Estimating causal effects from observational data is challenging, especially in the presence of latent confounders. Much work has been done on addressing this challenge, but most of the existing research ignores the bias introduced by the post-treatment variables. In this paper, we propose a novel method of joint Variational AutoEncoder (VAE) and identifiable Variational AutoEncoder (iVAE) for learning the representations of latent confounders and latent post-treatment variables from their proxy variables, termed CPTiVAE, to achieve unbiased causal effect estimation from observational data. We further prove the identifiability in terms of the representation of latent post-treatment variables. Extensive experiments on synthetic and semi-synthetic datasets demonstrate that the CPTiVAE outperforms the state-of-the-art methods in the presence of latent confounders and post-treatment variables. We further apply CPTiVAE to a real-world dataset to show its potential application.

In recent years, there has been increasing interest in causal reasoning for designing fair decision-making systems due to its compatibility with legal frameworks, interpretability for human stakeholders, and robustness to spurious correlations inherent in observational data, among other factors. The recent attention to causal fairness, however, has been accompanied with great skepticism due to practical and epistemological challenges with applying current causal fairness approaches in the literature. Motivated by the long-standing empirical work on causality in econometrics, social sciences, and biomedical sciences, in this paper we lay out the conditions for appropriate application of causal fairness under the "potential outcomes framework." We highlight key aspects of causal inference that are often ignored in the causal fairness literature. In particular, we discuss the importance of specifying the nature and timing of interventions on social categories such as race or gender. Precisely, instead of postulating an intervention on immutable attributes, we propose a shift in focus to their perceptions and discuss the implications for fairness evaluation. We argue that such conceptualization of the intervention is key in evaluating the validity of causal assumptions and conducting sound causal analysis including avoiding post-treatment bias. Subsequently, we illustrate how causality can address the limitations of existing fairness metrics, including those that depend upon statistical correlations. Specifically, we introduce causal variants of common statistical notions of fairness, and we make a novel observation that under the causal framework there is no fundamental disagreement between different notions of fairness. Finally, we conduct extensive experiments where we demonstrate our approach for evaluating and mitigating unfairness, specially when post-treatment variables are present.

Researchers often lack the necessary data to credibly estimate racial discrimination in policing. In particular, police administrative records lack information on civilians police observe but do not investigate. In this article, we show that if police racially discriminate when choosing whom to investigate, analyses using administrative records to estimate racial discrimination in police behavior are statistically biased, and many quantities of interest are unidentified--even among investigated individuals--absent strong and untestable assumptions. Using principal stratification in a causal mediation framework, we derive the exact form of the statistical bias that results from traditional estimation. We develop a bias-correction procedure and nonparametric sharp bounds for race effects, replicate published findings, and show the traditional estimator can severely underestimate levels of racially biased policing or mask discrimination entirely.