Abstract:
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The design of learning algorithms requires training and testing data points be drawn according to the same distribution. In practice, however, this assumption often does not hold. A particular class of problems fall under domain adaptation where no labeled data is available from the target domain, but labeled data from a related source domain are accessible. The domain adaptation problem then consists of using the source labeled and target unlabeled data to learn a hypothesis performing well on the target domain. Recent advances in optimal transport have led to a recent surge in research articles dealing with this problem, regression tasks and high dimensions have proved to be an obstacle. In this talk, we describe a framework based on learning pushforwards via diffeomorphic latent spaces while discussing various issues that could plague a successful domain adaptation. In particular we use Integral measures on the latent spaces and normalizing flows to estimate pushforward measures. We develop the necessary theory and highlight the underlying issues while simultaneously looking at a concrete problem of predicting material composition from Mars Spectral data where spectral data obtained by the Mars Rover differ from Laboratory instruments in Earth under Mars-like environment.
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