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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.
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
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number of outliers
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 h
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 m
Causal inference is the process of capturing cause-effect relationship among variables. Most existing works focus on dealing with structured data, while mining causal relationship among factors from unstructured data, like text, has been less examine