#### Truyen Tran, Dinh Phung, Hung Bui, Svetha Venkatesh, **Hierarchical semi-Markov conditional random fields for deep recursive sequential data,** Artificial Intelligence, Volume 246, May 2017, Pages 53-85, ISSN 0004-3702, DOI: 10.1016/j.artint.2017.02.003.

We present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of linear-chain conditional random fields to model deep nested Markov processes. It is parameterised as a conditional log-linear model and has polynomial time algorithms for learning and inference. We derive algorithms for partially-supervised learning and constrained inference. We develop numerical scaling procedures that handle the overflow problem. We show that when depth is two, the HSCRF can be reduced to the semi-Markov conditional random fields. Finally, we demonstrate the HSCRF on two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. The HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.