Localized Lasso for High-Dimensional Regression
Localized Lasso for High-Dimensional Regression
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发表时间：
2016-03
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通讯作者：
M. Yamada;Koh Takeuchi;Tomoharu Iwata;J. Shawe-Taylor;Samuel Kaski
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作者：
M. Yamada;Koh Takeuchi;Tomoharu Iwata;J. Shawe-Taylor;Samuel Kaski
我们引入了本地化的Lasso，它适用于学习模型，这些模型既可解释，又在高维$d$和小样本量$n$的问题中具有很高的预测能力。更具体地说，我们考虑由局部稀疏模型定义的函数，每个数据点一个。我们引入了样本网络正则化来借用模型之间的强度，以及样本排他性组稀疏性（也称为，$\ell_{1，2}$ norm）来将多样性引入局部模型中的特征集选择。局部模型的稀疏模式的相似性方面的解释。成本函数是凸的，因此具有全局最优解。此外，我们针对局部Lasso提出了一种简单而高效的基于迭代最小二乘的优化过程，该过程不需要调整参数，并且保证收敛到全局最优解。经验表明，该解决方案优于模拟和基因组个性化医学数据的替代方案。
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. The cost function is convex, and thus has a globally optimal solution. Moreover, we propose a simple yet efficient iterative least-squares based optimization procedure for the localized Lasso, which does not need a tuning parameter, and is guaranteed to converge to a globally optimal solution. The solution is empirically shown to outperform alternatives for both simulated and genomic personalized medicine data.