2022/06/01 by Kyeongwon Lee, Jaeyong Lee, Lee, Kyeongwon +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Approximation and Integration #Neural Networks and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2206.00241
openalex publication_date 2022/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Neural networks have shown great predictive power when dealing with various unstructured data such as images and natural languages. The Bayesian neural network captures the uncertainty of prediction by putting a prior distribution for the parameter of the model and computing the posterior distribution. In this paper, we show that the Bayesian neural network using spike-and-slab prior has consistency with nearly minimax convergence rate when the true regression function is in the Besov space. Even when the smoothness of the regression function is unknown the same posterior convergence rate holds and thus the spike-and-slab prior is adaptive to the smoothness of the regression function. We also consider the shrinkage prior, which is more feasible than other priors, and show that it has the same convergence rate. In other words, we propose a practical Bayesian neural network with guaranteed asymptotic properties.