Structure Learning for Directed Trees
- URL: http://arxiv.org/abs/2108.08871v1
- Date: Thu, 19 Aug 2021 18:38:30 GMT
- Title: Structure Learning for Directed Trees
- Authors: Martin Emil Jakobsen, Rajen D. Shah, Peter B\"uhlmann, Jonas Peters
- Abstract summary: Knowing the causal structure of a system is of fundamental interest in many areas of science and can aid the design of prediction algorithms that work well under manipulations to the system.
To learn the structure from data, score-based methods evaluate different graphs according to the quality of their fits.
For large nonlinear models, these rely on optimization approaches with no general guarantees of recovering the true causal structure.
- Score: 3.1523578265982235
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Knowing the causal structure of a system is of fundamental interest in many
areas of science and can aid the design of prediction algorithms that work well
under manipulations to the system. The causal structure becomes identifiable
from the observational distribution under certain restrictions. To learn the
structure from data, score-based methods evaluate different graphs according to
the quality of their fits. However, for large nonlinear models, these rely on
heuristic optimization approaches with no general guarantees of recovering the
true causal structure. In this paper, we consider structure learning of
directed trees. We propose a fast and scalable method based on Chu-Liu-Edmonds'
algorithm we call causal additive trees (CAT). For the case of Gaussian errors,
we prove consistency in an asymptotic regime with a vanishing identifiability
gap. We also introduce a method for testing substructure hypotheses with
asymptotic family-wise error rate control that is valid post-selection and in
unidentified settings. Furthermore, we study the identifiability gap, which
quantifies how much better the true causal model fits the observational
distribution, and prove that it is lower bounded by local properties of the
causal model. Simulation studies demonstrate the favorable performance of CAT
compared to competing structure learning methods.
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