Explainable Artificial Intelligence (XAI) is widely regarding as a cornerstone of trustworthy AI. Unfortunately, most work on XAI offers no guarantees of rigor. In high-stakes domains, e.g. uses of AI that impact humans, the lack of rigor of explanations can have disastrous consequences. Formal abductive explanations offer crucial guarantees of rigor and so are of interest in high-stakes uses of machine learning (ML). One drawback of abductive explanations is explanation size, justified by the cognitive limits of human decision-makers. Probabilistic abductive explanations (PAXps) address this limitation, but their theoretical and practical complexity makes their exact computation most often unrealistic. This paper proposes novel efficient algorithms for the computation of locally-minimal PXAps, which offer high-quality approximations of PXAps in practice. The experimental results demonstrate the practical efficiency of the proposed algorithms.
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