Single Point Transductive Prediction
This addresses the problem of reducing regularization bias in linear prediction for machine learning practitioners, offering a novel approach but likely incremental in the broader context of transductive learning.
The paper tackles the problem of improving prediction accuracy by exploiting knowledge of the next test point, showing that standard methods like ridge regression and Lasso incur significant bias in certain test directions, and demonstrates that transductive prediction rules provide improvements in settings with distribution shift.
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 $\mathbf{x}_{\star}$ be exploited to improve prediction accuracy? We address this question in the context of linear prediction, showing how techniques from semi-parametric inference can be used transductively to combat regularization bias. We first lower bound the $\mathbf{x}_{\star}$ 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 $\mathbf{x}_{\star}$ 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.