The Causal-Neural Connection: Expressiveness, Learnability, and Inference

Abstract

One of the central elements of any causal inference is an object called structural causal model (SCM), which represents a collection of mechanisms and exogenous sources of random variation of the system under investigation (Pearl, 2000). An important property of many kinds of neural networks is universal approximability: the ability to approximate any function to arbitrary precision. Given this property, one may be tempted to surmise that a collection of neural nets is capable of learning any SCM by training on data generated by that SCM. In this paper, we show this is not the case by disentangling the notions of expressivity and learnability. Specifically, we show that the causal hierarchy theorem (Thm. 1, Bareinboim et al., 2020), which describes the limits of what can be learned from data, still holds for neural models. For instance, an arbitrarily complex and expressive neural net is unable to predict the effects of interventions given observational data alone. Given this result, we introduce a special type of SCM called a neural causal model (NCM), and formalize a new type of inductive bias to encode structural constraints necessary for performing causal inferences. Building on this new class of models, we focus on solving two canonical tasks found in the literature known as causal identification and estimation. Leveraging the neural toolbox, we develop an algorithm that is both sufficient and necessary to determine whether a causal effect can be learned from data (i.e., causal identifiability); it then estimates the effect whenever identifiability holds (causal estimation). Simulations corroborate the proposed approach.Preprint. Under review.

VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries

“…in the political or medical domain. We thus encourage anyone who uses VACA (or any other ML method for causal inference) to i) fully understand the model assumptions and to verify (up to the possible extend) that they are fulfilled; as well as ii) to be aware of the identifiability problem in counterfactual queries [49,45].…”

“…We stress that the causal graph can often be inferred from expert knowledge [52] or via one of the approaches for causal discovery [12,42]. With this analysis we aim to complement the concurrent line of research that theoretically studies the use of Neural Networks (NN) [45], and more recently GNNs [49], for causal inference.…”

VACA: Designing Variational Graph Autoencoders for Causal Queries

“…We stress that the causal graph can often be inferred from expert knowledge (Zheng and Kleinberg 2019) or via one of the approaches for causal discovery (Glymour, Zhang, and Spirtes 2019;Vowels, Camgoz, and Bowden 2021). With this analysis we aim to complement the concurrent line of research that theoretically studies the use of Neural Networks (NN) (Xia et al 2021), and more recently GNNs (Zečević et al 2021), for causal inference.…”