Title: Spectral Methods for Nonparametric Models,
Abstract: Nonparametric models are versatile, albeit computationally expensive, tool
for modeling mixture models. In this paper, we introduce spectral methods for
the two most popular nonparametric models: the Indian Buffet Process (IBP) and
the Hierarchical Dirichlet Process (HDP). We show that using spectral methods
for the inference of nonparametric models are computationally and statistically
efficient. In particular, we derive the lower-order moments of the IBP and the
HDP, propose spectral algorithms for both models, and provide reconstruction
guarantees for the algorithms. For the HDP, we further show that applying
hierarchical models on dataset with hierarchical structure, which can be solved
with the generalized spectral HDP, produces better solutions to that of flat
models regarding likelihood performance.