# Multi-SpaCE: Multi-Objective Subsequence-based Sparse Counterfactual Explanations for Multivariate Time Series Classification

arXiv: https://arxiv.org/abs/2501.04009 · HTML: https://mlsanity.com/paper/2501.04009/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 14 Dec 2024.

## Builds on (most cited first, 26 of 26)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Explainable AI (XAI): A Systematic Meta-Survey of Current Challenges and Future Opportunities](https://mlsanity.com/paper/2111.06420/) (2021)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [Benchmarking Deep Learning Interpretability in Time Series Predictions](https://mlsanity.com/paper/2010.13924/) (2020)
- [Explainable Artificial Intelligence (XAI) on TimeSeries Data: A Survey](https://mlsanity.com/paper/2104.00950/) (2021)
- [Instance-based Counterfactual Explanations for Time Series Classification](https://mlsanity.com/paper/2009.13211/) (2020)
- [Counterfactual Explanations for Machine Learning on Multivariate Time Series Data](https://mlsanity.com/paper/2008.10781/) (2020)
- [Explainable Artificial Intelligence: A Survey of Needs, Techniques, Applications, and Future Direction](https://mlsanity.com/paper/2409.00265/) (2024)
- [Explainable AI for Time Series via Virtual Inspection Layers](https://mlsanity.com/paper/2303.06365/) (2023)
- [Generating Sparse Counterfactual Explanations For Multivariate Time Series](https://mlsanity.com/paper/2206.00931/) (2022)
- [M-CELS: Counterfactual Explanation for Multivariate Time Series Data Guided by Learned Saliency Maps](https://mlsanity.com/paper/2411.02649/) (2024)
- [Plausible Counterfactuals: Auditing Deep Learning Classifiers with Realistic Adversarial Examples](https://mlsanity.com/paper/2003.11323/) (2020)
- [Shapelet-Based Counterfactual Explanations for Multivariate Time Series](https://mlsanity.com/paper/2208.10462/) (2022)
- [Fast, Interpretable, and Deterministic Time Series Classification With a Bag-of-Receptive-Fields](https://mlsanity.com/paper/2311.18029/) (2023)
- [TX-Gen: Multi-Objective Optimization for Sparse Counterfactual Explanations for Time-Series Classification](https://mlsanity.com/paper/2409.09461/) (2024)

## Built on by (most cited first, 3 of 3)

- [What-If Explanations Over Time: Counterfactuals for Time Series Classification](https://mlsanity.com/paper/2603.27792/) (2026)
- [GenFacts-Generative Counterfactual Explanations for Multi-Variate Time Series](https://mlsanity.com/paper/2509.20936/) (2025)
- [Counterfactual Explanation for Multivariate Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2511.06906/) (2025)

## Abstract (arXiv)

Deep Learning systems excel in complex tasks but often lack transparency, limiting their use in critical applications. Counterfactual explanations, a core tool within eXplainable Artificial Intelligence (XAI), offer insights into model decisions by identifying minimal changes to an input to alter its predicted outcome. However, existing methods for time series data are limited by univariate assumptions, rigid constraints on modifications, or lack of validity guarantees. This paper introduces Multi-SpaCE, a multi-objective counterfactual explanation method for multivariate time series. Using non-dominated ranking genetic algorithm II (NSGA-II), Multi-SpaCE balances proximity, sparsity, plausibility, and contiguity. Unlike most methods, it ensures perfect validity, supports multivariate data and provides a Pareto front of solutions, enabling flexibility to different end-user needs. Comprehensive experiments in diverse datasets demonstrate the ability of Multi-SpaCE to consistently achieve perfect validity and deliver superior performance compared to existing methods.