Each attribute combination, called an'arm', is associated with a Beta density from which the service's accuracy is sampled. We expect the GP to smooth the parameters of the Beta density over related arms to mitigate sparsity.

In contrast, we show that the computation of one PI-explanation for an NBC can be achieved in log-linear time, and that the same result also applies to the more general class of linear classifiers. Furthermore, we show that the enumeration of PI-explanations can be obtained with polynomial delay.

However, many real-world problems are "anti-causal" in the sense that

A key component to a MoE model is the routing (gating) strategy.

The ever increasing availability of cameras produces an endless stream of images.

Pre-trained machine learning (ML) predictions have been increasingly used to complement incomplete data to enable downstream scientific inquiries, but their naive integration risks biased inferences. Recently, multiple methods have been developed to provide valid inference with ML imputations regardless of prediction quality and to enhance efficiency relative to complete-case analyses. However, existing approaches are often limited to missing outcomes under a missing-completely-at-random (MCAR) assumption, failing to handle general missingness patterns under the more realistic missing-at-random (MAR) assumption. This paper develops a novel method which delivers valid statistical inference framework for general Z-estimation problems using ML imputations under the MAR assumption and for general missingness patterns. The core technical idea is to stratify observations by distinct missingness patterns and construct an estimator by appropriately weighting and aggregating pattern-specific information through a masking-and-imputation procedure on the complete cases. We provide theoretical guarantees of asymptotic normality of the proposed estimator and efficiency dominance over weighted complete-case analyses. Practically, the method affords simple implementations by leveraging existing weighted complete-case analysis software. Extensive simulations are carried out to validate theoretical results. The paper concludes with a brief discussion on practical implications, limitations, and potential future directions.