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Score-based Integrated Gradient for Root Cause Explanations of Outliers

Phuoc Nguyen, Truyen Tran, Sunil Gupta, Svetha Venkatesh

TL;DR

This paper tackles root-cause explanations for outliers in high-dimensional causal networks by introducing SIREN, a score-based integrated gradient framework. SIREN estimates conditional score functions and performs diffusion-based path integration to attribute leaf-outlier scores to upstream latent noises, accommodating nonlinear and heteroscedastic causal models. The approach satisfies key Shapley axioms (dummy, efficiency, linearity) and derives an asymmetry property from the causal structure, enabling principled, uncertainty-aware attributions without requiring access to training data at inference. Empirical results on synthetic random graphs and real cloud service and supply chain datasets show that SIREN achieves superior attribution accuracy and computational efficiency compared with state-of-the-art baselines.

Abstract

Identifying the root causes of outliers is a fundamental problem in causal inference and anomaly detection. Traditional approaches based on heuristics or counterfactual reasoning often struggle under uncertainty and high-dimensional dependencies. We introduce SIREN, a novel and scalable method that attributes the root causes of outliers by estimating the score functions of the data likelihood. Attribution is computed via integrated gradients that accumulate score contributions along paths from the outlier toward the normal data distribution. Our method satisfies three of the four classic Shapley value axioms - dummy, efficiency, and linearity - as well as an asymmetry axiom derived from the underlying causal structure. Unlike prior work, SIREN operates directly on the score function, enabling tractable and uncertainty-aware root cause attribution in nonlinear, high-dimensional, and heteroscedastic causal models. Extensive experiments on synthetic random graphs and real-world cloud service and supply chain datasets show that SIREN outperforms state-of-the-art baselines in both attribution accuracy and computational efficiency.

Score-based Integrated Gradient for Root Cause Explanations of Outliers

TL;DR

This paper tackles root-cause explanations for outliers in high-dimensional causal networks by introducing SIREN, a score-based integrated gradient framework. SIREN estimates conditional score functions and performs diffusion-based path integration to attribute leaf-outlier scores to upstream latent noises, accommodating nonlinear and heteroscedastic causal models. The approach satisfies key Shapley axioms (dummy, efficiency, linearity) and derives an asymmetry property from the causal structure, enabling principled, uncertainty-aware attributions without requiring access to training data at inference. Empirical results on synthetic random graphs and real cloud service and supply chain datasets show that SIREN achieves superior attribution accuracy and computational efficiency compared with state-of-the-art baselines.

Abstract

Identifying the root causes of outliers is a fundamental problem in causal inference and anomaly detection. Traditional approaches based on heuristics or counterfactual reasoning often struggle under uncertainty and high-dimensional dependencies. We introduce SIREN, a novel and scalable method that attributes the root causes of outliers by estimating the score functions of the data likelihood. Attribution is computed via integrated gradients that accumulate score contributions along paths from the outlier toward the normal data distribution. Our method satisfies three of the four classic Shapley value axioms - dummy, efficiency, and linearity - as well as an asymmetry axiom derived from the underlying causal structure. Unlike prior work, SIREN operates directly on the score function, enabling tractable and uncertainty-aware root cause attribution in nonlinear, high-dimensional, and heteroscedastic causal models. Extensive experiments on synthetic random graphs and real-world cloud service and supply chain datasets show that SIREN outperforms state-of-the-art baselines in both attribution accuracy and computational efficiency.
Paper Structure (22 sections, 1 theorem, 32 equations, 3 figures, 4 tables, 1 algorithm)

This paper contains 22 sections, 1 theorem, 32 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Outlier Measures
  4. Functional Causal Models (FCMs)
  5. Additive Noise Model (ANM) hoyer2009nonlinearbuhlmann2014cam
  6. Location-scale Noise Model (LSN) huang2015generalized
  7. Root Cause Attributions
  8. Shapley Values
  9. Integrated Gradient (IG)
  10. Methods
  11. Score-based Integrated Gradient
  12. Score Function Estimator
  13. Conditional Score Matching (CSM)
  14. Sampling Data and Gradient Paths
  15. Fitting Mean Models
  16. ...and 7 more sections

Key Result

Theorem 1

Properties of the score-based outlier attribution. The score-based outlier attribution in Definition def:Score-based-Outlier-Attribution. satisfies the efficiency, linearity, dummy, and asymmetry axioms for the outlier attribution problem.

Figures (3)

  • Figure 1: Outlier measure difference between a target outlier $x$ and a reference point $x'$ as the difference in tail probabilities. For score-based outlier attribution, the expected contribution is the triangle area which is approximately the difference in tail probability $p(X\ge x')-p(X\ge x)$.
  • Figure 2: NDCG@$k$ ranking across different $k$ values.
  • Figure 3: NDCG@$k$ with varying the number of $k$.

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • proof