# chiSPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains

arXiv: https://arxiv.org/abs/2408.07545 · HTML: https://mlsanity.com/paper/2408.07545/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 19 of 19)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [A Characteristic Function Approach to Deep Implicit Generative Modeling](https://mlsanity.com/paper/1909.07425/) (2019)
- [Bayesian Learning of Sum-Product Networks](https://mlsanity.com/paper/1905.10884/) (2019)
- [Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models](https://mlsanity.com/paper/2102.10440/) (2021)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [On the Relationship between Sum-Product Networks and Bayesian Networks](https://mlsanity.com/paper/1501.01239/) (2015)
- [Characteristic Circuits](https://mlsanity.com/paper/2312.07790/) (2023)
- [On the Relative Expressiveness of Bayesian and Neural Networks](https://mlsanity.com/paper/1812.08957/) (2018)
- [Probabilistic Circuits That Know What They Don't Know](https://mlsanity.com/paper/2302.06544/) (2023)
- [High-dimensional Mixed Graphical Models](https://mlsanity.com/paper/1304.2810/) (2013)
- [Inference in Hybrid Networks: Theoretical Limits and Practical Algorithms](https://mlsanity.com/paper/1301.2288/) (2013)

## Built on by (most cited first, 3 of 3)

- [What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?](https://mlsanity.com/paper/2409.07953/) (2024)
- [Interpretable Neural Causal Models with TRAM-DAGs](https://mlsanity.com/paper/2503.16206/) (2025)
- [Context-specific Credibility-aware Multimodal Fusion with Conditional Probabilistic Circuits](https://mlsanity.com/paper/2603.26629/) (2026)

## Abstract (arXiv)

Causal inference in hybrid domains, characterized by a mixture of discrete and continuous variables, presents a formidable challenge. We take a step towards this direction and propose Characteristic Interventional Sum-Product Network (chiSPN) that is capable of estimating interventional distributions in presence of random variables drawn from mixed distributions. chiSPN uses characteristic functions in the leaves of an interventional SPN (iSPN) thereby providing a unified view for discrete and continuous random variables through the Fourier-Stieltjes transform of the probability measures. A neural network is used to estimate the parameters of the learned iSPN using the intervened data. Our experiments on 3 synthetic heterogeneous datasets suggest that chiSPN can effectively capture the interventional distributions for both discrete and continuous variables while being expressive and causally adequate. We also show that chiSPN generalize to multiple interventions while being trained only on a single intervention data.