Interpolation Methods in Statistics and Machine Learning

在统计学和机器学习课程中教授的一个关键原则是，数据内插(或数据记忆)不可避免地会导致过度拟合和糟糕的预测性能。然而，大多数现代大规模模型，包括过度参数化的神经网络，都经过例行优化，以实现训练数据的零误差。这个项目的研究目标是挑战普遍的智慧，并为内插训练数据的方法发展理论和算法基础。该项目将侧重于插值法的统计和计算方面。在插值法中，将导出回归和分类方法的一致性和有限样本界，并将开发内插规则的信息论极限。该项目还将重点放在插补的计算方面。PI旨在阐明有能力完美拟合数据的过度参数化模型的相对优势和劣势。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

One of the key tenets taught in courses on Statistics and Machine Learning is that data interpolation (or, data memorization) inevitably leads to overfitting and poor prediction performance. Yet, most of the modern large-scale models, including over-parametrized neural networks, are routinely optimized to achieve zero error on training data. The research objective of this project is to challenge the common wisdom and develop theoretical and algorithmic foundations for methods that interpolate the training data. The project will focus on the statistical and computational aspects of interpolation methods. Consistency and finite-sample bounds will be derived for regression and classification methods in the interpolation regime, and information-theoretic limits of interpolating rules will be developed. The project will also focus on the computational aspects of interpolation. The PI aims to shed light on the relative advantages and disadvantages of over-parametrized models that have capacity to perfectly fit the data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.