Sparse regularization such as ℓ1 regularization is a quite powerful and widely used strategy for high-dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by several studies. However, one of the biggest issues in sparse regularization is that its performance is quite sensitive to correlations between features. Ordinary ℓ1 regularization selects variables correlated with each other under weak regularizations, which results in deterioration of not only its estimation error but also interpretability. In this letter, we propose a new regularization method, independently interpretable lasso (IILasso), for generalized linear models. Our proposed regularizer suppresses selecting correlated variables, so that each active variable affects the response independently in the model. Hence, we can interpret regression coefficients intuitively, and the performance is also improved by avoiding overfitting. We analyze the theoretical property of the IILasso and show that the proposed method is advantageous for its sign recovery and achieves almost minimax optimal convergence rate. Synthetic and real data analyses also indicate the effectiveness of the IILasso.

中文翻译：

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广义线性模型的可独立解释的套索

稀疏正则化（例如ℓ1 正则化）是一种非常强大且广泛用于高维学习问题的策略。稀疏正则化的有效性已得到多项研究的实践和理论支持。然而，稀疏正则化的最大问题之一是其性能对特征之间的相关性非常敏感。普通ℓ1正则化选择弱正则化下相互关联的变量，这不仅导致其估计误差变差，而且可解释性变差。在这封信中，我们为广义线性模型提出了一种新的正则化方法，独立可解释套索（IILasso）。我们提出的正则化器抑制选择相关变量，以便每个活动变量独立影响模型中的响应。因此，我们可以直观地解释回归系数，并且通过避免过度拟合也提高了性能。我们分析了 IILasso 的理论特性，并表明所提出的方法有利于其符号恢复，并实现了几乎极小极大的最优收敛速度。合成和真实数据分析也表明了 IILasso 的有效性。