论文标题
部分可观测时空混沌系统的无模型预测
Asymptotic Properties for Bayesian Neural Network in Besov Space
论文作者
论文摘要
在处理各种非结构化数据（例如图像和自然语言）时，神经网络已经显示出很大的预测能力。贝叶斯神经网络通过将模型参数的先验分布和计算后验分布放置，从而捕获了预测的不确定性。在本文中，我们表明，当真正的回归函数在BESOV空间中时，使用Spike and-Slab Prie的贝叶斯神经网络与几乎最小的收敛速率保持一致。即使回归函数的平滑度未知时，相同的后收敛速率也保持不变，因此，尖峰和slab先验对回归函数的平滑度也具有适应性。我们还考虑了与其他先验更可行的收缩先验，并表明它具有相同的收敛速率。换句话说，我们提出了一个具有保证渐近特性的实用贝叶斯神经网络。
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.
