Empirical risk minimization offers well-known learning guarantees when training and test data come from the same domain. In the real world, though, we often wish to adapt a classifier from a source domain with a large amount of training data to different target domain with very little training data. In this work we give uniform convergence bounds for algorithms that minimize a convex combinatio...

Graphical models are often used “inappropriately,” with approximations in the topology, inference, and prediction. Yet it is still common to train their parameters to approximately maximize training likelihood. We argue that instead, one should seek the parameters that minimize the empirical risk of the entire imperfect system. We show how to locally optimize this risk using back-propagation an...

Functional data analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case is when the observed functions are densities, that is also an example of infinite dimensional compositional data. We focus on the dimensionality reduction problem for this particular type of data. Several methods are considered here: functional principal components analysi...

An accurate estimation of ionospheric variables such as the total electron content (TEC) is important for many space weather, communication, and satellite geodetic applications. Empirical physics-based models are often used to determine TEC in these However, it known that cannot reproduce all variability due various reasons their simplified model structure, coarse sampling inputs, dependencies ...