Confound Elimination

4 Confound Elimination

A naive ensemble in which path roughness, $Cs$ , and $SE$ all co-vary together could produce a spuriously high correlation. We eliminate this confound by design:

Coefficients $A k$ and $B k$ are drawn independently per mode.
Amplitudes are drawn from a log-uniform distribution on $[0.05,3.0]$ , so that high- $k$ modes can carry large amplitudes (high $SE$ , moderate $Cs$ ) and low- $k$ modes can have small amplitudes (low $SE$ , low $Cs$ ).
The number of active modes per path is chosen independently of the amplitude magnitudes.

We additionally report the partial Spearman correlation $ρ(Cs,SE | roughness)$ , where roughness is defined as the frequency-weighted amplitude sum:

K∑max ( ) R = (2k − 1) |Ak|+ |Bk |. k=1

This quantity is an explicit proxy for path roughness that is independent of the spectral complexity definition. If the full correlation $ρ(Cs,SE )$ collapses to near zero after conditioning on $R$ , the correlation would be a confound artifact. If it survives, the conjecture $Cs ∝ SE$ is supported beyond the common roughness dependence.

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