发表机构
Ruhr University Bochum; Radboud University Nijmegen（波鸿鲁尔大学; 拉德堡德大学奈梅亨分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究隐马尔可夫模型可识别性的计算复杂度，证明相关决策问题可在PSPACE内判定，且确定性变体对简单参数化族是coETR-难的。
AI 中文摘要
识别是从采样数据中恢复未知真实模型参数的任务。当除真实参数外的其他参数也产生相同的输出分布时，仅凭数据不足以恢复真实参数，因此该模型被称为不可识别的。我们研究隐马尔可夫模型（HMM）的可识别性问题：给定一个HMM，它是否可识别？现有关于HMM识别的工作建立了真实HMM可被识别的条件。然而，这些条件大多为充分条件而非必要条件，这意味着当模型不满足这些条件时，其可识别性仍无定论。我们转而采取计算视角：是否存在一个可靠且完备的算法来决定给定的HMM是否可识别，若存在，该决策问题的复杂度如何？我们考虑文献中各种可识别性概念所引发的决策问题，包括确定性、一般性、全局、局部、状态置换不变性以及有限字母表可识别性。我们证明所有这些问题的可判定性均在PSPACE内，通过归约到实数理论在其量词交替层次的不同级别。我们进一步证明，对于简单参数化族，确定性变体已经是coETR-难的（因此也是coNP-难的）。
英文摘要
Identification is the task of recovering the parameters of an unknown ground-truth model from sampled data. When parameters other than the ground truth induce the same output distribution, data alone does not provide enough information to recover the ground truth, and the model is thus called unidentifiable. We study the identifiability problem for hidden Markov models (HMMs): given an HMM, is it identifiable? Existing work on HMM identification establishes conditions under which the ground-truth HMM can be identified. However, most of these conditions are sufficient but not necessary, meaning that, when a model does not satisfy them, its identifiability remains inconclusive. We instead take a computational perspective: is there a sound and complete algorithm that decides whether a given HMM is identifiable, and if so, what is the complexity of this decision problem? We consider the decision problems arising from the various notions of identifiability in the literature, including deterministic, generic, global, local, state-permutation- invariant, and finite-alphabet identifiability. We show that all of these problems are decidable in PSPACE, via reductions to the theory of the reals at various levels of its quantifier-alternation hierarchy. We further show that the deterministic variants are already coETR-hard (and hence coNP-hard) for simply parameterized families.
