How to ensure fairness in algorithmic decision making models is an important task in machine learning [12,15]. Over the past years, many researchers have been devoted to the design of fair classification algorithms withrespecttoapre-defined protected attribute,suchasraceorsex,anda decision task/model, such as hiring [1,11,24]. In particular,one line of the work istoincorporate fairness constraints into classic learning algorithms tobuild fair classifiers from potentially biased data [4,13,29,31-33]. Most of previous research generally focuses on a single decision model.

Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions. We here show that identifiability can still be achieved with unobserved causal variables, given a generalized notion of faithfulness. Our results guarantee that we can recover the latent causal model up to an equivalence class and predict the effect of unseen combinations of interventions, in the limit of infinite data. We implement our causal disentanglement framework by developing an autoencoding variational Bayes algorithm and apply it to the problem of predicting combinatorial perturbation effects in genomics.

The challenge of learning the causal structure underlying a certain phenomenon is undertaken by connecting the set of conditional independences (CIs) readable from the observational data, on the one side, with the set of corresponding constraints implied over the graphical structure, on the other, which are tied through a graphical criterion known as d-separation (Pearl, 1988). In this paper, we investigate the more general scenario where multiple observational and experimental distributions are available. We start with the simple observation that the invariances given by CIs/d-separation are just one special type of a broader set of constraints, which follow from the careful comparison of the different distributions available. Remarkably, these new constraints are intrinsically connected with do-calculus (Pearl, 1995) in the context of soft-interventions. We introduce a novel notion of interventional equivalence class of causal graphs with latent variables based on these invariances, which associates each graphical structure with a set of interventional distributions that respect the do-calculus rules. Given a collection of distributions, two causal graphs are called interventionally equivalent if they are associated with the same family of interventional distributions, where the elements of the family are indistinguishable using the invariances obtained from a direct application of the calculus rules. We introduce a graphical representation that can be used to determine if two causal graphs are interventionally equivalent. We provide a formal graphical characterization of this equivalence. Finally, we extend the FCI algorithm, which was originally designed to operate based on CIs, to combine observational and interventional datasets, including new orientation rules particular to this setting.

The challenge of generalizing causal knowledge across different environments is pervasive in scientific explorations, including in AI, ML, and Data Science. Experiments are usually performed in one environment (e.g., in a lab, on Earth) with the intent, almost invariably, of being used elsewhere (e.g., outside the lab, on Mars), where the conditions are likely to be different. In the causal inference literature, this generalization task has been formalized under the rubric of transportability (Pearl and Bareinboim, 2011), where a number of criteria and algorithms have been developed for various settings. Despite the generality of such results, transportability theory has been confined to atomic, do()-interventions. In practice, many real-world applications require more complex, stochastic interventions; for instance, in reinforcement learning, agents need to continuously adapt to the changing conditions of an uncertain and unknown environment. In this paper, we extend transportability theory to encompass these more complex types of interventions, which are known as soft, both relative to the input as well as the target distribution of the analysis. Specifically, we develop a graphical condition that is both necessary and sufficient for deciding soft-transportability. Second, we develop an algorithm to determine whether a non-atomic intervention is computable from a combination of the distributions available across domains. As a corollary, we show that the $\sigma$-calculus is complete for the task of soft-transportability.

One fundamental problem in the empirical sciences is of reconstructing the causal structure that underlies a phenomenon of interest through observation and experimentation. While there exists a plethora of methods capable of learning the equivalence class of causal structures that are compatible with observations, it is less well-understood how to systematically combine observations and experiments to reconstruct the underlying structure. In this paper, we investigate the task of structural learning in non-Markovian systems (i.e., when latent variables affect more than one observable) from a combination of observational and soft experimental data when the interventional targets are unknown. Using causal invariances found across the collection of observational and interventional distributions (not only conditional independences), we define a property called psi-Markov that connects these distributions to a pair consisting of (1) a causal graph D and (2) a set of interventional targets I. Building on this property, our main contributions are two-fold: First, we provide a graphical characterization that allows one to test whether two causal graphs with possibly different sets of interventional targets belong to the same psi-Markov equivalence class. Second, we develop an algorithm capable of harnessing the collection of data to learn the corresponding equivalence class. We then prove that this algorithm is sound and complete, in the sense that it is the most informative in the sample limit, i.e., it discovers as many tails and arrowheads as can be oriented within a psi-Markov equivalence class.

Despite the multifaceted recent advances in interventional causal representation learning (CRL), they primarily focus on the stylized assumption of single-node interventions.