Localized Lasso for High-Dimensional Regression

Understand

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$.

• More specifically, we consider a function defined by local sparse models, one at each data point.
• We introduce sample-wise network regularization to borrow strength across the models, and sample-wise exclusive group sparsity (a.k.a., $\ell_{1,2}$ norm) to introduce diversity into the choice of feature sets in the local models.
• The local models are interpretable in terms of similarity of their sparsity patterns.