Statistical models for spatial processes play a central role in statistical
analyses of spatial data. Yet, it is the simple, interpretable, and well
understood models that are routinely employed even though, as is revealed
through prior and posterior predictive checks, these can poorly characterise
the spatial heterogeneity in the underlying process of interest. Here, we
propose a new, flexible class of spatial-process models, which we refer to as
spatial Bayesian neural networks (SBNNs). An SBNN leverages the
representational capacity of a Bayesian neural network; it is tailored to a
spatial setting by incorporating a spatial "embedding layer" into the network
and, possibly, spatially-varying network parameters. An SBNN is calibrated by
matching its finite-dimensional distribution at locations on a fine gridding of
space to that of a target process of interest. That process could be easy to
simulate from or we have many realisations from it. We propose several variants
of SBNNs, most of which are able to match the finite-dimensional distribution
of the target process at the selected grid better than conventional BNNs of
similar complexity. We also show that a single SBNN can be used to represent a
variety of spatial processes often used in practice, such as Gaussian processes
and lognormal processes. We briefly discuss the tools that could be used to
make inference with SBNNs, and we conclude with a discussion of their
advantages and limitations.

我们提出了一种新的灵活类的空间过程模型，称为空间贝叶斯神经网络（SBNNs），它通过将空间嵌入层和可能的空间变化的网络参数结合到贝叶斯神经网络中，能更好地匹配目标过程的有限维分布。

空间贝叶斯神经网络

Spatial Bayesian Neural Networks

Model-based disease mapping remains a fundamental policy-informing tool in
public health and disease surveillance with hierarchical Bayesian models being
the current state-of-the-art approach. When working with areal data, e.g.
aggregates at the administrative unit level such as district or province,
routinely used models rely on the adjacency structure of areal units to account
for spatial correlations. The goal of disease surveillance systems is to track
disease outcomes over time, but this provides challenging in situations of
crises, such as political changes, leading to changes of administrative
boundaries. Kenya is an example of such country. Moreover, adjacency-based
approach ignores the continuous nature of spatial processes and cannot solve
the change-of-support problem, i.e. when administrative boundaries change. We
present a novel, practical, and easy to implement solution relying on a
methodology combining deep generative modelling and fully Bayesian inference.
We build on the recent work of PriorVAE able to encode spatial priors over
small areas with variational autoencoders, to map malaria prevalence in Kenya.
We solve the change-of-support problem arising from Kenya changing its district
boundaries in 2010. We draw realisations of the Gaussian Process (GP) prior
over a fine artificial spatial grid representing continuous space and then
aggregate these realisations to the level of administrative boundaries. The
aggregated values are then encoded using the PriorVAE technique. The trained
priors (aggVAE) are then used at the inference stage instead of the GP priors
within a Markov chain Monte Carlo (MCMC) scheme. We demonstrate that it is
possible to use the flexible and appropriate model for areal data based on
aggregation of continuous priors, and that inference is orders of magnitude
faster when using aggVAE than combining the original GP priors and the
aggregation step.

通过结合深度生成建模和完全贝叶斯推断的方法，我们解决了基于行政单元的空间相关性模型在行政边界变化时所面临的支持变化问题，从而更好地绘制肯尼亚疟疾患病率地图。

深度学习和 MCMC 与 aggVAE 用于调整行政边界：在肯尼亚绘制疟疾流行地图

Deep learning and MCMC with aggVAE for shifting administrative  boundaries: mapping malaria prevalence in Kenya

We explore the use of graph neural networks (GNNs) to model spatial processes
in which there is no a priori graphical structure. Similar to finite element
analysis, we assign nodes of a GNN to spatial locations and use a computational
process defined on the graph to model the relationship between an initial
function defined over a space and a resulting function in the same space. We
use GNNs as a computational substrate, and show that the locations of the nodes
in space as well as their connectivity can be optimized to focus on the most
complex parts of the space. Moreover, this representational strategy allows the
learned input-output relationship to generalize over the size of the underlying
space and run the same model at different levels of precision, trading
computation for accuracy. We demonstrate this method on a traditional PDE
problem, a physical prediction problem from robotics, and learning to predict
scene images from novel viewpoints.

本文探讨了使用图神经网络模拟没有先验图形结构的空间过程，以及通过计算优化和泛化学习输入输出关系等相关问题。

图元网络：自适应、结构化的计算和记忆

Graph Element Networks: adaptive, structured computation and memory

We introduce a dynamical spatio-temporal model formalized as a recurrent
neural network for forecasting time series of spatial processes, i.e. series of
observations sharing temporal and spatial dependencies. The model learns these
dependencies through a structured latent dynamical component, while a decoder
predicts the observations from the latent representations. We consider several
variants of this model, corresponding to different prior hypothesis about the
spatial relations between the series. The model is evaluated and compared to
state-of-the-art baselines, on a variety of forecasting problems representative
of different application areas: epidemiology, geo-spatial statistics and
car-traffic prediction. Besides these evaluations, we also describe experiments
showing the ability of this approach to extract relevant spatial relations.

本研究提出了以循环神经网络为基础的动态时空模型，用于预测具有时空依赖的空间过程的时间序列，通过结构化的潜在动态组件学习这些依赖关系，从而预测观测结果，模型经过多种预测问题的评估和比较，被证明能够从中提取出相关的空间关系。