  Simulated DAG models may exhibit properties that, perhaps inadvertently,
render their structure identifiable and unexpectedly affect structure learning
algorithms. Here, we show that marginal variance tends to increase along the
causal order for generically sampled additive noise models. We introduce
varsortability as a measure of the agreement between the order of increasing
marginal variance and the causal order. For commonly sampled graphs and model
parameters, we show that the remarkable performance of some continuous
structure learning algorithms can be explained by high varsortability and
matched by a simple baseline method. Yet, this performance may not transfer to
real-world data where varsortability may be moderate or dependent on the choice
of measurement scales. On standardized data, the same algorithms fail to
identify the ground-truth DAG or its Markov equivalence class. While
standardization removes the pattern in marginal variance, we show that data
generating processes that incur high varsortability also leave a distinct
covariance pattern that may be exploited even after standardization. Our
findings challenge the significance of generic benchmarks with independently
drawn parameters. The code is available at
https://github.com/Scriddie/Varsortability.
