  The estimation of categorical distributions under marginal constraints
summarizing some sample from a population in the most-generalizable way is key
for many machine-learning and data-driven approaches. We provide a
parameter-agnostic theoretical framework that enables this task ensuring (i)
that a categorical distribution of Maximum Entropy under marginal constraints
always exists and (ii) that it is unique. The procedure of iterative
proportional fitting (IPF) naturally estimates that distribution from any
consistent set of marginal constraints directly in the space of probabilities,
thus deductively identifying a least-biased characterization of the population.
The theoretical framework together with IPF leads to a holistic workflow that
enables modeling any class of categorical distributions solely using the
phenomenological information provided.
