Counterfactual analysis is intuitively performed by humans on a daily basis
eg. "What should I have done differently to get the loan approved?". Such
counterfactual questions also steer the formulation of scientific hypotheses.
More formally it provides insights about potential improvements of a system by
inferring the effects of hypothetical interventions into a past observation of
the system's behaviour which plays a prominent role in a variety of industrial
applications. Due to the hypothetical nature of such analysis, counterfactual
distributions are inherently ambiguous. This ambiguity is particularly
challenging in continuous settings in which a continuum of explanations exist
for the same observation. In this paper, we address this problem by following a
hierarchical Bayesian approach which explicitly models such uncertainty. In
particular, we derive counterfactual distributions for a Bayesian Warped
Gaussian Process thereby allowing for non-Gaussian distributions and
non-additive noise. We illustrate the properties our approach on a synthetic
and on a semi-synthetic example and show its performance when used within an
algorithmic recourse downstream task.

通过采用贝叶斯层级模型来建模不确定性，本文解决了连续设置中对反事实分布的模棱两可性问题，特别是在贝叶斯变形高斯过程中，允许非高斯分布和非加法噪声，成功应用于一个合成和半合成的案例，并展示了在算法补救下游任务中的性能。