Abstract
We propose a continuous optimization framework for discovering a latent directed acyclic graph (DAG) from observational data. Our approach optimizes over the polytope of permutation vectors, the so-called Permutahedron, to learn a topological ordering. Edges can be optimized jointly, or learned conditional on the ordering via a non-differentiable subroutine. Compared to existing continuous optimization approaches our formulation has a number of advantages including: 1. validity: optimizes over exact DAGs as opposed to other relaxations optimizing approximate DAGs; 2. modularity: accommodates any edge-optimization procedure, edge structural parameterization, and optimization loss; 3. end-to-end: either alternately iterates between node-ordering and edge-optimization, or optimizes them jointly. We demonstrate, on real-world data problems in protein-signaling and transcriptional network discovery, that our approach lies on the Pareto frontier of two key metrics, the SID and SHD.
Abstract (translated)
我们提出了一种连续优化框架,用于从观察数据中发现隐式的有向无环图(DAG)。我们的算法优化了permutahedron这个复数的多面体,以学习拓扑排序。边可以一起优化,或者通过一个不可变子程序根据排序学习条件。与现有的连续优化方法相比,我们的 formulation具有以下几个优点:1. 有效性:优化的是准确的DAG,而不是其他放松优化准确的DAG;2. 模块化:能够适应任何边优化程序、边结构参数化和优化损失;3. 端到端:要么在节点排序和边优化之间交替迭代,要么同时优化它们。我们利用在蛋白质信号传导和转录网络发现中的实际数据问题展示了,我们的算法处于两个关键指标SID和SHD的帕累托前沿。
URL
https://arxiv.org/abs/2301.11898
