Accumulated DMA Error on Cyclic Graphs

Bound the accumulated approximation error of Direct Message Approximation after more than one sweep on cyclic factor graphs, thereby establishing end-to-end convergence guarantees.

Background

Direct Message Approximation establishes an edge-local bound relating marginal KL divergence to the KL error of an individual approximate factor-to-variable message. The paper’s guarantees are primarily local or concern a single forward/backward sweep, and they do not characterize how approximation errors accumulate when multiple sweeps are performed on graphs containing cycles.

The authors identify extending the analysis to K > 1 sweeps on cyclic graphs as the most pressing unresolved theoretical issue. A successful bound would connect the local message-quality guarantees to global, end-to-end convergence behavior of iterative DMA inference.