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双层层级模型的分布无关预测集AI 解读

We consider the problem of constructing distribution-free prediction sets for data from two-layer hierarchical distributions. For iid data, prediction sets can be constructed using the method of conformal prediction. The validity of conformal prediction hinges on the exchangeability of the data, which does not hold when groups of observations come from distinct distributions, such as multiple observations on each patient in a medical database. We extend conformal methods to…

高斯模型中的通用似然比检验AI 解读

Summary The classical likelihood ratio test based on the asymptotic chi-squared distribution of the log-likelihood is one of the fundamental tools of statistical inference. A recent universal likelihood ratio test approach based on sample splitting provides valid hypothesis tests and confidence sets in any setting for which we can compute the split likelihood ratio statistic, or, more generally, an upper bound on the null maximum likelihood. The universal likelihood ratio…