Applicability of GASP to non-i.i.d. measurement matrices

Characterize the derivation and validity of generalized approximate survey propagation (GASP) and its replica-based saddle point equations for generalized linear models when the measurement matrix H has non-i.i.d. entries, and determine how the algorithm’s behavior and guarantees extend to such non-i.i.d. cases.

Background

GASP was proposed to address performance degradation of GAMP under model mismatch by incorporating glassy effects via 1RSB analysis, but its derivation assumes i.i.d. measurement matrices. This limits direct application to correlated or structured matrices, which are common in practice.

The paper highlights that VASP was introduced to capture correlations via vector-form surveys, but explicitly notes that the situation for non-i.i.d. cases remains unclear for GASP, marking a concrete unresolved question about extending or validating GASP in non-i.i.d. settings.