  Current variational inference methods for hierarchical Bayesian nonparametric
models can neither characterize the correlation structure among latent
variables due to the mean-field setting, nor infer the true posterior dimension
because of the universal truncation. To overcome these limitations, we propose
the conditional and adaptively truncated variational inference method (CATVI)
by maximizing the nonparametric evidence lower bound and integrating Monte
Carlo into the variational inference framework. CATVI enjoys several advantages
over traditional methods, including a smaller divergence between variational
and true posteriors, reduced risk of underfitting or overfitting, and improved
prediction accuracy. Empirical studies on three large datasets reveal that
CATVI applied in Bayesian nonparametric topic models substantially outperforms
competing models, providing lower perplexity and clearer topic-words
clustering.
