# Generating Sparse Counterfactual Explanations For Multivariate Time Series

arXiv: https://arxiv.org/abs/2206.00931 · HTML: https://mlsanity.com/paper/2206.00931/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 19 references that are in the map.
- First posted on arXiv 2 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [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)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Benchmarking Deep Learning Interpretability in Time Series Predictions](https://mlsanity.com/paper/2010.13924/) (2020)
- [Good Counterfactuals and Where to Find Them: A Case-Based Technique for Generating Counterfactuals for Explainable AI (XAI)](https://mlsanity.com/paper/2005.13997/) (2020)
- [Mobile Sensor Data Anonymization](https://mlsanity.com/paper/1810.11546/) (2018)
- [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)
- [CounteRGAN: Generating Realistic Counterfactuals with Residual Generative Adversarial Nets](https://mlsanity.com/paper/2009.05199/) (2020)
- [Conditional Generative Models for Counterfactual Explanations](https://mlsanity.com/paper/2101.10123/) (2021)
- [Sparsely Changing Latent States for Prediction and Planning in Partially Observable Domains](https://mlsanity.com/paper/2110.15949/) (2021)
- [Early Recognition of Ball Catching Success in Clinical Trials with RNN-Based Predictive Classification](https://mlsanity.com/paper/2107.02442/) (2021)

## Built on by (most cited first, 11 of 11)

- [Deep Backtracking Counterfactuals for Causally Compliant Explanations](https://mlsanity.com/paper/2310.07665/) (2023)
- [TX-Gen: Multi-Objective Optimization for Sparse Counterfactual Explanations for Time-Series Classification](https://mlsanity.com/paper/2409.09461/) (2024)
- [What-If Explanations Over Time: Counterfactuals for Time Series Classification](https://mlsanity.com/paper/2603.27792/) (2026)
- [Multi-SpaCE: Multi-Objective Subsequence-based Sparse Counterfactual Explanations for Multivariate Time Series Classification](https://mlsanity.com/paper/2501.04009/) (2024)
- [WARP-LCA: Efficient Convolutional Sparse Coding with Locally Competitive Algorithm](https://mlsanity.com/paper/2410.18794/) (2024)
- [Counterfactual Explanations for Time Series Should be Human-Centered and Temporally Coherent in Interventions](https://mlsanity.com/paper/2512.14559/) (2025)
- [Towards Explainable Land Cover Mapping: a Counterfactual-based Strategy](https://mlsanity.com/paper/2301.01520/) (2023)
- [On the Connection between Game-Theoretic Feature Attributions and Counterfactual Explanations](https://mlsanity.com/paper/2307.06941/) (2023)
- [Representation Learning of Multivariate Time Series using Attention and Adversarial Training](https://mlsanity.com/paper/2401.01987/) (2024)
- [SSET: Swapping-Sliding Explanation for Time Series Classifiers in Affect Detection](https://mlsanity.com/paper/2410.12996/) (2024)
- [GenFacts-Generative Counterfactual Explanations for Multi-Variate Time Series](https://mlsanity.com/paper/2509.20936/) (2025)

## Abstract (arXiv)

Since neural networks play an increasingly important role in critical sectors, explaining network predictions has become a key research topic. Counterfactual explanations can help to understand why classifier models decide for particular class assignments and, moreover, how the respective input samples would have to be modified such that the class prediction changes. Previous approaches mainly focus on image and tabular data. In this work we propose SPARCE, a generative adversarial network (GAN) architecture that generates SPARse Counterfactual Explanations for multivariate time series. Our approach provides a custom sparsity layer and regularizes the counterfactual loss function in terms of similarity, sparsity, and smoothness of trajectories. We evaluate our approach on real-world human motion datasets as well as a synthetic time series interpretability benchmark. Although we make significantly sparser modifications than other approaches, we achieve comparable or better performance on all metrics. Moreover, we demonstrate that our approach predominantly modifies salient time steps and features, leaving non-salient inputs untouched.