Title: Hidden Markov Mixture of Gaussian Process Functional Regression: Utilizing Multi-Scale Structure for Time-Series Forecasting. Abstract: The mixture of Gaussian process functional regressions (GPFRs) assumes that there are a batch of time-series or sample curves which are  generated by independent random processes with different temporal structures. However, in the real situations, these structures are actually transferred in a random manner from a long time scale. Therefore, the assumption of independent curves is not true in practice. In order to get rid of this limitation, we propose the hidden Markov based GPFR mixture model (HM-GPFR) by describing these curves with both fine and coarse level temporal structures. Specifically, the temporal structure is described by the Gaussian process model at the fine level and hidden Markov process at the coarse level. The whole model can be regarded as a random process with state switching dynamics. To further enhance the robustness of the model, we also give a priori to the model parameters and develop Bayesian hidden Markov based GPFR mixture model (BHM-GPFR). Experimental results demonstrate that the proposed methods have both high prediction accuracy and good interpretability.
