贝叶斯神经网络能否做出自信的预测？
Can Bayesian Neural Networks Make Confident Predictions?
AI总结：
该研究在离散化先验下精确刻画贝叶斯神经网络的后验预测分布为高斯混合，识别预测多模态性，并评估不同缩放机制下的后验收缩性，以揭示单模态近似的局限与模型学习能力。
摘要：
贝叶斯推断为神经网络预测的原则性不确定性量化提供了一个框架。其采用的障碍包括完全刻画网络参数的后验分布的困难以及后验预测分布的可解释性。我们证明，在内层权重的离散化先验下，我们可以将后验预测分布精确刻画为高斯混合分布。这一设定使我们能够定义产生相同似然（训练误差）的网络参数值的等价类，并将这些类的元素与网络的缩放机制联系起来——缩放机制通过训练样本量、每层大小和最终层参数数量的比率来定义。特别令人感兴趣的是，不同的参数实现映射到低训练误差，却对应于后验预测分布中的不同模态。我们识别出展现这种预测多模态性的设定，从而为单模态后验近似的准确性提供见解。我们还通过评估不同缩放机制下后验预测的收缩性，刻画了模型“从数据中学习”的能力。
英文摘要：
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the interpretability of posterior predictive distributions. We demonstrate that under a discretized prior for the inner layer weights, we can exactly characterize the posterior predictive distribution as a Gaussian mixture. This setting allows us to define equivalence classes of network parameter values which produce the same likelihood (training error) and to relate the elements of these classes to the network's scaling regime -- defined via ratios of the training sample size, the size of each layer, and the number of final layer parameters. Of particular interest are distinct parameter realizations that map to low training error and yet correspond to distinct modes in the posterior predictive distribution. We identify settings that exhibit such predictive multimodality, and thus provide insight into the accuracy of unimodal posterior approximations. We also characterize the capacity of a model to "learn from data" by evaluating contraction of the posterior predictive in different scaling regimes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
