模糊预测误差归因下贝叶斯与逆贝叶斯推断中的惊奇减少与消除

中文摘要 AI 辅助

在非平稳环境中，预测误差可能标志着环境变化或瞬时异常值，自适应系统必须跟踪此类变化而不对异常值过度反应。我们区分了惊奇减少（更新信念以拟合观测）与惊奇消除（削弱预测结构所施加的约束），并在贝叶斯与逆贝叶斯（BIB）推断中形式化两者。信念和似然更新源自共享消除强度的变分目标，该强度通过最小化候选更新后预测分布下的惊奇内生确定。在高斯情形下，消除使信念和似然方差相对于标准贝叶斯更新按共同因子扩大，保持比值不变。因此，BIB推迟了预测误差的归因，既不承诺潜在状态变化，也不承诺观测过程不确定性。消除强度作为候选被保留，并根据下一次观测的预测惊奇被维持或释放。在具有异常值和变化点的均值估计任务中，Sage-Husa型自适应卡尔曼滤波器、固定强度BIB变体或仅信念遗忘变体的任何扫描参数设置，在变化点跟踪和异常值后稳定性方面均未优于BIB。一个基于神谕的简化贝叶斯模型能更好地跟踪变化点，但在异常值后稳定性较差。尽管BIB不维护关于变化点或异常值的显式假设，它产生了事件依赖的动态。变化点后学习率增加，而异常值后消除被释放，这种增加被抑制。推迟归因并让后续观测区分响应，可能构成非平稳环境中自适应推断的一个原则。

英文摘要

In non-stationary environments, prediction errors may signal environmental change or transient outliers, and adaptive systems must track such changes without overreacting to outliers. We distinguish surprise reduction, which updates beliefs to fit observations, from surprise nullification, which weakens constraints imposed by the predictive structure, and formalize both within Bayesian and inverse Bayesian (BIB) inference. Belief and likelihood updates are derived from variational objectives sharing a nullification strength, determined endogenously by minimizing surprise under the candidate post-update predictive distribution. In the Gaussian case, nullification expands belief and likelihood variances by a common factor relative to standard Bayesian updating, leaving the ratio unchanged. BIB thus defers attribution of the prediction error, committing to neither latent-state change nor observation-process uncertainty. The nullification strength is carried over as a candidate and is maintained or released according to the predictive surprise of the next observation. In a mean estimation task with outliers and changepoints, no scanned parameter setting of a Sage-Husa-type adaptive Kalman filter, fixed-strength BIB variant, or belief-forgetting-only variant outperforms BIB in both changepoint tracking and post-outlier stability. An oracle-informed reduced Bayesian model tracks changepoints better but is less stable after outliers. Although BIB maintains no explicit hypotheses about changepoints or outliers, it generates event-dependent dynamics. The learning rate increases after changepoints, whereas after outliers, nullification is released, and this increase is suppressed. Deferring attribution and letting subsequent observations differentiate the responses may constitute a principle of adaptive inference in non-stationary environments.

发表机构

• Tokyo Denki University（东京都立大学）
• Osaka Metropolitan University（大阪公立大学）
• The University of Tokyo（东京大学）
• Utsunomiya University（宇都宫大学）
• Waseda University（早稻田大学）

机构由 AI 辅助整理，请以论文原文为准。