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.
This paper addresses the general problem of modelling and learning rank data
with ties. We propose a probabilistic generative model, that models the process
as permutations over partitions. This results in super-exponential
combinatorial state space with unknown numbers of partitions and unknown
ordering among them. We approach the problem from the discrete choice theory,
where subsets are chosen in a stagewise manner, reducing the state space per
each stage significantly. Further, we show that with suitable parameterisation,
we can still learn the models in linear time.