A Survey of Methods, Challenges and Perspectives in Causality

TL;DR

This paper performs an extensive overview of the theories and methods for Causality from different perspectives, with an emphasis on Deep Learning and the challenges met by the two domains.

Abstract

Deep Learning models have shown success in a large variety of tasks by extracting correlation patterns from high-dimensional data but still struggle when generalizing out of their initial distribution. As causal engines aim to learn mechanisms independent from a data distribution, combining Deep Learning with Causality can have a great impact on the two fields. In this paper, we further motivate this assumption. We perform an extensive overview of the theories and methods for Causality from different perspectives, with an emphasis on Deep Learning and the challenges met by the two domains. We show early attempts to bring the fields together and the possible perspectives for the future. We finish by providing a large variety of applications for techniques from Causality.

Figures (8)

• Figure 1: Example of Structural Causal Model (SCM) with two endogenous variables $V_1$ and $V_2$ and two exogenous variables $U_1$ and $U_2$. $\mathcal{F}$ is the set of mapping functions linking $V_1$, $V_2$ and $U_1$, $U_2$ together. $P(\mathbf{U})$ is the probability function defined over $U_1$ and $U_2$.
• Figure 2: Examples of Markov-equivalent and semi-Markovian (acyclic) DAG causal structures. (\ref{['fig:mr_dag_eq_1']}) a Markov-relative DAG modeling the causal effects of smoke (S) on the risk of cancer (C) with an intermediate variable corresponding to the presence of tar (T) in the lungs. (\ref{['fig:mr_dag_eq_2']}) a Markov-equivalent model that can be obtained with the same observational data interpreted differently. (\ref{['fig:mr_dag_exo']}) another Markov-relative DAG where exogenous variables forbid the previous interpretation. (\ref{['fig:mr_dag_conf']}) the same model where the unobserved variables have been merged to a single latent confounder: a genetic factor (G) causing both the tendency to smoke and the high risk of cancer. The last graph is semi-Markovian.
• Figure 3: Causal graphs involved in the computation of layer $\mathcal{L}_i$ queries. In an $\mathcal{L}_2$ query, the intervened variable (represented with a double edge) has its value forced into the graph and does not depend on its parent variables. For the $\mathcal{L}_3$ query, the factual world and the counterfactual world (variables with a *) are linked by the same exogenous factors. The observations from the factual worlds are used to estimate the $U_1$ and $env$ variables (abduction), then the counterfactual graph is intervened on (action) and the final estimation is computed (prediction).
• Figure 4: Examples of front-door and back-door paths. The hidden confounder $C$ is not known but the query $P(y|do(x))$ can be answered nonetheless using do-calculus under these graph structures.
• Figure 5: Example of causal graph. Smoke (S) is a parent cause of cancer (C), a hidden variable (G), corresponding to genetic factors, acts as a confounding effect. The model becomes identifiable if a causal link can be made with an intermediate variable (T), tar in the lungs.