Logical Hierarchical Hidden Markov Models for Modeling User Activities

Hidden Markov Models (HMM) have been successfully used in applications such as speech recognition, activity recognition, bioinformatics etc. There have been previous attempts such as Hierarchical HMMs and Abstract HMMs to elegantly extend HMMs at multiple levels of temporal abstraction (for example to represent the user's activities). Similarly, there has been previous work such as Logical HMMs on extending HMMs to domains with relational structure. In this work we develop a representation that naturally combines the power of both relational and hierarchical models in the form of Logical Hierarchical Hidden Markov Models (LoHiHMMs). LoHiHMMs inherit the compactness of representation from Logical HMMs and the tractability of inference from Hierarchical HMMs. We outline two inference algorithms: one based on grounding the LoHiHMM to a propositional HMM and the other based on particle filtering adapted for this setting. We present the results of our experiments with the model in two simulated domains.