We introduce a novel class of sample-based explanations we term
high-dimensional representers, that can be used to explain the predictions of a
regularized high-dimensional model in terms of importance weights for each of
the training samples. Our workhorse is a novel representer theorem for general
regularized high-dimensional models, which decomposes the model prediction in
terms of contributions from each of the training samples: with positive
(negative) values corresponding to positive (negative) impact training samples
to the model's prediction. We derive consequences for the canonical instances
of $\ell_1$ regularized sparse models, and nuclear norm regularized low-rank
models. As a case study, we further investigate the application of low-rank
models in the context of collaborative filtering, where we instantiate
high-dimensional representers for specific popular classes of models. Finally,
we study the empirical performance of our proposed methods on three real-world
binary classification datasets and two recommender system datasets. We also
showcase the utility of high-dimensional representers in explaining model
recommendations.

本研究提出了一种名为高维表现者的新型基于样本的解释方法，可用于解释正则化高维模型的预测结果；同时也进一步研究了低秩模型在协作过滤中的应用，并对三个二分类数据集和两个推荐系统数据集的实证表现进行了研究。