2017/11/06 by Masaaki Takada, Taiji Suzuki, Takada, Masaaki +3 · 1 citation
Computer Science · Engineering · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1711.01796
openalex publication_date 2017/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 can select variables correlated with each other, which results in deterioration of not only its generalization error but also interpretability. In this paper, we propose a new regularization method, "Independently Interpretable Lasso" (IILasso). Our proposed regularizer suppresses selecting correlated variables, and thus each active variable independently affects the objective variable in the model. Hence, we can interpret regression coefficients intuitively and also improve the performance by avoiding overfitting. We analyze theoretical property of IILasso and show that the proposed method is much advantageous for its sign recovery and achieves almost minimax optimal convergence rate. Synthetic and real data analyses also indicate the effectiveness of IILasso.