Mixture Gaussian process model with Gaussian mixture distribution for big data

In the era of chemical big data, the high complexity and strong interdependencies present in the datasets pose considerable challenges when constructing accurate parametric models. The Gaussian process model, owing to its non-parametric nature, demonstrates better adaptability when confronted with complex and interdependent data. However, the standard Gaussian process has two significant limitations. Firstly, the time complexity of inverting its kernel matrix during the inference process is $O{\left(n\right)}^3$. Secondly, all data share a common kernel function parameter, which mixes different data types and reduces the model accuracy in mixing-category data identification problems. In light of this, this paper proposes a mixture Gaussian process model that addresses these limitations. This model reduces time complexity and distinguishes data based on different data features. It incorporates a Gaussian mixture distribution for the inducing variables to approximate the original data distribution. Stochastic Variational Inference is utilized to reduce the computational time required for parameter inference. The inducing variables have distinct parameters for the kernel function based on the data category, leading to improved analytical accuracy and reduced time complexity of the Gaussian process model. Numerical experiments are conducted to analyze and compare the performance of the proposed model on different-sized datasets and various data category cases.