Representing Independence Models with Elementary Triplets
This work provides incremental improvements for researchers in probabilistic graphical models and causal inference by enabling more efficient operations on independence models.
The paper tackles the problem of representing independence models using elementary triplets, showing how this representation facilitates operations like finding dominant triplets, minimal independence maps, and computing unions or intersections of models, as well as rephrasing Pearl's causal reasoning results in terms of conditional independences.
In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this paper, we show how this representation helps performing some operations with independence models, such as finding the dominant triplets or a minimal independence map of an independence model, or computing the union or intersection of a pair of independence models, or performing causal reasoning. For the latter, we rephrase in terms of conditional independences some of Pearl's results for computing causal effects.