用于解释正则化高维模型的代表点选择方法
Representer Point Selection for Explaining Regularized High-dimensional Models
AI总结：
本文提出高维代表器，通过新颖的代表器定理将正则化高维模型预测分解为训练样本的贡献，并在稀疏模型、低秩模型及协同过滤中验证其解释效力。
摘要：
我们引入了一类新颖的基于样本的解释方法，将其称为高维代表器，可用于通过为每个训练样本分配重要性权重来解释正则化高维模型的预测。我们的核心工具是针对一般正则化高维模型的新颖代表器定理，该定理将模型预测分解为每个训练样本的贡献：正值（负值）对应于对模型预测产生正向（负向）影响的训练样本。我们推导了该定理在 $\ell_1$ 正则化稀疏模型和核范数正则化低秩模型这两个典型实例上的推论。作为案例研究，我们进一步探讨了低秩模型在协同过滤背景下的应用，并为特定流行的模型类别实例化了高维代表器。最后，我们在三个真实世界的二分类数据集和两个推荐系统数据集上研究了所提方法的实证性能。我们还展示了高维代表器在解释模型推荐方面的效用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
