This paper presents a novel kind of HMM, called Product-HMM, that can be used for sub-sequence modelling. A subvector is formed by selecting particular components from the original vector. A sequence of such sub-vectors forms a sub-sequence. This paper considers the case of modelling a vector sequence in terms of its two sub-sequences. In the present framework of HMM, the architecture of the HMM is fixed for a class of vector sequences. The freedom of selecting a suitable architecture for each of the sub-sequences (of the class of vector sequences considered earlier) is not possible. Product-HMM offers this flexibility of selecting a separate architecture for each of the sub-sequences. Number of states and structure of the transition matrix (which decides whether the HMM is a left-to-right one or an ergodic one) constitute the architecture of a HMM. So, Product-HMM offers the freedom to choose different number of states for each of the sub-sequences and to choose independently whether each of them is to be modelled by a left-to-right or an ergodic HMM. It is shown that modelling using Product-HMM is better than modelling the two sub-sequences using two independent HMMs. This way of joint training of a HMM from two streams of sequential data has not been tried before. Product-HMM is an integrated statistical model which provides a way of integrating different HMMs that model the sub-sequences of a vector sequence. The possibility of having optimal HMM architectures for the sub-sequences results in utilising the training data better and hence in better estimates of model parameters.
Cite as: Nagarajan, M., Sreenivas, T.V. (2003) Product-HMM - a novel class of HMMs for sub-sequence modelling. Proc. Workshop on Spoken Language Processing, 117-124
@inproceedings{nagarajan03b_wslp,
author={Mukundh Nagarajan and T. V. Sreenivas},
title={{Product-HMM - a novel class of HMMs for sub-sequence modelling}},
year=2003,
booktitle={Proc. Workshop on Spoken Language Processing},
pages={117--124}
}