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.
Bibliographical noteThis work was supported in part by the National Natural Science Foundation of China under Grant 61672443, Grant 61402460, and Grant 61772344, and in part by the Hong Kong RGC General Research Fund under Grant 9042322 (CityU 11200116) and Grant 9042038 (CityU 11205314).
- Closed-from solutions
- log-gamma Gaussian approximation
- Poisson regression (PR)
- sparse Bayesian kernel PR (SBKPR)
- sparse Bayesian learning (SBL)