Stationary graph process models are commonly used in the analysis and
inference of data sets collected on irregular network topologies. While most of
the existing methods represent graph signals with a single stationary process
model that is globally valid on the entire graph, in many practical problems,
the characteristics of the process may be subject to local variations in
different regions of the graph. In this work, we propose a locally stationary
graph process (LSGP) model that aims to extend the classical concept of local
stationarity to irregular graph domains. We characterize local stationarity by
expressing the overall process as the combination of a set of component
processes such that the extent to which the process adheres to each component
varies smoothly over the graph. We propose an algorithm for computing LSGP
models from realizations of the process, and also study the approximation of
LSGPs locally with WSS processes. Experiments on signal interpolation problems
show that the proposed process model provides accurate signal representations
competitive with the state of the art.

本文提出了一种局部平稳图过程（LSGP）模型，旨在将局部平稳的概念扩展到不规则图域，通过表示整体过程为一组组成部分过程的组合来描述局部平稳性，提出了一种计算 LSGP 模型的算法，并研究了利用 WSS 过程在本地近似 LSGPs，实验结果显示该过程模型在信号插值问题上提供了与现有技术相媲美的准确信号表示。

局部平稳图过程

Locally Stationary Graph Processes

We introduce a new family of non-linear neural network activation functions
that mimic the properties induced by the widely-used Mat\'ern family of kernels
in Gaussian process (GP) models. This class spans a range of locally stationary
models of various degrees of mean-square differentiability. We show an explicit
link to the corresponding GP models in the case that the network consists of
one infinitely wide hidden layer. In the limit of infinite smoothness the
Mat\'ern family results in the RBF kernel, and in this case we recover RBF
activations. Mat\'ern activation functions result in similar appealing
properties to their counterparts in GP models, and we demonstrate that the
local stationarity property together with limited mean-square differentiability
shows both good performance and uncertainty calibration in Bayesian deep
learning tasks. In particular, local stationarity helps calibrate
out-of-distribution (OOD) uncertainty. We demonstrate these properties on
classification and regression benchmarks and a radar emitter classification
task.

介绍了一种新的基于 Matern 家族核函数的非线性神经网络激活函数，具有一定的局部平稳性和多样的可微性，表现出良好的表现和不确定性校准能力，并在分类和回归基准测试和雷达发射机分类任务中得到了证明。