提出一种预测优先的在线隐马尔可夫模型推断方法，实现高效实时状态识别。
A Predictive View on Streaming Hidden Markov Models
- 以预测为导向，通过约束路径混合逼近后验分布
- 在固定假设预算下，用前向KL最优的S条路径混合实现准确预测
- 算法递归确定性执行，无需迭代或采样，适合实时场景
我们构建了一种面向流式隐马尔可夫模型的预测优先优化框架。不同于传统方法强调在完整生成模型下恢复全后验，我们假设存在可在线学习的分段预测模型，并保持对状态转移的固定先验。目标是在逐步识别潜在状态的同时维持精确的一步预测分布。由于可能的状态路径数量呈指数增长，精确滤波不可行。因此，我们将流式推断建模为预测分布空间中的约束投影问题：在固定假设预算下，用支持在S条路径上的前向KL最优混合近似全后验预测。解为归一化的前S名后验加权混合，为HMM的束搜索提供了理论基础。所得算法完全递归且确定性，采用闭式预测更新进行束式截断，无需EM或采样。在相同计算预算下与在线EM和序列蒙特卡洛的实验对比显示其具有竞争力的预序性能。
原文摘要 · Abstract (English)
We develop a predictive-first optimisation framework for streaming hidden Markov models. Unlike classical approaches that prioritise full posterior recovery under a fully specified generative model, we assume access to regime-specific predictive models whose parameters are learned online while maintaining a fixed transition prior over regimes. Our objective is to sequentially identify latent regimes while maintaining accurate step-ahead predictive distributions. Because the number of possible regime paths grows exponentially, exact filtering is infeasible. We therefore formulate streaming inference as a constrained projection problem in predictive-distribution space: under a fixed hypothesis budget, we approximate the full posterior predictive by the forward-KL optimal mixture supported on $S$ paths. The solution is the renormalised top-$S$ posterior-weighted mixture, providing a principled derivation of beam search for HMMs. The resulting algorithm is fully recursive and deterministic, performing beam-style truncation with closed-form predictive updates and requiring neither EM nor sampling. Empirical comparisons against Online EM and Sequential Monte Carlo under matched computational budgets demonstrate competitive prequential performance.
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