隐马尔可夫模型（Hidden Markov Models，简称HMM）和条件随机场（Conditional Random Fields，简称CRF）是两种常用的序列数据建模技术。推理算法设计的CRF和阻碍允许估计的状态序列的意见。在一些应用中，状态序列的估计不是最终目标;相反，目标是计算它的一些函数。在这种情况下，通过传统的推理技术估计状态序列，然后从估计值计算函数映射不一定是最优的。一种更正式的方法是直接从观察结果中推断出最终结果。特别是，我们考虑的具体实例的问题，其目标是找到没有确切的过渡点的状态轨迹，并得出一种新的多项式时间推理算法，优于香草推理技术。我们发现，这个特殊的问题通常出现在许多不同的应用程序，并提出了对其中三个实验：（1）玩具机器人跟踪;（2）单笔字符识别;（3）手写字识别。
英文摘要：
Hidden Markov models (HMMs) and conditional random fields (CRFs) are two popular techniques for modeling sequential data. Inference algorithms designed over CRFs and HMMs allow estimation of the state sequence given the observations. In several applications, estimation of the state sequence is not the end goal; instead the goal is to compute some function of it. In such scenarios, estimating the state sequence by conventional inference techniques, followed by computing the functional mapping from the estimate is not necessarily optimal. A more formal approach is to directly infer the final outcome from the observations. In particular, we consider the specific instantiation of the problem where the goal is to find the state trajectories without exact transition points and derive a novel polynomial time inference algorithm that outperforms vanilla inference techniques. We show that this particular problem arises commonly in many disparate applications and present experiments on three of them: (1) Toy robot tracking; (2) Single stroke character recognition; (3) Handwritten word recognition.
Constraint-aware Learning of Probabilistic Sequential Models for Multi-Label Classification
Ukrainian Catholic University Lviv Ukraine；HUN-REN Alfr\' e d R\' e nyi Institute of Mathematics E \"o tv \"o s Lor\' a nd University Budapest Hungary；University of Oxford Oxford UK；Ukrainian Catholic University；HUN-REN Alfr\' e d R\' e nyi Institute of Mathematics；E \"o tv \"o s Lor\' a nd University；University of Oxford
