FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2988331362> ?p ?o ?g. }

• W2988331362 abstract "We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the sketch is either computed once (fixed preconditioner), or, the random projection is refreshed at each iteration, i.e., sampled independently of previous ones (varying preconditioners). Although fixed sketching-based preconditioners have received considerable attention in the recent literature, little is known about the performance of refreshed sketches. For a fixed sketch, we characterize the optimal iterative method, that is, the preconditioned conjugate gradient as well as its rate of convergence in terms of the subspace embedding properties of the random embedding. For refreshed sketches, we provide a closed-form formula for the expected error of the iterative Hessian sketch (IHS), a.k.a. preconditioned steepest descent. In contrast to the guarantees and analysis for fixed preconditioners based on subspace embedding properties, our formula is exact and it involves the expected inverse moments of the random projection. Our main technical contribution is to show that this convergence rate is, surprisingly, unimprovable with heavy-ball momentum. Additionally, we construct the locally optimal first-order method whose convergence rate is bounded by that of the IHS. Based on these theoretical and numerical investigations, we do not observe that the additional randomness of refreshed sketches provides a clear advantage over a fixed preconditioner. Therefore, we prescribe PCG as the method of choice along with an optimized sketch size according to our analysis. Our prescribed sketch size yields state-of-the-art computational complexity for solving highly overdetermined linear systems. Lastly, we illustrate the numerical benefits of our algorithms." @default.
• W2988331362 created "2019-11-22" @default.
• W2988331362 creator A5001436196 @default.
• W2988331362 creator A5064802020 @default.
• W2988331362 date "2019-11-06" @default.
• W2988331362 modified "2023-09-27" @default.
• W2988331362 title "Faster Least Squares Optimization." @default.
• W2988331362 cites W1536902572 @default.
• W2988331362 cites W1546004968 @default.
• W2988331362 cites W1577111082 @default.
• W2988331362 cites W1629785033 @default.
• W2988331362 cites W1945899805 @default.
• W2988331362 cites W1972161707 @default.
• W2988331362 cites W1981452262 @default.
• W2988331362 cites W1988720110 @default.
• W2988331362 cites W2007399394 @default.
• W2988331362 cites W2007500622 @default.
• W2988331362 cites W2008776938 @default.
• W2988331362 cites W2018525258 @default.
• W2988331362 cites W2023488486 @default.
• W2988331362 cites W2032576830 @default.
• W2988331362 cites W2037757210 @default.
• W2988331362 cites W2045390367 @default.
• W2988331362 cites W2060581589 @default.
• W2988331362 cites W2083715026 @default.
• W2988331362 cites W2085927849 @default.
• W2988331362 cites W2106965455 @default.
• W2988331362 cites W2107599050 @default.
• W2988331362 cites W2121689290 @default.
• W2988331362 cites W2124659530 @default.
• W2988331362 cites W2152326788 @default.
• W2988331362 cites W2152402969 @default.
• W2988331362 cites W2161992803 @default.
• W2988331362 cites W2167266655 @default.
• W2988331362 cites W2316564661 @default.
• W2988331362 cites W2407643974 @default.
• W2988331362 cites W2580753685 @default.
• W2988331362 cites W2787248994 @default.
• W2988331362 cites W2940073586 @default.
• W2988331362 cites W2951863880 @default.
• W2988331362 cites W2953683526 @default.
• W2988331362 cites W2962937842 @default.
• W2988331362 cites W2963060476 @default.
• W2988331362 cites W2963624229 @default.
• W2988331362 cites W2970072822 @default.
• W2988331362 cites W3004280950 @default.
• W2988331362 cites W3029645440 @default.
• W2988331362 cites W3034919836 @default.
• W2988331362 cites W3108770165 @default.
• W2988331362 cites W597568752 @default.
• W2988331362 hasPublicationYear "2019" @default.
• W2988331362 type Work @default.
• W2988331362 sameAs 2988331362 @default.
• W2988331362 citedByCount "14" @default.
• W2988331362 countsByYear W29883313622020 @default.
• W2988331362 countsByYear W29883313622021 @default.
• W2988331362 crossrefType "posted-content" @default.
• W2988331362 hasAuthorship W2988331362A5001436196 @default.
• W2988331362 hasAuthorship W2988331362A5064802020 @default.
• W2988331362 hasConcept C11413529 @default.
• W2988331362 hasConcept C126255220 @default.
• W2988331362 hasConcept C127162648 @default.
• W2988331362 hasConcept C147060835 @default.
• W2988331362 hasConcept C154945302 @default.
• W2988331362 hasConcept C159694833 @default.
• W2988331362 hasConcept C167431342 @default.
• W2988331362 hasConcept C28826006 @default.
• W2988331362 hasConcept C31258907 @default.
• W2988331362 hasConcept C33923547 @default.
• W2988331362 hasConcept C41008148 @default.
• W2988331362 hasConcept C41608201 @default.
• W2988331362 hasConcept C57869625 @default.
• W2988331362 hasConceptScore W2988331362C11413529 @default.
• W2988331362 hasConceptScore W2988331362C126255220 @default.
• W2988331362 hasConceptScore W2988331362C127162648 @default.
• W2988331362 hasConceptScore W2988331362C147060835 @default.
• W2988331362 hasConceptScore W2988331362C154945302 @default.
• W2988331362 hasConceptScore W2988331362C159694833 @default.
• W2988331362 hasConceptScore W2988331362C167431342 @default.
• W2988331362 hasConceptScore W2988331362C28826006 @default.
• W2988331362 hasConceptScore W2988331362C31258907 @default.
• W2988331362 hasConceptScore W2988331362C33923547 @default.
• W2988331362 hasConceptScore W2988331362C41008148 @default.
• W2988331362 hasConceptScore W2988331362C41608201 @default.
• W2988331362 hasConceptScore W2988331362C57869625 @default.
• W2988331362 hasLocation W29883313621 @default.
• W2988331362 hasOpenAccess W2988331362 @default.
• W2988331362 hasPrimaryLocation W29883313621 @default.
• W2988331362 hasRelatedWork W1999352252 @default.
• W2988331362 hasRelatedWork W2007500622 @default.
• W2988331362 hasRelatedWork W2008776938 @default.
• W2988331362 hasRelatedWork W2045390367 @default.
• W2988331362 hasRelatedWork W2082727440 @default.
• W2988331362 hasRelatedWork W2107599050 @default.
• W2988331362 hasRelatedWork W2117756735 @default.
• W2988331362 hasRelatedWork W2121689290 @default.
• W2988331362 hasRelatedWork W2152402969 @default.
• W2988331362 hasRelatedWork W2157988812 @default.
• W2988331362 hasRelatedWork W2185932763 @default.
• W2988331362 hasRelatedWork W2394933259 @default.

• next