论文标题
模型依赖性概括性界限的失败，用于最小值插值
Failures of model-dependent generalization bounds for least-norm interpolation
论文作者
论文摘要
我们在过度参数化的制度中考虑了最小值线性回归器的概括性能的界限，在那里它可以插入数据。我们描述了一种意义，即在统计学习理论中通常证明的任何类型的概括有时都必须非常松散，以分析最小值的interpolant。特别是，对于培训示例的各种自然关节分布，任何仅取决于学习算法的输出，训练示例的数量和置信参数，并且满足轻度条件（在样本量中比单调性大大弱）的任何有效的概括性结合，有时必须非常松散 - 在不断下方的情况下，真实的风险会限制下来。
We consider bounds on the generalization performance of the least-norm linear regressor, in the over-parameterized regime where it can interpolate the data. We describe a sense in which any generalization bound of a type that is commonly proved in statistical learning theory must sometimes be very loose when applied to analyze the least-norm interpolant. In particular, for a variety of natural joint distributions on training examples, any valid generalization bound that depends only on the output of the learning algorithm, the number of training examples, and the confidence parameter, and that satisfies a mild condition (substantially weaker than monotonicity in sample size), must sometimes be very loose -- it can be bounded below by a constant when the true excess risk goes to zero.
