# Anomaly Attribution with Likelihood Compensation

arXiv: https://arxiv.org/abs/2208.10679 · HTML: https://mlsanity.com/paper/2208.10679/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 11 of 11)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Visualizing the Feature Importance for Black Box Models](https://mlsanity.com/paper/1804.06620/) (2018)
- [Why Does My Model Fail? Contrastive Local Explanations for Retail Forecasting](https://mlsanity.com/paper/1908.00085/) (2019)
- [Interpretable, Multidimensional, Multimodal Anomaly Detection with Negative Sampling for Detection of Device Failure](https://mlsanity.com/paper/2007.10088/) (2020)
- [Anomaly Detection in the Presence of Missing Values](https://mlsanity.com/paper/1809.01605/) (2018)
- [ACE -- An Anomaly Contribution Explainer for Cyber-Security Applications](https://mlsanity.com/paper/1912.00314/) (2019)

## Built on by (most cited first, 7 of 7)

- [The PetShop Dataset -- Finding Causes of Performance Issues across Microservices](https://mlsanity.com/paper/2311.04806/) (2023)
- [A Survey on Explainable Artificial Intelligence for Cybersecurity](https://mlsanity.com/paper/2303.12942/) (2023)
- [Generative Perturbation Analysis for Probabilistic Black-Box Anomaly Attribution](https://mlsanity.com/paper/2308.04708/) (2023)
- [Causal-discovery-based root-cause analysis and its application in time-series prediction error diagnosis](https://mlsanity.com/paper/2411.06990/) (2024)
- [Black-Box Anomaly Attribution](https://mlsanity.com/paper/2305.18440/) (2023)
- [A Bayesian explanation of machine learning models based on modes and functional ANOVA](https://mlsanity.com/paper/2411.02746/) (2024)
- [An Identifiable Cost-Aware Causal Decision-Making Framework Using Counterfactual Reasoning](https://mlsanity.com/paper/2505.08343/) (2025)

## Abstract (arXiv)

This paper addresses the task of explaining anomalous predictions of a black-box regression model. When using a black-box model, such as one to predict building energy consumption from many sensor measurements, we often have a situation where some observed samples may significantly deviate from their prediction. It may be due to a sub-optimal black-box model, or simply because those samples are outliers. In either case, one would ideally want to compute a ``responsibility score'' indicative of the extent to which an input variable is responsible for the anomalous output. In this work, we formalize this task as a statistical inverse problem: Given model deviation from the expected value, infer the responsibility score of each of the input variables. We propose a new method called likelihood compensation (LC), which is founded on the likelihood principle and computes a correction to each input variable. To the best of our knowledge, this is the first principled framework that computes a responsibility score for real valued anomalous model deviations. We apply our approach to a real-world building energy prediction task and confirm its utility based on expert feedback.