Based on the paper
Michiaki Hamada, Hisanori Kiryu, Wataru Iwasaki, Kiyoshi Asai (2011) Generalized centroid estimators in bioinformatics. PLoS One 6: 2
the theoretical aspect of generalized centroid estimator on binary space is discussed.

Estimation on binary space
Bayesian ML estimator
Maximum Expected Gain estimator