A note on approximations to discrete probability distributions

An iterative method is presented which gives an optimum approximationto the joint probability distribution of a set of binary variables given the joint probability distributions of any subsets of the variables (any set of component distributions). The most significant feature of this approximation procedure is that there is no limitation to the number or type of component distributions that can be employed. Each step of the iteration gives an improved approximation, and the procedure converges to give an approximation that is the minimum information (i.e. maximum entropy) extension of the component distributions employed