Single Point Transductive Prediction

Standard methods in supervised learning separate training and prediction: the model is fit independently of any test points it may encounter. However, can knowledge of the next test point x_* be exploited to improve prediction accuracy? We address this question in the context of linear prediction, showing how techniques from semiparametric inference can be used transductively to combat regularization bias. We first lower bound the x_* prediction error of ridge regression and the Lasso, showing that they must incur significant bias in certain test directions. We then provide non-asymptotic upper bounds on the x_* prediction error of two transductive prediction rules. We conclude by showing the efficacy of our methods on both synthetic and real data, highlighting the improvements single point transductive prediction can provide in settings with distribution shift.