  Traditional hidden Markov models have been a useful tool to understand and
model stochastic dynamic data; in the case of non-Gaussian data, models such as
mixture of Gaussian hidden Markov models can be used. However, these suffer
from the computation of precision matrices and have a lot of unnecessary
parameters. As a consequence, such models often perform better when it is
assumed that all variables are independent, a hypothesis that may be
unrealistic. Hidden Markov models based on kernel density estimation are also
capable of modeling non-Gaussian data, but they assume independence between
variables. In this article, we introduce a new hidden Markov model based on
kernel density estimation, which is capable of capturing kernel dependencies
using context-specific Bayesian networks. The proposed model is described,
together with a learning algorithm based on the expectation-maximization
algorithm. Additionally, the model is compared to related HMMs on synthetic and
real data. From the results, the benefits in likelihood and classification
accuracy from the proposed model are quantified and analyzed.
