  Artificial Intelligence (AI) is often an integral part of modern decision
support systems. The best-performing predictive models used in AI-based
decision support systems lack transparency. Explainable Artificial Intelligence
(XAI) aims to create AI systems that can explain their rationale to human
users. Local explanations in XAI can provide information about the causes of
individual predictions in terms of feature importance. However, a critical
drawback of existing local explanation methods is their inability to quantify
the uncertainty associated with a feature's importance. This paper introduces
an extension of a feature importance explanation method, Calibrated
Explanations, previously only supporting classification, with support for
standard regression and probabilistic regression, i.e., the probability that
the target is above an arbitrary threshold. The extension for regression keeps
all the benefits of Calibrated Explanations, such as calibration of the
prediction from the underlying model with confidence intervals, uncertainty
quantification of feature importance, and allows both factual and
counterfactual explanations. Calibrated Explanations for standard regression
provides fast, reliable, stable, and robust explanations. Calibrated
Explanations for probabilistic regression provides an entirely new way of
creating probabilistic explanations from any ordinary regression model,
allowing dynamic selection of thresholds. The method is model agnostic with
easily understood conditional rules. An implementation in Python is freely
available on GitHub and for installation using both pip and conda, making the
results in this paper easily replicable.
