Robust Leave-One-Out Cross-Validation for High-Dimensional Bayesian Models
提出一种新的混合估计方法，用于计算贝叶斯留一法交叉验证准则，保证估计量的渐近方差有限，在高维问题和有强影响观测值时更稳健高效，计算成本仅相当于拟合一次原模型。
Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the Bayesian context, importance sampling provides a possible solution but classical approaches can easily produce estimators whose asymptotic variance is infinite, making them potentially unreliable. Here we propose and analyze a novel mixture estimator to compute Bayesian LOO-CV criteria. Our method retains the simplicity and computational convenience of classical approaches, while guaranteeing finite asymptotic variance of the resulting estimators. Both theoretical and numerical results are provided to illustrate the improved robustness and efficiency. The computational benefits are particularly significant in high-dimensional problems, allowing to perform Bayesian LOO-CV for a broader range of models, and datasets with highly influential observations. The proposed methodology is easily implementable in standard probabilistic programming software and has a computational cost roughly equivalent to fitting the original model once. Supplementary materials for this article are available online.