通过专家聚合实现自适应贝叶斯在线学习，提升不确定性预测能力。
Adaptive Bayesian Online Learning via Expert Aggregation
- 将贝叶斯更新规则视为专家，按预测损失动态聚合
- 在在线共形推断和高斯过程回归中均实现最优性能
- 适合需要实时不确定性建模的流数据场景
贝叶斯在线学习能对数据流提供带不确定性的预测，但其性能依赖于学习率、先验分布和变分族等推断选择，这些通常在看到数据流前固定。本文将贝叶斯更新规则视为专家，根据序列预测损失进行聚合。证明了聚合结果在事后与最优专家竞争，聚合代价由每轮评估方式决定。在在线共形推断和高斯过程回归中实例化该框架：共形推断应用得到平滑的自适应共形推断版本，具有长期随机覆盖性；高斯过程应用给出累积预测KL散度风险的泛化界，并在未知霍尔德光滑度下实现对数因子内的自适应。实验表明，聚合器可跟踪强专家而无需事先知晓最优专家。
原文摘要 · Abstract (English)
Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream. We address this by treating Bayesian update rules as experts and aggregating the Bayesian experts according to sequential predictive losses. We prove that the resulting aggregate competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. We instantiate the framework in online conformal inference and Gaussian process regression. The conformal inference application yields a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage, while the Gaussian process application gives an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown Hölder smoothness up to logarithmic factors. Experiments show that the aggregate tracks strong experts without oracle expert selection.
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