Z is drawn from a multinomial parameterized by a vector θ of length L. Definition 1 A Sparse Backoff Tree SBT (T , δ θ , Q(z)) for the discrete random variable Z consists of a rooted tree T containing L leaves, one for each value of Z; a coefficient δ a > 0 for each interior node a of T ; and a backoff distribution Q(z).
as argued above, existing hierarchical models require inference that becomes expensive as the topic space increases in size.