Smoothness of conditional independence models for discrete data

We investigate the family of conditional independence models require constraints on complete but non hierarchical marginal log-linear parameters; by exploiting results on the mixed parameterization, we show that they are smooth when the jacobian of a reconstruction algorithm has spectral radius strictly less than 1. This condition is always satisfies in simple contexts where only two marginals are involved. For the general case, we describe an efficient algorithm for checking whether the condition is satisfied with high probability; this approach is applied to assess smoothness of several conditional independence models.