Matrix Completion for the Independence Model

We investigate the problem of completing partial matrices to rank-1 probability matrices. The motivation for studying this problem comes from statistics: A lack of desired completion can provide a falsification test for partial observations to come from the independence model. For each type of partial matrix, we give an inequality in the observed entries which is satisfied if and only if a desired completion exists. We explain how to construct such completions and, in case a partial matrix has more than one rank-1 probability completion, completions that minimize a distance function are studied.