  Recently diversity-inducing regularization methods for latent variable models
(LVMs), which encourage the components in LVMs to be diverse, have been studied
to address several issues involved in latent variable modeling: (1) how to
capture long-tail patterns underlying data; (2) how to reduce model complexity
without sacrificing expressivity; (3) how to improve the interpretability of
learned patterns. While the effectiveness of diversity-inducing regularizers
such as the mutual angular regularizer has been demonstrated empirically, a
rigorous theoretical analysis of them is still missing. In this paper, we aim
to bridge this gap and analyze how the mutual angular regularizer (MAR) affects
the generalization performance of supervised LVMs. We use neural network (NN)
as a model instance to carry out the study and the analysis shows that
increasing the diversity of hidden units in NN would reduce estimation error
and increase approximation error. In addition to theoretical analysis, we also
present empirical study which demonstrates that the MAR can greatly improve the
performance of NN and the empirical observations are in accordance with the
theoretical analysis.
