We revisit the classical kernel method of approximation/interpolation theory
in a very specific context motivated by the desire to obtain a robust procedure
to approximate discrete data sets by (super)level sets of functions that are
merely continuous at the data set arguments but are otherwise smooth. Special
functions, called data signals, are defined for any given data set and are used
to succesfully solve supervised classification problems in a robust way that
depends continuously on the data set. The efficacy of the method is illustrated
with a series of low dimensional examples and by its application to the
standard benchmark high dimensional problem of MNIST digit classification.

本研究中，我们在核方法逼近 / 插值理论的一个特定背景下重新审视这一方法。我们定义了特殊函数作为数据信号用于解决监督分类问题，其有效性通过低维例子和高维 MNIST 数字分类问题的应用得到了证明。

维度无关数据集近似及其在分类中的应用

Dimension Independent Data Sets Approximation and Applications to Classification

Contemporary predictive models are hard to interpret as their deep nets
exploit numerous complex relations between input elements. This work suggests a
theoretical framework for model interpretability by measuring the contribution
of relevant features to the functional entropy of the network with respect to
the input. We rely on the log-Sobolev inequality that bounds the functional
entropy by the functional Fisher information with respect to the covariance of
the data. This provides a principled way to measure the amount of information
contribution of a subset of features to the decision function. Through
extensive experiments, we show that our method surpasses existing
interpretability sampling-based methods on various data signals such as image,
text, and audio.

本文提出模型可解释性的理论框架，通过测量相关特征对于网络对输入的功能熵的贡献来解释深度网络，通过广泛的实验，我们证明了我们的方法在图像、文本和音频等各种数据信号上超过了现有的可解释性采样方法。