Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313305448> ?p ?o ?g. }
Showing items 1 to 53 of
53
with 100 items per page.
- W4313305448 abstract "In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment the objective with a regularizer to address challenges associated with ill-posedness. The choice of a suitable regularizer is typically driven by prior domain information and computational considerations. Convex regularizers are attractive as they are endowed with certificates of optimality as well as the toolkit of convex analysis, but exhibit a computational scaling that makes them ill-suited beyond moderate-sized problem instances. On the other hand, nonconvex regularizers can often be deployed at scale, but do not enjoy the certification properties associated with convex regularizers. In this paper, we seek a systematic understanding of the power and the limitations of convex regularization by investigating the following questions: Given a distribution, what are the optimal regularizers, both convex and nonconvex, for data drawn from the distribution? What properties of a data source govern whether it is amenable to convex regularization? We address these questions for the class of continuous and positively homogenous regularizers for which convex and nonconvex regularizers correspond, respectively, to convex bodies and star bodies. By leveraging dual Brunn-Minkowski theory, we show that a radial function derived from a data distribution is the key quantity for identifying optimal regularizers and for assessing the amenability of a data source to convex regularization. Using tools such as $Gamma$-convergence, we show that our results are robust in the sense that the optimal regularizers for a sample drawn from a distribution converge to their population counterparts as the sample size grows large. Finally, we give generalization guarantees that recover previous results for polyhedral regularizers (i.e., dictionary learning) and lead to new ones for semidefinite regularizers." @default.
- W4313305448 created "2023-01-06" @default.
- W4313305448 creator A5022642787 @default.
- W4313305448 creator A5045492746 @default.
- W4313305448 creator A5056040198 @default.
- W4313305448 creator A5089517213 @default.
- W4313305448 date "2022-12-27" @default.
- W4313305448 modified "2023-09-23" @default.
- W4313305448 title "Optimal Convex and Nonconvex Regularizers for a Data Source" @default.
- W4313305448 doi "https://doi.org/10.48550/arxiv.2212.13597" @default.
- W4313305448 hasPublicationYear "2022" @default.
- W4313305448 type Work @default.
- W4313305448 citedByCount "0" @default.
- W4313305448 crossrefType "posted-content" @default.
- W4313305448 hasAuthorship W4313305448A5022642787 @default.
- W4313305448 hasAuthorship W4313305448A5045492746 @default.
- W4313305448 hasAuthorship W4313305448A5056040198 @default.
- W4313305448 hasAuthorship W4313305448A5089517213 @default.
- W4313305448 hasBestOaLocation W43133054481 @default.
- W4313305448 hasConcept C112680207 @default.
- W4313305448 hasConcept C12108790 @default.
- W4313305448 hasConcept C126255220 @default.
- W4313305448 hasConcept C154945302 @default.
- W4313305448 hasConcept C157972887 @default.
- W4313305448 hasConcept C2524010 @default.
- W4313305448 hasConcept C2776135515 @default.
- W4313305448 hasConcept C33923547 @default.
- W4313305448 hasConcept C41008148 @default.
- W4313305448 hasConceptScore W4313305448C112680207 @default.
- W4313305448 hasConceptScore W4313305448C12108790 @default.
- W4313305448 hasConceptScore W4313305448C126255220 @default.
- W4313305448 hasConceptScore W4313305448C154945302 @default.
- W4313305448 hasConceptScore W4313305448C157972887 @default.
- W4313305448 hasConceptScore W4313305448C2524010 @default.
- W4313305448 hasConceptScore W4313305448C2776135515 @default.
- W4313305448 hasConceptScore W4313305448C33923547 @default.
- W4313305448 hasConceptScore W4313305448C41008148 @default.
- W4313305448 hasLocation W43133054481 @default.
- W4313305448 hasOpenAccess W4313305448 @default.
- W4313305448 hasPrimaryLocation W43133054481 @default.
- W4313305448 hasRelatedWork W2081395119 @default.
- W4313305448 hasRelatedWork W2175532135 @default.
- W4313305448 hasRelatedWork W2233843222 @default.
- W4313305448 hasRelatedWork W3003165794 @default.
- W4313305448 hasRelatedWork W3036599379 @default.
- W4313305448 hasRelatedWork W3094945934 @default.
- W4313305448 hasRelatedWork W3135094205 @default.
- W4313305448 hasRelatedWork W3159351664 @default.
- W4313305448 hasRelatedWork W4287899549 @default.
- W4313305448 hasRelatedWork W4297899479 @default.
- W4313305448 isParatext "false" @default.
- W4313305448 isRetracted "false" @default.
- W4313305448 workType "article" @default.