Knothe-Rosenblatt transport for Unsupervised Domain Adaptation

Unsupervised domain adaptation (UDA) aims at exploiting related but different data sources to tackle a common task in a target domain. UDA remains a central yet challenging problem in machine learning. In this paper, we present an approach tailored to moderate-dimensional tabular problems which are hugely important in industrial applications and less well-served by the plethora of methods designed for image and language data. Knothe-Rosenblatt Domain Adaptation (KRDA) is based on the Knothe-Rosenblatt transport: we exploit autoregressive density estimation algorithms to accurately model the different sources by an autoregressive model using a mixture of Gaussians. KRDA then takes advantage of the triangularity of the autoregressive models to build an explicit mapping of the source samples into the target domain. We show that the transfer map built by KRDA preserves each component quantiles of the observations, hence aligning the representations of the different data sets in the same target domain. Finally, we show that KRDA has state-of-the-art performance on both synthetic and real world UDA problems.