论文标题
宽贝叶斯神经网络的确切后部分布
Exact posterior distributions of wide Bayesian neural networks
论文作者
论文摘要
最近的工作表明，深贝叶斯神经网络（BNN）引起的先前的过度功能表现为高斯过程（GP），因为所有层的宽度变得很大。但是，许多BNN应用与BNN功能后部有关。尼尔（Neal，1996）和Matthews等人的原始作品中提供了后逆变的一些经验证据。 （2018年），由于臭名昭著的难度获得和验证BNN后近似值的精确性，它仅限于小型数据集或架构。我们提供了缺少的理论证明，即确切的BNN后验（弱）与先前的GP限制引起的一个。对于经验验证，我们展示了如何通过拒绝采样在小数据集上从有限的BNN生成精确的样品。
Recent work has shown that the prior over functions induced by a deep Bayesian neural network (BNN) behaves as a Gaussian process (GP) as the width of all layers becomes large. However, many BNN applications are concerned with the BNN function space posterior. While some empirical evidence of the posterior convergence was provided in the original works of Neal (1996) and Matthews et al. (2018), it is limited to small datasets or architectures due to the notorious difficulty of obtaining and verifying exactness of BNN posterior approximations. We provide the missing theoretical proof that the exact BNN posterior converges (weakly) to the one induced by the GP limit of the prior. For empirical validation, we show how to generate exact samples from a finite BNN on a small dataset via rejection sampling.
