Transformation Function Based Methods for Model Shift

Inputs: Source domain data: T so = {(X i , Y so i )} nso i=1, target domain data: T ta = {(X i , Y ta i )} nta i=1, transformation function: G, algorithm to train f : Aso and an algorithm to train wG: AwG . Outputs: Regression function for the target domain: f̂ . 1: Train the source domain regression function f̂ = Aso (T ). 2: Construct new data to train wG with f̂ and T : T wG = {(X i ,Wi)} nta i=1, where Wi = G−1 (f(Xi) (Y ta i ). 3: Train the auxiliary function: ŵG = AWG (T G). 4: f̂ (X) = G ( f̂(X), ŵG(X) ) . THEORETICAL ANALYSIS 3.1 Excess Risk Analysis for Kernel Smoothing