Causal structure based root cause analysis of outliers

TL;DR

This paper presents a formal method for root cause analysis of outliers in multivariate data using causal graphs, outlier scores, and Shapley values to attribute anomalies to causal ancestors.

Contribution

It introduces a systematic outlier scoring framework and a novel approach to attribute outliers to causal ancestors using Shapley values within a known DAG structure.

Findings

Defines a systematic outlier score based on causal structure

Introduces conditional outlier scores given parent variables

Uses Shapley values to attribute outliers to ancestors

Abstract

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.