Understanding causality is challenging and often complicated by changing causal relationships over time and across environments. Climate patterns, for example, shift over time with recurring seasonal trends, while also depending on geographical characteristics such as ecosystem variability. Existing methods for discovering causal graphs from time series either assume stationarity, do not permit both temporal and spatial distribution changes, or are unaware of locations with the same causal relationships. In this work, we therefore unify the three tasks of causal graph discovery in the non-stationary multi-context setting, of reconstructing temporal regimes, and of partitioning datasets and time intervals into those where invariant causal relationships hold. To construct a consistent score that forms the basis of our method, we employ the Minimum Description Length principle. Our resulting algorithm SPACETIME simultaneously accounts for heterogeneity across space and non-stationarity over time. Given multiple time series, it discovers regime changepoints and a temporal causal graph using non-parametric functional modeling and kernelized discrepancy testing. We also show that our method provides insights into real-world phenomena such as river-runoff measured at different catchments and biosphere-atmosphere interactions across ecosystems.

Identifying causal relationships is a cornerstone task in science, but most data-driven methods offer ambiguous results or require restrictive assumptions. Recent work on the basis of information theory shows promising results across many domains, but leaves open how to provably identify causal graphs. Here, we develop a general information-theoretic framework called TOPIC for causal discovery in topological order. TOPIC is based on the universal measure of Kolmogorov complexity and is fully identifiable. We show that TOPIC’s guarantees extend to both the i.i.d. and non-i.i.d. continuous settings. Our evaluations on continuous, time series, and interventional data show that TOPIC, using domain-specific approximations of Kolmogorov complexity, learns faithful topological orderings and frequently outperforms specialized methods.

Real-world datasets are often a combination of unobserved subpopulations that follow distinct causal generating processes. In an observational study, for example, participants may fall into unknown groups that either (a) respond effectively to a drug, or (b) show no response due to drug resistance. Not accounting for such heterogeneity then risks biased estimates of drug effectiveness. In this work, we formulate this setting through a causal mixture model, in which the data-generating process of each variable depends on latent group membership (a or b). Specifically, we model each variable as a mixture of structural causal equation models, where latent categorical (mixing) variables index assignment to subpopulations. Unlike prior work, the approach allows for multiple independent mixing variables, each affecting distinct sets of observed variables. To infer both the graph, mixing variables, and assignments jointly, we integrate mixture modeling into score-based causal discovery; show theoretically that the resulting scoring criterion is consistent; and demonstrate empirically that the resulting causal discovery approach discovers the causal model in synthetic and real-world evaluations.

Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured confounding variables. In practice, neither is likely to hold, and detecting confounding in non-i.i.d. settings poses a significant challenge. Motivated by this, we explore how to discover confounders from data in multiple environments with causal mechanism shifts. We show that the mechanism changes of observed variables can reveal which variable sets are confounded. Based on this idea, we propose an empirically testable criterion based on mutual information, show under which conditions it can identify confounding, and introduce CoCo to discover confounders from data in multiple contexts. In our experiments, we show that CoCo works well on synthetic and real-world data.

In numerous real-world domains, spanning from environmental monitoring to long-term medical studies, observations do not arrive in a single batch but rather over time in episodes. This challenges the traditional assumption in causal discovery of a single, observational dataset, not only because each episode may be a biased sample of the population but also because multiple episodes could differ in the causal interactions underlying the observed variables. We address these issues using notions of context switches and episodic selection bias, and introduce a framework for causal modeling of episodic data. We show under which conditions we can apply information-theoretic scoring criteria for causal discovery while preserving consistency. To in practice discover the causal model progressively over time, we propose the CONTINENT algorithm which, taking inspiration from continual learning, discovers the causal model in an online fashion without having to re-learn the model upon arrival of each new episode. Our experiments over a variety of settings including selection bias, unknown interventions, and network changes showcase that CONTINENT works well in practice and outperforms the baselines by a clear margin.

In many scientific applications, we observe a system in different conditions in which its components may change, rather than in isolation. In our work, we are interested in explaining the generating process of such a multi-context system using a finite mixture of causal mechanisms. Recent work shows that this causal model is identifiable from data, but is limited to settings where the sparse mechanism shift hypothesis holds and only a subset of the causal conditionals change. As this assumption is not easily verifiable in practice, we study the more general principle that mechanism shifts are independent, which we formalize using the algorithmic notion of independence. We introduce an approach for causal discovery beyond partially directed graphs using Gaussian Process models, and give conditions under which we provably identify the correct causal model. In our experiments, we show that our method performs well in a range of synthetic settings, on realistic gene expression simulations, as well as on real-world cell signaling data.

While invariance of causal mechanisms has inspired recent work in both robust machine learning and causal inference, causal mechanisms may also vary over domains due to, for example, population-specific differences, the context of data collection, or intervention. To discover invariant and changing mechanisms from data, we propose extending the algorithmic model for causation to mechanism changes and instantiating it using Minimum Description Length. In essence, for a continuous variable Y in multiple contexts C, we identify variables X as causal if the regression functions g : X → Y have succinct descriptions in all contexts. In empirical evaluations we show that our method, VARIO, finds invariant variable sets, reveals mechanism changes, and discovers causal networks, such as on real-world data that gives insight into the signaling pathways in human immune cells.