  Topic evolution modeling has received significant attentions in recent
decades. Although various topic evolution models have been proposed, most
studies focus on the single document corpus. However in practice, we can easily
access data from multiple sources and also observe relationships between them.
Then it is of great interest to recognize the relationship between multiple
text corpora and further utilize this relationship to improve topic modeling.
In this work, we focus on a special type of relationship between two text
corpora, which we define as the "lead-lag relationship". This relationship
characterizes the phenomenon that one text corpus would influence the topics to
be discussed in the other text corpus in the future. To discover the lead-lag
relationship, we propose a jointly dynamic topic model and also develop an
embedding extension to address the modeling problem of large-scale text corpus.
With the recognized lead-lag relationship, the similarities of the two text
corpora can be figured out and the quality of topic learning in both corpora
can be improved. We numerically investigate the performance of the jointly
dynamic topic modeling approach using synthetic data. Finally, we apply the
proposed model on two text corpora consisting of statistical papers and the
graduation theses. Results show the proposed model can well recognize the
lead-lag relationship between the two corpora, and the specific and shared
topic patterns in the two corpora are also discovered.
