The models no longer satisfy the constraints exactly, but work much better on test data.
instead of attempting to maximize the probability of the training data, they maximize a slightly different objective function, the probability of the training data times the prior probability of the model: where In other words, the probability of the λs is a simple normal distribution with 0 mean, and a standard deviation of σ. Chen and Rosenfeld describe a modified update rule in which to find the updates, one solves for δ i in SCGIS can be modified in a similar way to use an update rule in which one solves for δ i in Although sequential updating was described for joint probabilities in the original paper on GIS by Darroch and Ratcliff (1972), GIS with sequential updating for conditional models appears previously unknown.