Most causal discovery procedures assume that there are no latent confounders
in the system, which is often violated in real-world problems. In this paper,
we consider a challenging scenario for causal structure identification, where
some variables are latent and they form a hierarchical graph structure to
generate the measured variables; the children of latent variables may still be
latent and only leaf nodes are measured, and moreover, there can be multiple
paths between every pair of variables (i.e., it is beyond tree structure). We
propose an estimation procedure that can efficiently locate latent variables,
determine their cardinalities, and identify the latent hierarchical structure,
by leveraging rank deficiency constraints over the measured variables. We show
that the proposed algorithm can find the correct Markov equivalence class of
the whole graph asymptotically under proper restrictions on the graph
structure.

本文提出了一种估算过程，可以高效确定潜在变量的位置，确定它们的基数，并识别潜在的分层结构，同时考虑到多个变量之间的多条路径，使得提出的算法可以在合适的图结构限制下渐近地找到整个图的正确马尔科夫等价类。

使用排名约束的潜在分层因果结构发现

Latent Hierarchical Causal Structure Discovery with Rank Constraints

Recent studies have shown great promise in applying graph neural networks for
multivariate time series forecasting, where the interactions of time series are
described as a graph structure and the variables are represented as the graph
nodes. Along this line, existing methods usually assume that the graph
structure (or the adjacency matrix), which determines the aggregation manner of
graph neural network, is fixed either by definition or self-learning. However,
the interactions of variables can be dynamic and evolutionary in real-world
scenarios. Furthermore, the interactions of time series are quite different if
they are observed at different time scales. To equip the graph neural network
with a flexible and practical graph structure, in this paper, we investigate
how to model the evolutionary and multi-scale interactions of time series. In
particular, we first provide a hierarchical graph structure cooperated with the
dilated convolution to capture the scale-specific correlations among time
series. Then, a series of adjacency matrices are constructed under a recurrent
manner to represent the evolving correlations at each layer. Moreover, a
unified neural network is provided to integrate the components above to get the
final prediction. In this way, we can capture the pair-wise correlations and
temporal dependency simultaneously. Finally, experiments on both single-step
and multi-step forecasting tasks demonstrate the superiority of our method over
the state-of-the-art approaches.

本研究提出了一种基于层级图结构和扩张卷积的时变序列的预测方法，该方法使用一系列的邻接矩阵来表示不断演化的变量之间的相关性，并通过一个统一的神经网络模型来捕捉它们之间的动态和多尺度的交互作用，实验表明该方法在单步和多步预测任务中均优于现有的方法。