Algorithmic syntactic causal identification

Dhurim Cakiqi, Max A Little

Keywords: Artificial intelligence, causal inference, category theory

Abstract:

Causal identification in causal Bayes nets (CBNs) is an important tool in causal inference allowing the derivation of interventional distributions from observational distributions
where this is possible in principle. However, most existing formulations of causal identification using techniques such as d-separation and do-calculus are expressed within the
mathematical language of classical probability theory on CBNs. However, there are many
causal settings where probability theory and hence current causal identification techniques
are inapplicable such as relational databases, dataflow programs such as hardware description languages, distributed systems and most modern machine learning algorithms. We
show that this restriction can be lifted by replacing the use of classical probability theory
with the alternative axiomatic foundation of symmetric monoidal categories. In this alternative axiomatization, we show how an unambiguous and clean distinction can be drawn
between the general syntax of causal models and any specific semantic implementation of
that causal model. This allows a purely syntactic algorithmic description of general causal
identification by a translation of recent formulations of the general ID algorithm through
fixing. Our description is given entirely in terms of the non-parametric ADMG structure
specifying a causal model and the algebraic signature of the corresponding monoidal category, to which a sequence of manipulations is then applied so as to arrive at a modified
monoidal category in which the desired, purely syntactic interventional causal model, is
obtained. We use this idea to derive purely syntactic analogues of classical back-door and
front-door causal adjustment, and illustrate an application to a more complex causal model.

Submission Number: 2