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Beyond Short Snippets: Deep Networks for Video Classification](https://mlsanity.com/paper/1503.08909/) (2015)
- [Visual Interpretability for Deep Learning: a Survey](https://mlsanity.com/paper/1802.00614/) (2018)
- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [On the Latent Variable Interpretation in Sum-Product Networks](https://mlsanity.com/paper/1601.06180/) (2016)
- [Random Feature Expansions for Deep Gaussian Processes](https://mlsanity.com/paper/1610.04386/) (2016)
- [SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networks](https://mlsanity.com/paper/1901.03704/) (2019)
- [Deep Probabilistic Programming](https://mlsanity.com/paper/1701.03757/) (2017)
- [Identifying Causal Effects via Context-specific Independence Relations](https://mlsanity.com/paper/2009.09768/) (2020)
- [Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models](https://mlsanity.com/paper/2102.10440/) (2021)
- [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)
- [On the Relationship between Sum-Product Networks and Bayesian Networks](https://mlsanity.com/paper/1501.01239/) (2015)
- [A New Perspective on Learning Context-Specific Independence](https://mlsanity.com/paper/2006.06896/) (2020)
- [Stratified Graphical Models - Context-Specific Independence in Graphical Models](https://mlsanity.com/paper/1309.6415/) (2013)
- [Context-specific independence in graphical log-linear models](https://mlsanity.com/paper/1409.2713/) (2014)

## Built on by (most cited first, 1 of 1)

- [Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation](https://mlsanity.com/paper/2507.19368/) (2025)

## Abstract (arXiv)

We consider the problem of explaining a class of tractable deep probabilistic models, the Sum-Product Networks (SPNs) and present an algorithm ExSPN to generate explanations. To this effect, we define the notion of a context-specific independence tree(CSI-tree) and present an iterative algorithm that converts an SPN to a CSI-tree. The resulting CSI-tree is both interpretable and explainable to the domain expert. We achieve this by extracting the conditional independencies encoded by the SPN and approximating the local context specified by the structure of the SPN. Our extensive empirical evaluations on synthetic, standard, and real-world clinical data sets demonstrate that the CSI-tree exhibits superior explainability.