We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials.

We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials.

However,DBNsonly allow for a fixed chain of Markov dependencies between time slices and cannot represent nested hierarchicalstructures.

Incorporating the natural document-sentence-word structure into hierarchical Bayesian modeling, we propose convolutional Poisson gamma dynamical systems (PGDS) that introduce not only word-level probabilistic convolutions, but alsosentence-levelstochastic temporaltransitions.

We analyze the complexity of learning directed acyclic graphical models from observational dataingeneral settings without specific distributional assumptions.