Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, however, this assumption is almost always violated due to distribution shifts between environments. Although valuable learning signals can be provided by heterogeneous data from changing distributions, it is also known that learning under arbitrary (adversarial) changes is impossible. Causality provides a useful framework for modeling distribution shifts, since causal models encode both observational and interventional distributions. In this work, we explore the sparse mechanism shift hypothesis which posits that distribution shifts occur due to a small number of changing causal conditionals. Motivated by this idea, we apply it to learning causal structure from heterogeneous environments, where i.i.d. data only allows for learning an equivalence class of graphs without restrictive assumptions. We propose the Mechanism Shift Score (MSS), a score-based approach amenable to various empirical estimators, which provably identifies the entire causal structure with high probability if the sparse mechanism shifts hypothesis holds. Empirically, we verify behavior predicted by the theory and compare multiple estimators and score functions to identify the best approaches in practice. Compared to other methods, we show how MSS bridges a gap by both being nonparametric as well as explicitly leveraging sparse changes.

As data are generated more and more from multiple disparate sources, multiview data sets, where each sample has features in distinct views, have grown in recent years. However, no comprehensive package exists that enables non-specialists to use these methods easily. mvlearn is a Python library which implements the leading multiview machine learning methods. Its simple API closely follows that of scikit-learn for increased ease-of-use. The package can be installed from Python Package Index (PyPI) and the conda package manager and is released under the MIT open-source license. The documentation, detailed examples, and all releases are available at https://mvlearn.github.io/.