Learning to Align the Supports of Distributions
Name
Tong-sytong-SM-EECS-2022-thesis.pdf
Description
Thesis PDF
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1002.56 KB
Format
Adobe PDF
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89ca3e17620f053d32d6209e98083181
Author(s)
Tong, Shangyuan
Advisor(s)
Jaakkola, Tommi S.
Date Issued
May 2022
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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