  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.
