Why Did This Model Forecast This Future? Information-Theoretic Saliency for Counterfactual Explanations of Probabilistic Regression Models

Abstract

We propose a post hoc saliency-based explanation framework for counterfactual reasoning in probabilistic multivariate time-series forecasting (regression) settings. Building upon Miller's framework of explanations derived from research in multiple social science disciplines, we establish a conceptual link between counterfactual reasoning and saliency-based explanation techniques. To address the lack of a principled notion of saliency, we leverage a unifying definition of information-theoretic saliency grounded in preattentive human visual cognition and extend it to forecasting settings. Specifically, we obtain a closed-form expression for commonly used density functions to identify which observed timesteps appear salient to an underlying model in making its probabilistic forecasts. We empirically validate our framework in a principled manner using synthetic data to establish ground-truth saliency that is unavailable for real-world data. Finally, using real-world data and forecasting models, we demonstrate how our framework can assist domain experts in forming new data-driven hypotheses about the causal relationships between features in the wild.