Navigating Time's Possibilities: Plausible Counterfactual Explanations for Multivariate Time-Series Forecast through Genetic Algorithms

Gianlucca Zuin; Adriano Veloso

cs.LGMar 1, 2026

Navigating Time's Possibilities: Plausible Counterfactual Explanations for Multivariate Time-Series Forecast through Genetic Algorithms

Authors: Gianlucca Zuin, Adriano Veloso

Organizations: Universidade Federal de Minas Gerais, C.S. Dept. Belo Horizonte, Brazil. · Kunumi. Belo Horizonte, Brazil.

Abstract

Counterfactual learning has become promising for understanding and modeling causality in complex and dynamic systems. This paper presents a novel method for counterfactual learning in the context of multivariate time series analysis and forecast. The primary objective is to uncover hidden causal relationships and identify potential interventions to achieve desired outcomes. The proposed methodology integrates genetic algorithms and rigorous causality tests to infer and validate counterfactual dependencies within temporal sequences. More specifically, we employ Granger causality to enhance the reliability of identified causal relationships, rigorously assessing their statistical significance. Then, genetic algorithms, in conjunction with quantile regression, are used to exploit these intricate causal relationships to project future scenarios. The synergy between genetic algorithms and causality tests ensures a thorough exploration of the temporal dynamics present in the data, revealing hidden dependencies and enabling the projection of outcomes under hypothetical interventions. We evaluate the performance of our algorithm on real-world data, showcasing its ability to handle complex causal relationships, revealing meaningful counterfactual insights, and allowing for the prediction of outcomes under hypothetical interventions.

Figures & tables

Fig. 1 : Alkaline Closed Loop vacuum system.

Model	MAE	MSE	$\text{R}^{2}$	Training Time (s)	Inference Time (s)
lightGBM	0.889	2.210	0.505	37.81	2.55
Linear Reg.	1.055	2.375	0.401	6.88	2.03
Elastic Net	1.082	2.179	0.393	9.52	2.17
SVR	1.393	5.398	0.183	432.65	529.39
LSTM	1.288	3.432	0.074	1405.32	7.76
LSTM+Bias	1.259	3.563	0.108	544.65	7.26s

TABLE I : Model comparison and predictive performance.

Panel of Figure 3 — Fig. 2 : Prediction and ground-truth values during cross-validation for a subset of the data.

Fig. 3 : Granger Causality Heatmap. Darker cells are associated with a stronger relationship with statistically significant pairs being marked.

Fig. 4 : Quantile forecasts for an actionable variables and some possible future pathways. Solid lines represent the historical values, while dashed lines illustrate the possible futures. The red dashed line highlights the most likely pathway. Specifically, values in the range [1.84, 1.98] are plausible for 15 seconds (5 steps) into the future.

Panel of Figure 6 — Fig. 5 : Population fitness during the GA execution projecting a plausible return from a near vacuum break. While searching for a near future where the pressure level reaches 5.0 Pa. The solution found lies in the range between 4.0 Pa and 6.0 Pa, satisfying the constraint of recovering from a vacuum break.

Fig. 6 : Forecast of a future that enables the system to recover from a near vacuum break and satisfies the desired counterfactual explanation. Scenario likelihood: 42.9%. Projected Pressure: 5.87 Pa.

Counterfactual Prediction

Counterfactual prediction estimates outcomes under hypothetical interventions using observed data and assumptions about how systems generate outcomes.

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ConTex: Reformulating Counterfactual Generation For Time Series Forecasting

Jan Voets, Hasan Tercan, Tobias Meisen, Sebastian Baum

Institute for Technologies and Management of Digital Transformation University of Wuppertal

Explainable Time Series Forecasting Counterfactual Explanations Causal Counterfactual Generation Time Series Forecasting Graph Counterfactual Explanations Counterfactual Learning

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Decision-making with deep learning-based time series forecasting requires not only accurate predictions but also actionable insights. However, current architectures do not inherently provide such information. Specifically, guidance is needed on how current conditions must be modified to shift from a predicted outcome to a desired future scenario. Counterfactual explanations provide a natural framework for this task, as they represent minimal input changes that alter the model's prediction, indicating when and how intervention is required. Existing approaches rely on instance-wise optimization, leading to inconsistency across instances, high computational costs, and limited applicability in real-time settings. To address these limitations, we reformulate counterfactual generation for time series forecasting as the problem of learning a globally consistent intervention strategy, allowing counterfactuals to be generated through a single shared function. We propose Counterfactual Time Series Explanations (ConTex), a model-agnostic, decomposed architecture comprising a temporal context encoder and a conditional encoder, followed by two heads that capture interventions in terms of temporal relevance and modification strength. This structure overcomes the instability and inconsistency of instance-based approaches by producing targeted, interpretable interventions across time and feature dimensions in a single forward pass, making it suitable for real-time applications. Across multiple forecasting architectures and benchmark datasets, ConTex achieves state-of-the-art validity while generating sparse counterfactuals that minimize the number of necessary interventions. Additionally, our approach reduces computational cost by at least 12-36x compared to instance-wise generation and supports real-time inference at approximately 0.007 seconds.

Abstract

Counterfactual Prediction

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