Let X be an instance space and X = {x 1 , . . . , x n } ⊂ X a sample from some marginal distribution ρ X . A tuple D = (X , ρ X ) is called a domain. Given a specific domain D, a task T consists of a label space Y and an objective predictive function f : X → Y that is unknown and needs to be learnt from training data given by examples (x i , y i ) ∈ X × Y with i = 1, . . . , n. To simplify the presentation, we restrict ourselves to the setting where there is a single source domain D S , and a single target domain D T . We also assume that X T ⊆ X S , and denote with D S = {(x S1 , y S1 ), . . . , (x Sn , y Sn )} and D T = {(x T1 , y T1 ), . . . , (x Tm , y Tm )}, the observed examples from source and target domains. While the source domain task is associated with low-fidelity data, the target domain task is considered to be sparse and high-fidelity, i.e. it holds that m ≪ n.