Learning Sparse Group Models Through Boolean RelaxationDownload PDF

Published: 01 Feb 2023, Last Modified: 02 Mar 2023ICLR 2023 notable top 25%Readers: Everyone
Keywords: Structured sparisity, Convex relaxation, Cardinality-constrained program, Small sample size
Abstract: We introduce an efficient algorithmic framework for learning sparse group models formulated as the natural convex relaxation of a cardinality-constrained program with Boolean variables. We provide theoretical techniques to characterize the equivalent condition when the relaxation achieves the exact integral optimal solution, as well as a rounding algorithm to produce a feasible integral solution once the optimal relaxation solution is fractional. We demonstrate the power of our equivalent condition by applying it to two ensembles of random problem instances that are challenging and popularly used in literature and prove that our method achieves exactness with overwhelming probability and nearly optimal sample complexity. Empirically, we use synthetic datasets to demonstrate that our proposed method significantly outperforms the state-of-the-art group sparse learning models in terms of individual and group support recovery when the number of samples is small. Furthermore, we show the out-performance of our method in cancer drug response prediction.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Submission Guidelines: Yes
Please Choose The Closest Area That Your Submission Falls Into: General Machine Learning (ie none of the above)
5 Replies