论文标题
通过邻里晶格的有条件独立性的非图形表示
A non-graphical representation of conditional independence via the neighbourhood lattice
论文作者
论文摘要
我们介绍并研究了分布的邻里晶格分解，这是有条件独立性的紧凑，非图形表示，在没有忠实的图形表示的情况下是有效的。这个想法是将变量的一组社区视为子集晶格，然后将此晶格分配到凸sublattices中，每个晶格都直接编码有条件的独立关系集合。我们表明，这种分解存在于任何组成型绘图中，并且可以在高维度中有效且一致地计算出来。 {特别是，这给了一种方法，可以通过满足组成公理的分布所隐含的所有独立关系，该分布严格比图形方法通常假定的忠诚假设要弱。}我们还讨论了各种特殊案例，例如图形模型和投影lattices，每种都具有直观的解释。一路上，我们看到了这个问题与邻里回归密切相关的，该回归已在图形模型和结构方程的背景下进行了广泛的研究。
We introduce and study the neighbourhood lattice decomposition of a distribution, which is a compact, non-graphical representation of conditional independence that is valid in the absence of a faithful graphical representation. The idea is to view the set of neighbourhoods of a variable as a subset lattice, and partition this lattice into convex sublattices, each of which directly encodes a collection of conditional independence relations. We show that this decomposition exists in any compositional graphoid and can be computed efficiently and consistently in high-dimensions. {In particular, this gives a way to encode all of independence relations implied by a distribution that satisfies the composition axiom, which is strictly weaker than the faithfulness assumption that is typically assumed by graphical approaches.} We also discuss various special cases such as graphical models and projection lattices, each of which has intuitive interpretations. Along the way, we see how this problem is closely related to neighbourhood regression, which has been extensively studied in the context of graphical models and structural equations.
