Non Parametric Hidden Markov Models with Finite State Space: Posterior Concentration Rates
Non Parametric Hidden Markov Models with Finite State Space: Posterior Concentration Rates
复制标题
具有有限状态空间的非参数隐马尔可夫模型：后验浓度率
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
E. Vernet
中科院分区：
文献类型：
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作者：
E. Vernet
具有有限状态空间的非参数隐马尔可夫模型的使用在实践中蓬勃发展，但在该框架中几乎没有理论保证。在这里，我们研究贝叶斯框架中这些模型的渐近保证。我们获得了关于一般定理中连续观测值的联合边际密度的 $L_1$-范数的后验集中率。我们将该定理应用于两种情况并获得极小极大集中率。我们考虑具有从狄利克雷过程分布的发射分布的离散观测值和具有从高斯分布的狄利克雷过程混合分布的发射分布的连续观测值。
The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework. We obtain posterior concentration rates with respect to the $L_1$-norm on joint marginal densities of consecutive observations in a general theorem. We apply this theorem to two cases and obtain minimax concentration rates. We consider discrete observations with emission distributions distributed from a Dirichlet process and continuous observations with emission distributions distributed from Dirichlet process mixtures of Gaussian distributions.
影响因子：
1.1
作者：
Jankowski,HannaK;Wellner,JonA
通讯作者：
Wellner,JonA