Effect of richer component laws on the separation deficit

Determine by how much replacing Gaussian-mixture components with richer component laws, such as Gaussian scale-mixture or Student components, can reduce the posterior-variance deficit of the posterior-mean estimator relative to the real-gain ceiling.

Background

The paper proves that Gaussian scale mixtures preserve the structural results: under the relevant phase symmetry, their posterior means remain on the mixture line and their excess error is still a posterior variance. Thus, changing the component law cannot alter the applicable operator-class mechanism, although it may alter the magnitude of the posterior variance.

The paper suggests that heavier-tailed component laws could improve the fit by representing source tails more efficiently, but the theoretical results do not determine the resulting performance improvement. The unresolved issue concerns the empirical size of any reduction in the deficit, rather than whether the structural propositions remain valid.

References

What it can change is the level, a sharper prior having a smaller variance to incur, and by how much is an empirical question that no proposition settles.

— Geometric Ceilings on Time-Frequency Masking for Single-Channel Separation  (2609.03481 - Baelde, 3 Sep 2026) in Section 6.5, “Invariance to the Component Law”

Which criterion that should be remains open.

— Geometric Ceilings on Time-Frequency Masking for Single-Channel Separation  (2609.03481 - Baelde, 3 Sep 2026) in Section 7.6, “Position of the Estimator and Scope of the Measurement”