Message passing on factor graphs is a powerful framework for probabilistic
inference, which finds important applications in various scientific domains.
The most wide-spread message passing scheme is the sum-product algorithm (SPA)
which gives exact results on trees but often fails on graphs with many small
cycles. We search for an alternative message passing algorithm that works
particularly well on such cyclic graphs. Therefore, we challenge the extrinsic
principle of the SPA, which loses its objective on graphs with cycles. We
further replace the local SPA message update rule at the factor nodes of the
underlying graph with a generic mapping, which is optimized in a data-driven
fashion. These modifications lead to a considerable improvement in performance
while preserving the simplicity of the SPA. We evaluate our method for two
classes of cyclic graphs: the 2x2 fully connected Ising grid and factor graphs
for symbol detection on linear communication channels with inter-symbol
interference. To enable the method for large graphs as they occur in practical
applications, we develop a novel loss function that is inspired by the Bethe
approximation from statistical physics and allows for training in an
unsupervised fashion.

基于数据驱动优化的替代消息传递算法，可在环形图上实现更好的表现和性能，适用于各种科学领域，并且还开发了一种新型损失函数以实现无监督训练。

受挫系统上的局部消息传递

Local Message Passing on Frustrated Systems

Learning the causal structure of observable variables is a central focus for
scientific discovery. Bayesian causal discovery methods tackle this problem by
learning a posterior over the set of admissible graphs given our priors and
observations. Existing methods primarily consider observations from static
systems and assume the underlying causal structure takes the form of a directed
acyclic graph (DAG). In settings with dynamic feedback mechanisms that regulate
the trajectories of individual variables, this acyclicity assumption fails
unless we account for time. We focus on learning Bayesian posteriors over
cyclic graphs and treat causal discovery as a problem of sparse identification
of a dynamical system. This imposes a natural temporal causal order between
variables and captures cyclic feedback loops through time. Under this lens, we
propose a new framework for Bayesian causal discovery for dynamical systems and
present a novel generative flow network architecture (DynGFN) tailored for this
task. Our results indicate that DynGFN learns posteriors that better
encapsulate the distributions over admissible cyclic causal structures compared
to counterpart state-of-the-art approaches.

本文提出了一个针对动态系统的基于 Bayesian 原理的因果关系发现框架，采用生成流网络架构来学习循环图的贝叶斯后验概率，该框架通过时间建立自然的因果关系，并通过实验表明其与同类算法相比，能够更好的表征同时具有循环性和因果性的问题。