  Conversation structure is useful for both understanding the nature of
conversation dynamics and for providing features for many downstream
applications such as summarization of conversations. In this work, we define
the problem of conversation structure modeling as identifying the parent
utterance(s) to which each utterance in the conversation responds to. Previous
work usually took a pair of utterances to decide whether one utterance is the
parent of the other. We believe the entire ancestral history is a very
important information source to make accurate prediction. Therefore, we design
a novel masking mechanism to guide the ancestor flow, and leverage the
transformer model to aggregate all ancestors to predict parent utterances. Our
experiments are performed on the Reddit dataset (Zhang, Culbertson, and
Paritosh 2017) and the Ubuntu IRC dataset (Kummerfeld et al. 2019). In
addition, we also report experiments on a new larger corpus from the Reddit
platform and release this dataset. We show that the proposed model, that takes
into account the ancestral history of the conversation, significantly
outperforms several strong baselines including the BERT model on all datasets
