  The discovery of causal relationships from observational data is very
challenging. Many recent approaches rely on complexity or uncertainty concepts
to impose constraints on probability distributions, aiming to identify specific
classes of directed acyclic graph (DAG) models. In this paper, we introduce a
novel identifiability criterion for DAGs that places constraints on the
conditional variances of additive noise models. We demonstrate that this
criterion extends and generalizes existing identifiability criteria in the
literature that employ (conditional) variances as measures of uncertainty in
(conditional) distributions. For linear Structural Equation Models, we present
a new algorithm that leverages the concept of weak majorization applied to the
diagonal elements of the Cholesky factor of the covariance matrix to learn a
topological ordering of variables. Through extensive simulations and the
analysis of bank connectivity data, we provide evidence of the effectiveness of
our approach in successfully recovering DAGs. The code for reproducing the
results in this paper is available in Supplementary Materials.
