# A Taxonomy for Inference in Causal Model Families

arXiv: https://arxiv.org/abs/2110.12052 · HTML: https://mlsanity.com/paper/2110.12052/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 47 references that are in the map.
- First posted on arXiv 22 Oct 2021.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [Relating Graph Neural Networks to Structural Causal Models](https://mlsanity.com/paper/2109.04173/) (2021)
- [Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures](https://mlsanity.com/paper/1905.08550/) (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)
- [Visualizing and Understanding Sum-Product Networks](https://mlsanity.com/paper/1608.08266/) (2016)
- [Sum-product networks: A survey](https://mlsanity.com/paper/2004.01167/) (2020)
- [On the Relationship between Sum-Product Networks and Bayesian Networks](https://mlsanity.com/paper/1501.01239/) (2015)
- [Sum-Product-Quotient Networks](https://mlsanity.com/paper/1710.04404/) (2017)
- [Interventions and Counterfactuals in Tractable Probabilistic Models: Limitations of Contemporary Transformations](https://mlsanity.com/paper/2001.10905/) (2020)

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

- [Continual Causal Abstractions](https://mlsanity.com/paper/2212.12575/) (2022)

## Abstract (arXiv)

Neurally-parameterized Structural Causal Models in the Pearlian notion to causality, referred to as NCM, were recently introduced as a step towards next-generation learning systems. However, said NCM are only concerned with the learning aspect of causal inference but totally miss out on the architecture aspect. That is, actual causal inference within NCM is intractable in that the NCM won't return an answer to a query in polynomial time. This insight follows as corollary to the more general statement on the intractability of arbitrary SCM parameterizations, which we prove in this work through classical 3-SAT reduction. Since future learning algorithms will be required to deal with both high dimensional data and highly complex mechanisms governing the data, we ultimately believe work on tractable inference for causality to be decisive. We also show that not all ``causal'' models are created equal. More specifically, there are models capable of answering causal queries that are not SCM, which we refer to as partially causal models (PCM). We provide a tabular taxonomy in terms of tractability properties for all of the different model families, namely correlation-based, PCM and SCM. To conclude our work, we also provide some initial ideas on how to overcome parts of the intractability of causal inference with SCM by showing an example of how parameterizing an SCM with SPN modules can at least allow for tractable mechanisms. We hope that our impossibility result alongside the taxonomy for tractability in causal models can raise awareness for this novel research direction since achieving success with causality in real world downstream tasks will not only depend on learning correct models as we also require having the practical ability to gain access to model inferences.