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Causal Discovery methods aim to identify a DAG structure that represents causal relationships from observational data. In this article, we stress that it is important to test such methods for robustness in practical settings. As our main example, we analyze the NOTEARS method, for which we demonstrate a lack of scale-invariance. We show that NOTEARS is a method that aims to identify a parsimonious DAG from the data that explains the residual variance. We conclude that NOTEARS is not suitable for identifying truly causal relationships from the data.
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We describe a formal approach to identify root causes of outliers observed in $n$ variables $X_1,dots,X_n$ in a scenario where the causal relation between the variables is a known directed acyclic graph (DAG). To this end, we first introduce a systematic way to define outlier scores. Further, we introduce the concept of conditional outlier score which measures whether a value of some variable is unexpected *given the value of its parents* in the DAG, if one were to assume that the causal structure and the corresponding conditional distributions are also valid for the anomaly. Finally, we quantify to what extent the high outlier score of some target variable can be attributed to outliers of its ancestors. This quantification is defined via Shapley values from cooperative game theory.
Domain adaptation (DA) arises as an important problem in statistical machine learning when the source data used to train a model is different from the target data used to test the model. Recent advances in DA have mainly been application-driven and have largely relied on the idea of a common subspace for source and target data. To understand the empirical successes and failures of DA methods, we propose a theoretical framework via structural causal models that enables analysis and comparison of the prediction performance of DA methods. This framework also allows us to itemize the assumptions needed for the DA methods to have a low target error. Additionally, with insights from our theory, we propose a new DA method called CIRM that outperforms existing DA methods when both the covariates and label distributions are perturbed in the target data. We complement the theoretical analysis with extensive simulations to show the necessity of the devised assumptions. Reproducible synthetic and real data experiments are also provided to illustrate the strengths and weaknesses of DA methods when parts of the assumptions of our theory are violated.
The problem of inferring the direct causal parents of a response variable among a large set of explanatory variables is of high practical importance in many disciplines. Recent work in the field of causal discovery exploits invariance properties of models across different experimental conditions for detecting direct causal links. However, these approaches generally do not scale well with the number of explanatory variables, are difficult to extend to nonlinear relationships, and require data across different experiments. Inspired by {em Debiased} machine learning methods, we study a one-vs.-the-rest feature selection approach to discover the direct causal parent of the response. We propose an algorithm that works for purely observational data, while also offering theoretical guarantees, including the case of partially nonlinear relationships. Requiring only one estimation for each variable, we can apply our approach even to large graphs, demonstrating significant improvements compared to established approaches.
The problem of inferring the direct causal parents of a response variable among a large set of explanatory variables is of high practical importance in many disciplines. Recent work exploits stability of regression coefficients or invariance properties of models across different experimental conditions for reconstructing the full causal graph. These approaches generally do not scale well with the number of the explanatory variables and are difficult to extend to nonlinear relationships. Contrary to existing work, we propose an approach which even works for observational data alone, while still offering theoretical guarantees including the case of partially nonlinear relationships. Our algorithm requires only one estimation for each variable and in our experiments we apply our causal discovery algorithm even to large graphs, demonstrating significant improvements compared to well established approaches.
Going beyond correlations, the understanding and identification of causal relationships in observational time series, an important subfield of Causal Discovery, poses a major challenge. The lack of access to a well-defined ground truth for real-world data creates the need to rely on synthetic data for the evaluation of these methods. Existing benchmarks are limited in their scope, as they either are restricted to a static selection of data sets, or do not allow for a granular assessment of the methods performance when commonly made assumptions are violated. We propose a flexible and simple to use framework for generating time series data, which is aimed at developing, evaluating, and benchmarking time series causal discovery methods. In particular, the framework can be used to fine tune novel methods on vast amounts of data, without overfitting them to a benchmark, but rather so they perform well in real-world use cases. Using our framework, we evaluate prominent time series causal discovery methods and demonstrate a notable degradation in performance when their assumptions are invalidated and their sensitivity to choice of hyperparameters. Finally, we propose future research directions and how our framework can support both researchers and practitioners.
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