cfid-package {cfid}

The cfid package

Description

Identification of Counterfactual Queries in Causal Models

Details

This package provides tools necessary for identifying counterfactual queries in causal models. Causal graphs, counterfactual variables, and counterfactual conjunctions are defined via simple interfaces.

Counterfactuals

In simple terms, counterfactual are statements involving multiple conceptual "worlds" where the observed state of the worlds is different. As an example, consider two variables, Y = "headache", and X = "aspirin". A counterfactual statement could be "If I have a headache and did not take aspirin, would I not have a headache, had I taken aspirin instead". This statement involves two worlds: the real or "actual" world, where aspirin was not taken, and a hypothetical world, where it was taken. In more formal terms, this statement involves a counterfactual variable Y_x that attains two different values in two different worlds, forming a counterfactual conjunction: y_x \wedge y'_{x'}, where y and y' are two different values of Y, and x and x' are two different values of X.

Identifiability

Pearl's ladder of causation consists of the associational, interventional and counterfactual levels, with counterfactual being the highest level. The goal of identification is to find a transformation of a higher level query into a lower level one. For the interventional case, this transformation is known as causal effect identifiability, where interventional distributions are expressed in terms of observational quantities. Tools for this type of identification are readily available, such as in the causaleffect, dagitty, pcalg, and dosearch packages. Transformation from the highest counterfactual level, is more difficult, both conceptually and computationally, since to reach the observational level, we must first find a transformation of our counterfactual query into a interventional query, and then transform this yet again to observational. Also, there transformations may not always exist, for example in the presence of latent unobserved confounders, meaning that the queries are non-identifiable. This package deals with the first transformation, i.e., expressing the counterfactual queries in terms of interventional queries (and observational, when possible), as well as the second one, transforming interventional distributions to observational quantities.

Algorithms

Identification is carried out in terms of G and P_* and where G is a directed acyclic graph (DAG) depicting the causal model in question (a causal graph for short), and P_* is the set of all interventional distributions in causal models inducing G. Identification is carried out by the ID* and IDC* algorithms by Shpitser and Pearl (2008) which aim to convert the input counterfactual probability into an expression which can be represented solely in terms of interventional distributions. These algorithms are sound and complete, meaning that their output is always correct, and in the case of a non-identifiable counterfactual, one can always construct a counterexample, witnessing non-identifiability.

Graphs

The causal graph associated with the causal model is given via a simple text-based interface, similar to dagitty package syntax. Directed edges are given as X -> Y, and bidirected edges as ⁠X <-> Y⁠, which is a shorthand notation for latent confounders. For more details on graph construction, see dag().

Counterfactual variables and conjunctions

Counterfactual variables are defined by their name, value and the conceptual world that they belong to. A world is defined by a unique set of actions (interventions) via the do-operator (Pearl, 2009). We can define the two counterfactual variables of the headache/aspirin example as follows:

cf(var = "Y", obs = 0, sub = c(X = 0))
cf(var = "Y", obs = 1, sub = c(X = 1))

Here, var defines the name of the variable, obs gives level the variable is assigned to (not the actual value), and sub defines the vector of interventions that define the counterfactual world. For more details, see counterfactual_variable(). Counterfactual conjunctions on the other hand, are simply counterfactual statements (variables) that are observed at the same time. For more details, see counterfactual_conjunction().

For complete examples of identifiable counterfactual queries, see identifiable(), which is the main function of the package.

References

Tikka, S. (2023). Identifying counterfactual queries with the R package cfid. The R Journal, 15(2):330–343.

Pearl, J. (1995) Causal diagrams for empirical research. Biometrika, 82(4):669–688.

Pearl, J. (2009) Causality: Models, Reasoning, and Inference. Cambridge University Press, 2nd edition.

Shpitser, I. and Pearl, J. (2007). What counterfactuals can be tested. In Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence, 352–359.

Shpitser, I. and Pearl, J. (2008). Complete identification methods for the causal hierarchy. Journal of Machine Learning Research, 9(64):1941–1979.

Makhlouf, K., Zhioua, S. and Palamidessi, C. (2021). Survey on causal-based machine learning fairness notions. arXiv:2010.09553