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.

In this paper, we present two algorithms of this type and prove that both are consistent under the faithfulness assumption.

We will reflect this discussion in the paper.

Detecting large-scale system problems by mining console logs.

Our solution is application agnostic and relies only on the data collected for diagnosis. For the evaluation, we compare the proposed solution with a modified version of the PC algorithm and the state-of-the-art for root cause analysis.

Understanding causal relationships between variables is fundamental across scientific disciplines. Most causal discovery algorithms rely on two key assumptions: (i) all variables are observed, and (ii) the underlying causal graph is acyclic. While these assumptions simplify theoretical analysis, they are often violated in real-world systems, such as biological networks. Existing methods that account for confounders either assume linearity or struggle with scalability. To address these limitations, we propose DCCD-CONF, a novel framework for differentiable learning of nonlinear cyclic causal graphs in the presence of unmeasured confounders using interventional data. Our approach alternates between optimizing the graph structure and estimating the confounder distribution by maximizing the log-likelihood of the data. Through experiments on synthetic data and real-world gene perturbation datasets, we show that DCCD-CONF outperforms state-of-the-art methods in both causal graph recovery and confounder identification. Additionally, we also provide consistency guarantees for our framework, reinforcing its theoretical soundness.

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.

Learning directed acyclic graphs using both observational and interventional data is now a fundamentally important problem due to recent technological developments in genomics that generate such single-cell gene expression data at a very large scale. In order to utilize this data for learning gene regulatory networks, efficient and reliable causal inference algorithms are needed that can make use of both observational and interventional data. In this paper, we present two algorithms of this type and prove that both are consistent under the faithfulness assumption. These algorithms are interventional adaptations of the Greedy SP algorithm and are the first algorithms using both observational and interventional data with consistency guarantees. Moreover, these algorithms have the advantage that they are nonparametric, which makes them useful also for analyzing non-Gaussian data. In this paper, we present these two algorithms and their consistency guarantees, and we analyze their performance on simulated data, protein signaling data, and single-cell gene expression data.