Learning to Align the Supports of Distributions

This thesis studies the problem of aligning the supports of distributions. Compared to the existing work on distribution alignment, support alignment does not require the densities to be matched. We propose symmetric support difference as a divergence measure to quantify the mismatch between supports. We show that select discriminators (e.g. discriminator trained for Jensen–Shannon divergence) are able to map support differences as support differences in their one-dimensional output space. Following this result, our method aligns supports by minimizing a symmetrized relaxed optimal transport cost in the discriminator 1D space via an adversarial process. Furthermore, we show that our approach can be viewed as a limit of existing notions of alignment by increasing transportation assignment tolerance. We quantitatively evaluate the method across domain adaptation tasks with shifts in label distributions. Our experiments show that the proposed method is more robust against these shifts than other alignment-based baselines.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2022

Author dc:creator

• Tong, Shangyuan

Advisor dc:contributor.advisor

• Jaakkola, Tommi S.

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/145018

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/145018