Abstract
We introduce the localized Lasso, which learns models that both are 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., l12 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/precision medicine data.
Original language | English |
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Title of host publication | Proceedings of the 20th International Conference on Artificial Intelligence and Statistics |
Editors | Aarti Singh, Jerry Zhu |
Place of Publication | Fort Lauderdale, FL, USA |
Pages | 325-333 |
Number of pages | 9 |
Publication status | Published - 1 Aug 2017 |
MoE publication type | A4 Article in a conference publication |
Event | International Conference on Artificial Intelligence and Statistics - Hyatt Pier 66 Hotel, Fort Lauderdale, United States Duration: 20 Apr 2017 → 22 Apr 2017 Conference number: 20 |
Publication series
Name | Proceedings of Machine Learning Research |
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Publisher | PMLR |
Volume | 54 |
ISSN (Electronic) | 1938-7228 |
Conference
Conference | International Conference on Artificial Intelligence and Statistics |
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Abbreviated title | AISTATS |
Country | United States |
City | Fort Lauderdale |
Period | 20/04/2017 → 22/04/2017 |