Inferences from a network to a subnetwork and vice versa under an assumption of symmetry

Abstract

This note summarizes some mathematical relations between the probability distributions for the states of a network of binary units and a subnetwork thereof, under an assumption of symmetry. These relations are standard results of probability theory, but seem to be rarely used in neuroscience. Some of their consequences for inferences between network and subnetwork, especially in connection with the maximum-entropy principle, are briefly discussed. The meanings and applicability of the assumption of symmetry are also discussed.\n\nPACS: 87.19.L-,87.19.lo,05.90.+m\n\nMSC: 03B48,97K50