  Inspired by the hierarchical hidden Markov models (HHMM), we present the
hierarchical semi-Markov conditional random field (HSCRF), a generalisation of
embedded undirectedMarkov chains tomodel complex hierarchical, nestedMarkov
processes. It is parameterised in a discriminative framework and has polynomial
time algorithms for learning and inference. Importantly, we consider
partiallysupervised learning and propose algorithms for generalised
partially-supervised learning and constrained inference. We demonstrate the
HSCRF in two applications: (i) recognising human activities of daily living
(ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show
that the HSCRF is capable of learning rich hierarchical models with reasonable
accuracy in both fully and partially observed data cases.
