ON BINOMIAL APPROXIMATION FOR MAJORITY VOTE DETECTION

MAIN POINTS:

1. The 2 variants of the binomial approximation formula for partial partition function in Ising models with fixed edge potential and weak node potentials
2. Turns out, MAP makes the same number of mistakes as the trivial estimator! It still achieves lower error rate because the locations in which it makes these errors bear lesser mass compared to the trivial estimator.
3. Network effect is seen in moderate SNR region. Not much of a difference in the low and the High SNR regimes...

First order approximation for MAP detector for disparate weak external fields.

Finally, we have a closed form expression for the MAP detector. Its a the first order approximation valid for weakish edge and node potentials...
Icing on the cake: Decision statistic does not need the entire adjacency matrix, Just the first order degree information.