Sparse Bayesian Learning-Based Kernel Poisson Regression

In this paper, we introduce a closed-form sparse Bayesian kernel Poisson regression (SBKPR) model for count data regression problems based on the sparse Bayesian learning (SBL) approach. In Bayesian setting, a Gaussian prior is given to the model parameter, which is not the conjugate distribution of Poisson regression. Hence, the model parameters cannot be integrated analytically, which leads to the inference intractable problem. In this paper, the log-gamma Gaussian approximation method is proposed to solve this analytically intractable problem, which can give out the closed-form solutions. Furthermore, an individual Gaussian prior is given to the model parameters, which can enhance the flexibility of the proposed method. Finally, sparse solutions can be obtained by applying SBL, which can benefit the learning efficiency and reduce the computational time in practical applications. Experimental results demonstrate that the proposed SBKPR model can outperform some state-of-the-art count data regression models on both toy data and real-world data.