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Cause-and-effect relations are one of the most valuable types of knowledge sought after throughout the data-driven sciences since they translate into stable and generalizable explanations as well as efficient and robust decision-making capabilities. Inferring these relations from data, however, is a challenging task. Two of the most common barriers to this goal are known as confounding and selection biases. The former stems from the systematic bias introduced during the treat- ment assignment, while the latter comes from the systematic bias during the collection of units into the sample. In this paper, we consider the problem of identifiability of causal effects when both confounding and selection biases are simultaneously present. We first investigate the problem of identifiability when all the available data is biased. We prove that the algorithm proposed by [Bareinboim and Tian, 2015] is, in fact, complete, namely, whenever the algorithm returns a failure condition, no identifiability claim about the causal relation can be made by any other method. We then generalize this setting to when, in addition to the biased data, another piece of external data is available, without bias. It may be the case that a subset of the covariates could be measured without bias (e.g., from census). We examine the problem of identifiability when a combination of biased and unbiased data is available. We propose a new algorithm that subsumes the current state-of-the-art method based on the back-door criterion. 

Causal knowledge is sought after throughout data-driven fields due to its explanatory power and potential value to inform decision-making. If the targeted system is well-understood in terms of its causal components, one is able to design more precise and surgical interventions so as to bring certain desired outcomes about. The idea of leveraging the causal understand- ing of a system to improve decision-making has been studied in the literature under the rubric of structural causal bandits (Lee and Bareinboim, 2018). In this setting, (1) pulling an arm corresponds to performing a causal intervention on a set of variables, while (2) the associated rewards are governed by the underlying causal mechanisms. One key assumption of this work is that any observed variable (X) in the system is manipulable, which means that intervening and making do(X = x) is always realizable. In many real-world scenarios, however, this is a too stringent requirement. For instance, while scientific evidence may support that obesity shortens life, it’s not feasible to manipulate obesity directly, but, for example, by decreasing the amount of soda consumption (Pearl, 2018). In this paper, we study a relaxed version of the structural causal bandit problem when not all variables are manipulable. Specifically, we develop a procedure that takes as argument partially specified causal knowledge and identifies the possibly-optimal arms in structural bandits with non-manipulable variables. We further introduce an algorithm that uncovers non-trivial dependence structure among the possibly-optimal arms. Finally, we corroborate our findings with simulations, which shows that MAB solvers enhanced with causal knowledge and leveraging the newly discovered dependence structure among arms consistently outperform their causal-insensitive counterparts. 

Generalizing causal effects from a controlled experiment to settings beyond the particular study population is arguably one of the central tasks found in empirical circles. While a proper design and careful execution of the experiment would support, under mild conditions, the validity of inferences about the population in which the experiment was conducted, two challenges make the extrapolation step to different populations somewhat involved, namely, transportability and sampling selection bias. The former is concerned with disparities in the distributions and causal mechanisms between the domain (i.e., settings, population, environment) where the experiment is conducted and where the inferences are intended; the latter with distortions in the sample’s proportions due to preferential selection of units into the study. In this paper, we investigate the assumptions and machinery necessary for using \emph{covariate adjustment} to correct for the biases generated by both of these problems, and generalize experimental data to infer causal effects in a new domain. We derive complete graphical conditions to determine if a set of covariates is admissible for adjustment in this new setting. Building on the graphical characterization, we develop an efficient algorithm that enumerates all possible admissible sets with poly-time delay guarantee; this can be useful for when some variables are preferred over the others due to different costs or amenability to measurement. 

Randomized clinical trials (RCTs) like those conducted by the FDA provide medical practitioners with average effects of treatments, and are generally more desirable than observational studies due to their control of unobserved confounders (UCs), viz., latent factors that influence both treatment and recovery. However, recent results from causal inference have shown that randomization results in a subsequent loss of information about the UCs, which may impede treatment efficacy if left uncontrolled in practice (Bareinboim, Forney, and Pearl 2015). Our paper presents a novel experimental design that can be noninvasively layered atop past and future RCTs to not only expose the presence of UCs in a system, but also reveal patient- and practitioner-specific treatment effects in order to improve decision-making. Applications are given to personalized medicine, second opinions in diagnosis, and employing offline results in online recommender systems. 

We study the problem of identifying the best action in a sequential decision-making setting when the reward distributions of the arms exhibit a non-trivial dependence structure, which is governed by the underlying causal model of the domain where the agent is deployed. In this setting, playing an arm corresponds to intervening on a set of variables and setting them to specific values. In this paper, we show that whenever the underlying causal model is not taken into account during the decision-making process, the standard strategies of simultaneously intervening on all variables or on all the subsets of the variables may, in general, lead to suboptimal policies, regardless of the number of interventions performed by the agent in the environment. We formally acknowledge this phenomenon and investigate structural properties implied by the underlying causal model, which lead to a complete characterization of the relationships between the arms’ distributions. We leverage this characterization to build a new algorithm that takes as input a causal structure and finds a minimal, sound, and complete set of qualified arms that an agent should play to maximize its expected reward. We empirically demonstrate that the new strategy learns an optimal policy and leads to orders of magnitude faster convergence rates when compared with its causal-insensitive counterparts. 

Selection and confounding biases are the two most common impediments to the applicability of causal inference methods in large-scale settings. We generalize the notion of backdoor adjustment to account for both biases and leverage external data that may be available without selection bias (e.g., data from census). We introduce the notion of adjustment pair and present complete graphical conditions for identifying causal effects by adjustment. We further design an algorithm for listing all admissible adjustment pairs in polynomial delay, which is useful for researchers interested in evaluating certain properties of some admissible pairs but not all (common properties include cost, variance, and feasibility to measure). Finally, we describe a statistical estimation procedure that can be performed once a set is known to be admissible, which entails different challenges in terms of finite samples.