As the amount and complexity of available data increases, the need for robust statistical learning becomes more pressing. To enhance resilience against model misspecification, the generalized posterior inference method adjusts the likelihood term by exponentiating it with a learning rate, thereby fine-tuning the dispersion of the posterior distribution. This study proposes a computationally efficient strategy for selecting an appropriate learning rate. The proposed approach builds upon the generalized posterior calibration (GPC) algorithm, which is designed to select a learning rate that ensures nominal frequentist coverage. This algorithm, which evaluates the coverage probability using bootstrap samples, has high computational costs because of the repeated posterior simulations needed for bootstrap samples. To address this limitation, the study proposes an algorithm that combines elements of the GPC algorithm with the sequential Monte Carlo (SMC) sampler. By leveraging the similarity between the learning rate in generalized posterior inference and the inverse temperature in SMC sampling, the proposed algorithm efficiently calibrates the posterior distribution with a reduced computational cost. For demonstration, the proposed algorithm was applied to several statistical learning models and shown to be significantly faster than the original GPC.

翻译：随着可用数据量与复杂度的增长，对稳健统计学习的需求日益迫切。为增强模型误设下的鲁棒性，广义后验推断方法通过对似然项进行学习率指数化调整，从而微调后验分布的离散程度。本研究提出了一种计算高效的策略以选取合适的学习率。所提方法基于广义后验校准算法构建，该算法旨在选择能确保名义频率覆盖度的学习率。由于需要通过自助样本评估覆盖概率，且每个自助样本均需重复后验模拟，原算法计算成本高昂。为突破此局限，本研究提出一种融合广义后验校准算法与序贯蒙特卡洛采样器特性的新算法。通过利用广义后验推断中的学习率与序贯蒙特卡洛采样中逆温度的相似性，所提算法能以更低计算成本高效校准后验分布。为验证效果，该算法被应用于若干统计学习模型，结果显示其计算速度显著优于原始广义后验校准算法。