Mediation analysis (Robins & Greenland 1992, Pearl 2001, Imai, Keele & Tingley 2010, Tchetgen Tchetgen & Shpitser 2012) provides a principled framework for investigating causal mechanisms by decomposing the effect of a treatment A on an outcome Y into pathways operating through a mediator of interest M. Classical mediation analysis focuses on the natural indirect effect, corresponding to the pathway from Ato Y through M, and the natural direct effect, corresponding to pathways not through M. These estimands are well understood when a single mediator is present and strong identification assumptions hold. However, in many applications, there exist multiple intermediate variables between treatment and outcome. In such settings, conventional mediation analysis typically requires the absence of treatment-induced mediator-outcome confounders--often referred to as recanting witnesses--as well as the absence of unmeasured confounding. Under these circumstances, commonly used identification assumptions such as sequential ignorability (Imai, Keele & Yamamoto 2010) or nonparametric structural equation models with independent errors (NPSEM-IE) (Pearl 2009) no longer suffice to identify natural indirect effects (Avin et al. 2005, Tchetgen Tchetgen & VanderWeele 2014). Figure 1 illustrates this issue: the recanting witness D is directly affected by A and simultaneously confounds the relationship between M and Y. Such treatment-induced confounding is common in epidemiologic studies, particularly when the mediator of interest occurs long after the treatment initiation (Robins 1999). A motivating example arises in studies of preterm birth. Mediation analysis has been widely used to explore whether adequate prenatal care (A) reduces the risk of preterm birth (Y) through preeclampsia (M) (Vansteelandt & VanderWeele 2012, VanderWeele et al. 2014, Xia & Chan 2023).

Causal mediation analysis provides techniques for defining and estimating effects that may be endowed with mechanistic interpretations. With many scientific investigations seeking to address mechanistic questions, causal direct and indirect effects have garnered much attention. The natural direct and indirect effects, the most widely used among such causal mediation estimands, are limited in their practical utility due to stringent identification requirements. Accordingly, considerable effort has been invested in developing alternative direct and indirect effect decompositions with relaxed identification requirements. Such efforts often yield effect definitions with nuanced and challenging interpretations. By contrast, relatively limited attention has been paid to relaxing the identification assumptions of the natural direct and indirect effects. Motivated by a secondary aim of a recent non-randomized vaccine prospective cohort study (NCT05168813), we present a set of relaxed conditions under which the natural direct effect is identifiable in spite of unobserved baseline confounding of the exposure-mediator pathway; we use this result to investigate the effect mediated by putative immune correlates of protection. Relaxing the commonly used but restrictive cross-world counterfactual independence assumption, we discuss strategies for evaluating the natural direct effect in non-randomized settings that arise in the analysis of vaccine studies. We revisit prior studies of semi-parametric efficiency theory to demonstrate the construction of flexible, multiply robust estimators of the natural direct effect and discuss efficient estimation strategies that do not place restrictive modeling assumptions on nuisance functions.

To design an efficient intervention, decision-makers need not only to estimate the total effect of the intervention, but also understand the underlying causal mechanisms driving this effect.

We next discuss two lines of related literature.

A popular class of analysis methods, often called structural analysis, aims to extract this information using probing classifiers that predict linguistic properties from representations of trained models (e.g., Adi et al., 2017; Conneau et al., 2018; Hupkes et al., 2018; Tenney et al., 2019).

We next discuss two lines of related literature.

To design an efficient intervention, decision-makers need not only to estimate the total effect of the intervention, but also understand the underlying causal mechanisms driving this effect.

As machine learning models become increasingly embedded in decision-making systems, the ability to "unlearn" targeted data or features is crucial for enhancing model adaptability, fairness, and privacy in models which involves expensive training. To effectively guide machine unlearning, a thorough testing is essential. Existing methods for verification of machine unlearning provide limited insights, often failing in scenarios where the influence is indirect. In this work, we propose CAFÉ, a new causality based framework that unifies datapoint- and feature-level unlearning for verification of black-box ML models. CAFÉ evaluates both direct and indirect effects of unlearning targets through causal dependencies, providing actionable insights with fine-grained analysis. Our evaluation across five datasets and three model architectures demonstrates that CAFÉ successfully detects residual influence missed by baselines while maintaining computational efficiency.