Neural Processes (NPs) are appealing due to their ability to perform fast
adaptation based on a context set. This set is encoded by a latent variable,
which is often assumed to follow a simple distribution. However, in real-word
settings, the context set may be drawn from richer distributions having
multiple modes, heavy tails, etc. In this work, we provide a framework that
allows NPs' latent variable to be given a rich prior defined by a graphical
model. These distributional assumptions directly translate into an appropriate
aggregation strategy for the context set. Moreover, we describe a
message-passing procedure that still allows for end-to-end optimization with
stochastic gradients. We demonstrate the generality of our framework by using
mixture and Student-t assumptions that yield improvements in function modelling
and test-time robustness.

本研究提供一个框架，允许神经过程（NPs）的潜变量被赋予由图形模型定义的丰富先验。将分布假设直接转化为上下文集合的适当聚合策略，并通过消息传递过程进行端到端优化。使用混合和学生 - t 假设证明了该框架的普适性，从而提高了函数建模和测试时的鲁棒性。

神经过程中推理结构的利用

Exploiting Inferential Structure in Neural Processes

We consider a high-dimensional mixture of two Gaussians in the noisy regime
where even an oracle knowing the centers of the clusters misclassifies a small
but finite fraction of the points. We provide a rigorous analysis of the
generalization error of regularized convex classifiers, including ridge, hinge
and logistic regression, in the high-dimensional limit where the number $n$ of
samples and their dimension $d$ go to infinity while their ratio is fixed to
$\alpha= n/d$. We discuss surprising effects of the regularization that in some
cases allows to reach the Bayes-optimal performances. We also illustrate the
interpolation peak at low regularization, and analyze the role of the
respective sizes of the two clusters.

研究了高维混合的两个高斯类在噪声条件下的学习，正则化方法可以让分类器达到贝叶斯最优性能，同时分析了正则化程度的影响。