Quantifying the causal relationships from purely observational data between variables in a system is a problem that has attracted great attention in the fields of statistics and machine learning. Full knowledge of the causal relations allows predicting the outcome of direct manipulations on the system, which can generally only be known from interventional data obtained by performing experiments such as randomized controlled trials (Eberhardt and Scheines, 2007). Predicting the effect of such manipulations without the need of costly or infeasible experiments is of great practical relevance, specifically in the fields of computational biology (Sachs et al., 2005), medicine (Richens et al., 2020) or AI (Schölkopf, 2022), since a central question concerns how a complex system will react to some treatment or outside influence of the user. Pearl's rules of do-calculus (Pearl, 2000) allow computing the intervention distributions resulting from these external manipulations from the joint distribution of the set of random variables together with a Directed Acyclic Graph (DAG). The DAG represents the qualitative causal relationships among the variables; each node in the graph represents a variable and a directed edge indicates a direct causal effect. Probabilistic models that are based on such DAGs, commonly called causal Bayesian Networks (BNs), provide conventional grounds for probabilistic causal inference, due to their compact representation of the joint distribution and their intuitive graphical description of the causal structure.

Recommender systems play a key role in shaping modern web ecosystems. These systems alternate between (1) making recommendations (2) collecting user responses to these recommendations, and (3) retraining the recommendation algorithm based on this feedback. During this process the recommender system influences the user behavioral data that is subsequently used to update it, thus creating a feedback loop. Recent work has shown that feedback loops may compromise recommendation quality and homogenize user behavior, raising ethical and performance concerns when deploying recommender systems. To address these issues, we propose the Causal Adjustment for Feedback Loops (CAFL), an algorithm that provably breaks feedback loops using causal inference and can be applied to any recommendation algorithm that optimizes a training loss. Our main observation is that a recommender system does not suffer from feedback loops if it reasons about causal quantities, namely the intervention distributions of recommendations on user ratings. Moreover, we can calculate this intervention distribution from observational data by adjusting for the recommender system's predictions of user preferences. Using simulated environments, we demonstrate that CAFL improves recommendation quality when compared to prior correction methods.

Unobserved confounding is a major hurdle for causal inference from observational data. Confounders---the variables that affect both the causes and the outcome---induce spurious non-causal correlations between the two. Wang & Blei (2018) lower this hurdle with "the blessings of multiple causes," where the correlation structure of multiple causes provides indirect evidence for unobserved confounding. They leverage these blessings with an algorithm, called the deconfounder, that uses probabilistic factor models to correct for the confounders. In this paper, we take a causal graphical view of the deconfounder. In a graph that encodes shared confounding, we show how the multiplicity of causes can help identify intervention distributions. We then justify the deconfounder, showing that it makes valid inferences of the intervention. Finally, we expand the class of graphs, and its theory, to those that include other confounders and selection variables. Our results expand the theory in Wang & Blei (2018), justify the deconfounder for causal graphs, and extend the settings where it can be used.

Unobserved confounding is a central barrier to drawing causal inferences from observational data. Several authors have recently proposed that this barrier can be overcome in the case where one attempts to infer the effects of several variables simultaneously. In this paper, we present two simple, analytical counterexamples that challenge the general claims that are central to these approaches. In addition, we show that nonparametric identification is impossible in this setting. We discuss practical implications, and suggest alternatives to the methods that have been proposed so far in this line of work: using proxy variables and shifting focus to sensitivity analysis.

Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well-suited for evaluating graphs that are used for computing interventions. Instead of DAGs it is also possible to compare CPDAGs, completed partially directed acyclic graphs that represent Markov equivalence classes. Since it differs significantly from the popular Structural Hamming Distance (SHD), the SID constitutes a valuable additional measure. We discuss properties of this distance and provide an efficient implementation with software code available on the first author's homepage (an R package is under construction).