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... the performance of established causal discovery algorithms if R²-sortability is high, as is the case on many simulated ANMs. This opens up exciting new questions:
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... R² is scale-invariant, so it won't be affected by arbitrary data scales or standardization.
We show that this ordering-pattern is prevalent in many ANMs (especially with scale-free graphs as shown below), and give a sufficient criterion for causal chains.
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... along the causal order if effect sizes are strong and noise variances are drawn iid.
We can exploit this and sort variables by their R² given all other variables. We introduce “R²-sortability” to measure the agreement between the R² ordering and a causal order. Importantly...
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... the performance of established causal discovery algorithms if R²-sortability is high, as is the case on many simulated ANMs. This opens up exciting new questions:
When R²-sortability is high, as is often the case, we can exploit it using the simple “R²-sortability” algorithm:
1. sort by increasing R², and
2. regress each variable onto its predecessor in the resulting order.
This algorithm can match …
... R² is scale-invariant, so it won't be affected by arbitrary data scales or standardization.
We show that this ordering-pattern is prevalent in many ANMs (especially with scale-free graphs as shown below), and give a sufficient criterio…
... along the causal order if effect sizes are strong and noise variances are drawn iid.
We can exploit this and sort variables by their R² given all other variables. We introduce “R²-sortability” to measure the agreement between the R² or…
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