Filtering states with partial observations for the Logical hidden Markov model

The Logical hidden Markov model (LHMM) is a combination of the first-order logic and the hidden Markov Model (HMM). As a branch of statistical relational learning, the LHMM is of great potential in many fields. In this paper, we combine the logical definitions in LHMM with particle filtering (PF), and propose a logical particle filtering (LPF) algorithm to filter the states with partially missing observations. To reduce the cost of time, a logical particle filtering with parallel resampling (LPF-PR) is further proposed. In experiments, an existed case about UNIX commands is used to test the performances of the LPF and LPF-PR. The results prove that the LPF can perform nearly as well as an exact inference algorithm even when some observations are missing, and parallel resampling can reduce the cost of time significantly when the number of particles is large.