论文标题
向前靠背的潜在潜在推断隐藏的连续时间半马尔科夫连锁
Forward-Backward Latent State Inference for Hidden Continuous-Time semi-Markov Chains
论文作者
论文摘要
隐藏的半马尔科夫模型（HSMM）虽然广泛使用 - 仅限于离散且均匀的时间网格。因此，他们不适合从连续时间现象中解释通常不规则间隔的离散事件数据。我们表明，在HSMM中使用的非基于基于采样的潜在潜在推论可以推广到潜在的连续时间半马尔科夫链（CTSMC）。我们制定了调整到观测可能性的不分化向前和后方方程，并引入了贝叶斯后边缘的精确积分方程，并针对后路径估计值提出了可伸缩的viterbi-type算法。可以使用众所周知的数值方法有效地求解了所提出的方程。作为一种实用的工具，引入了可变步骤HSMM。与古典HSMM相比，我们在潜在状态推理方案中评估了我们的方法。
Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show that non-sampling-based latent state inference used in HSMM's can be generalized to latent Continuous-Time semi-Markov Chains (CTSMC's). We formulate integro-differential forward and backward equations adjusted to the observation likelihood and introduce an exact integral equation for the Bayesian posterior marginals and a scalable Viterbi-type algorithm for posterior path estimates. The presented equations can be efficiently solved using well-known numerical methods. As a practical tool, variable-step HSMM's are introduced. We evaluate our approaches in latent state inference scenarios in comparison to classical HSMM's.
