发表机构
Inha University（仁荷大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何改进贝叶斯在线学习，将其更新规则视为专家，按顺序预测损失聚合专家。通过在线共形推理和高斯过程回归实例化框架，得到平滑贝叶斯对应物及神谕不等式，实验显示聚合能跟踪强大专家且无需神谕专家选择。
AI 中文摘要
贝叶斯在线学习有望对数据流进行不确定性感知预测，但其性能取决于推理选择，如学习率、先验分布和变分族，这些通常在看到数据流之前就固定了。我们通过将贝叶斯更新规则视为专家，并根据顺序预测损失聚合贝叶斯专家来解决此问题。我们证明，所得聚合在由每个专家的每轮性能评估方式决定的聚合成本下，与事后最佳专家竞争。我们在在线共形推理和高斯过程回归中实例化该框架。共形推理应用产生具有长期随机覆盖的自适应共形推理的平滑贝叶斯对应物，而高斯过程应用在累积预测库尔贝克-莱布勒风险方面给出了一个神谕不等式，并适应未知的赫尔德平滑度直至对数因子。实验表明，聚合无需神谕专家选择就能跟踪强大专家。
英文摘要
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.
