We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given dataset. In doing so, they define a Bayesian model without explicitly positing a prior distribution over latent global parameters; they instead adopt priors over the relational structure of the given dataset, a task that is much simpler. We show how we can learn such models from data, demonstrate that they are scalable to large datasets through mini-batch optimization and describe how we can make predictions for new points via their posterior predictive distribution. We experimentally evaluate FNPs on the tasks of toy regression and image classification and show that, when compared to baselines that employ global latent parameters, they offer both competitive predictions as well as more robust uncertainty estimates.

本文介绍了一种新的可交换随机过程——函数神经过程（FNPs），它们通过学习数据集中点的潜在表示的依赖关系图，对函数分布进行建模。作者在不明确设定潜在全局参数的先验分布的情况下，采用了对给定数据集的关系结构的先验分布来定义贝叶斯模型，并通过小批量优化提高了可扩展性。作者还展示了如何通过后验预测分布对新点进行预测，并在玩具回归和图像分类任务上实验评估了FNPs，证明了相比采用全局潜在参数的基准模型，FNPs不仅提供了竞争性的预测性能，而且更具鲁棒性的不确定性估计。

功能性神经过程