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.

[1]  Kevin P. Murphy,et al.  Linear-time inference in Hierarchical HMMs , 2001, NIPS.

[2]  Svetha Venkatesh,et al.  Policy Recognition in the Abstract Hidden Markov Model , 2002, J. Artif. Intell. Res..

[3]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[4]  Tiziana D'Orazio,et al.  Human activity recognition for automatic visual surveillance of wide areas , 2004, VSSN '04.

[5]  Svetha Venkatesh,et al.  Learning Hierarchical Hidden Markov Models with General State Hierarchy , 2004, AAAI.

[6]  Yoram Singer,et al.  The Hierarchical Hidden Markov Model: Analysis and Applications , 1998, Machine Learning.

[7]  Jesse Hoey,et al.  A Decision-Theoretic Approach to Task Assistance for Persons with Dementia , 2005, IJCAI.

[8]  Stuart J. Russell,et al.  General-Purpose MCMC Inference over Relational Structures , 2006, UAI.

[9]  L. De Raedt,et al.  Logical Hidden Markov Models , 2011, J. Artif. Intell. Res..

[10]  Ben Taskar,et al.  Introduction to statistical relational learning , 2007 .

[11]  Deborah L. McGuinness,et al.  An Intelligent Personal Assistant for Task and Time Management , 2007, AI Mag..

[12]  Leslie Pack Kaelbling,et al.  Logical Particle Filtering , 2007, Probabilistic, Logical and Relational Learning - A Further Synthesis.

[13]  Sriraam Natarajan,et al.  A Relational Hierarchical Model for Decision-Theoretic Assistance , 2007, ILP.

[14]  Ben Taskar,et al.  Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning) , 2007 .