We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes.

When data and the associated topics are indexed by time dimension, it is of interest to study the temporal dynamics of such latent geometric structures.

We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes.

This is a very well written paper, both in style and substance. There are a few stylistic peculiarities that could surely be ruled out by thorough proof-reading. The authors present a nice introduction into the idea of modelling sets of topics, i.e. sets of points on a simplex, as the geometric structure of a polytope. They go on to describe, how evolution of such a polytope can be modelled over time by embedding a unit hypersphere into the simplex and modelling polytope evolution as random trajectories over this sphere. They further present a non-parametric hierarchical model for capturing polytopes with a varying number of topics and also multiple polytopes arising from different corpora.

We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes.

We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes. Papers published at the Neural Information Processing Systems Conference.

The topic or population polytope (Nguyen, 2015; Tang et al., 2014) is a fundamental geometric object that underlies the presence of latent topic variables in topic and admixture models (Blei et al., 2003; Pritchard et al., 2000). When data and the associated topics are indexed by time dimension, it is of interest to study the temporal dynamics of such latent geometric structures. In this paper, we will study the modeling and algorithms for learning the temporal dynamics of topic polytope that arises in the analysis of text corpora. The convex geometry of topic models provides the theoretical basis for posterior contraction analysis of latent topics (Nguyen, 2015; Tang et al., 2014). Furthermore, Yurochkin & Nguyen (2016); Yurochkin et al. (2017) exploited convex geometry to develop fast and quite accurate inference algorithms in a number of parametric and nonparametric settings.