Yamada, M;
Takeuchi, K;
Iwata, T;
Shawe-Taylor, J;
Kaski, S;
(2017)
Localized lasso for high-dimensional regression.
In:
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017.
PMLR: Fort Lauderdale, FL, USA.
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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., `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/precision medicine data.
| Type: | Proceedings paper |
|---|---|
| Title: | Localized lasso for high-dimensional regression |
| Event: | 20th International Conference on Artificial Intelligence and Statistics (AISTATS) |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://proceedings.mlr.press/v54/ |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10081070 |
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