Mixture of Gaussian Processes and its Applications
نویسندگان
چکیده
The rapid development of information technologies enables researchers to collect and store functional data at a low cost. As a result, the quantitative analysis of functional data becomes practically feasible, which naturally calls for new statistical methods to serve such a purpose. To this end, we propose a new model, namely, “Mixture of Gaussian Processes” in this paper. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. As a consequence, our model can be estimated efficiently by a novel combination of the ideas from EM algorithm, kernel regression, and functional principal component analysis. It is remarkable that no high-dimensional covariance matrix needs to be estimated in our computational process. This has been an inevitable step for a general normal mixture model and suffers from its estimation instability and inaccuracy. The proposed methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset is illustrated.
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