Matches in SemOpenAlex for { <https://semopenalex.org/work/W4286901831> ?p ?o ?g. }
Showing items 1 to 64 of
64
with 100 items per page.
- W4286901831 abstract "Factorization of matrices where the rank of the two factors diverges linearly with their sizes has many applications in diverse areas such as unsupervised representation learning, dictionary learning or sparse coding. We consider a setting where the two factors are generated from known component-wise independent prior distributions, and the statistician observes a (possibly noisy) component-wise function of their matrix product. In the limit where the dimensions of the matrices tend to infinity, but their ratios remain fixed, we expect to be able to derive closed form expressions for the optimal mean squared error on the estimation of the two factors. However, this remains a very involved mathematical and algorithmic problem. A related, but simpler, problem is extensive-rank matrix denoising, where one aims to reconstruct a matrix with extensive but usually small rank from noisy measurements. In this paper, we approach both these problems using high-temperature expansions at fixed order parameters. This allows to clarify how previous attempts at solving these problems failed at finding an asymptotically exact solution. We provide a systematic way to derive the corrections to these existing approximations, taking into account the structure of correlations particular to the problem. Finally, we illustrate our approach in detail on the case of extensive-rank matrix denoising. We compare our results with known optimal rotationally-invariant estimators, and show how exact asymptotic calculations of the minimal error can be performed using extensive-rank matrix integrals." @default.
- W4286901831 created "2022-07-25" @default.
- W4286901831 creator A5037000437 @default.
- W4286901831 creator A5068236230 @default.
- W4286901831 creator A5081188571 @default.
- W4286901831 creator A5089268172 @default.
- W4286901831 date "2021-10-17" @default.
- W4286901831 modified "2023-10-17" @default.
- W4286901831 title "Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising" @default.
- W4286901831 hasPublicationYear "2021" @default.
- W4286901831 type Work @default.
- W4286901831 citedByCount "0" @default.
- W4286901831 crossrefType "posted-content" @default.
- W4286901831 hasAuthorship W4286901831A5037000437 @default.
- W4286901831 hasAuthorship W4286901831A5068236230 @default.
- W4286901831 hasAuthorship W4286901831A5081188571 @default.
- W4286901831 hasAuthorship W4286901831A5089268172 @default.
- W4286901831 hasBestOaLocation W42869018311 @default.
- W4286901831 hasConcept C105795698 @default.
- W4286901831 hasConcept C106487976 @default.
- W4286901831 hasConcept C11413529 @default.
- W4286901831 hasConcept C114614502 @default.
- W4286901831 hasConcept C126255220 @default.
- W4286901831 hasConcept C134306372 @default.
- W4286901831 hasConcept C159985019 @default.
- W4286901831 hasConcept C164226766 @default.
- W4286901831 hasConcept C185429906 @default.
- W4286901831 hasConcept C187834632 @default.
- W4286901831 hasConcept C192562407 @default.
- W4286901831 hasConcept C25023664 @default.
- W4286901831 hasConcept C28826006 @default.
- W4286901831 hasConcept C33923547 @default.
- W4286901831 hasConcept C90199385 @default.
- W4286901831 hasConceptScore W4286901831C105795698 @default.
- W4286901831 hasConceptScore W4286901831C106487976 @default.
- W4286901831 hasConceptScore W4286901831C11413529 @default.
- W4286901831 hasConceptScore W4286901831C114614502 @default.
- W4286901831 hasConceptScore W4286901831C126255220 @default.
- W4286901831 hasConceptScore W4286901831C134306372 @default.
- W4286901831 hasConceptScore W4286901831C159985019 @default.
- W4286901831 hasConceptScore W4286901831C164226766 @default.
- W4286901831 hasConceptScore W4286901831C185429906 @default.
- W4286901831 hasConceptScore W4286901831C187834632 @default.
- W4286901831 hasConceptScore W4286901831C192562407 @default.
- W4286901831 hasConceptScore W4286901831C25023664 @default.
- W4286901831 hasConceptScore W4286901831C28826006 @default.
- W4286901831 hasConceptScore W4286901831C33923547 @default.
- W4286901831 hasConceptScore W4286901831C90199385 @default.
- W4286901831 hasLocation W42869018311 @default.
- W4286901831 hasOpenAccess W4286901831 @default.
- W4286901831 hasPrimaryLocation W42869018311 @default.
- W4286901831 hasRelatedWork W15203259 @default.
- W4286901831 hasRelatedWork W2969321 @default.
- W4286901831 hasRelatedWork W3097767 @default.
- W4286901831 hasRelatedWork W4094001 @default.
- W4286901831 hasRelatedWork W47426184 @default.
- W4286901831 hasRelatedWork W49026387 @default.
- W4286901831 hasRelatedWork W50557953 @default.
- W4286901831 hasRelatedWork W59044548 @default.
- W4286901831 hasRelatedWork W59808842 @default.
- W4286901831 hasRelatedWork W6467255 @default.
- W4286901831 isParatext "false" @default.
- W4286901831 isRetracted "false" @default.
- W4286901831 workType "article" @default.