
Conditional Independences and Causal Relations implied by Sets of Equations
Realworld systems are often modelled by sets of equations with exogenou...
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On Causal Discovery with Equal Variance Assumption
Prior work has shown that causal structure can be uniquely identified fr...
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A direct method for estimating a causal ordering in a linear nonGaussian acyclic model
Structural equation models and Bayesian networks have been widely used t...
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OrderingBased Causal Discovery with Reinforcement Learning
It is a longstanding question to discover causal relations among a set ...
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ParceLiNGAM: A causal ordering method robust against latent confounders
We consider learning a causal ordering of variables in a linear nonGaus...
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Optimizing Causal Orderings for Generating DAGs from Data
An algorithm for generating the structure of a directed acyclic graph fr...
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Causality and independence in perfectly adapted dynamical systems
Perfect adaptation in a dynamical system is the phenomenon that one or m...
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A note on the complexity of the causal ordering problem
In this note we provide a concise report on the complexity of the causal ordering problem, originally introduced by Simon to reason about causal dependencies implicit in systems of mathematical equations. We show that Simon's classical algorithm to infer causal ordering is NPHardan intractability previously guessed but never proven. We present then a detailed account based on Nayak's suggested algorithmic solution (the best available), which is dominated by computing transitive closurebounded in time by O( V·  S), where S( E, V) is the input system structure composed of a set E of equations over a set V of variables with number of variable appearances (density)  S. We also comment on the potential of causal ordering for emerging applications in largescale hypothesis management and analytics.
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