FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2912142320> ?p ?o ?g. }

• W2912142320 abstract "We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- frac{1}{2}}$ error. We investigate whether the Expectation-Maximization (EM) algorithm also converges slowly for these models. We first demonstrate via simulation studies a broad range of over-specified mixture models for which the EM algorithm converges very slowly, both in one and higher dimensions. We provide a complete analytical characterization of this behavior for fitting data generated from a multivariate standard normal distribution using two-component Gaussian mixture with varying location and scale parameters. Our results reveal distinct regimes in the convergence behavior of EM as a function of the dimension $d$. In the multivariate setting ($d geq 2$), when the covariance matrix is constrained to a multiple of the identity matrix, the EM algorithm converges in order $(n/d)^{frac{1}{2}}$ steps and returns estimates that are at a Euclidean distance of order ${(n/d)^{-frac{1}{4}}}$ and ${ (n d)^{- frac{1}{2}}}$ from the true location and scale parameter respectively. On the other hand, in the univariate setting ($d = 1$), the EM algorithm converges in order $n^{frac{3}{4} }$ steps and returns estimates that are at a Euclidean distance of order ${ n^{- frac{1}{8}}}$ and ${ n^{-frac{1} {4}}}$ from the true location and scale parameter respectively. Establishing the slow rates in the univariate setting requires a novel localization argument with two stages, with each stage involving an epoch-based argument applied to a different surrogate EM operator at the population level. We also show multivariate ($d geq 2$) examples, involving more general covariance matrices, that exhibit the same slow rates as the univariate case." @default.
• W2912142320 created "2019-02-21" @default.
• W2912142320 creator A5023047996 @default.
• W2912142320 creator A5029523984 @default.
• W2912142320 creator A5038379562 @default.
• W2912142320 creator A5049812527 @default.
• W2912142320 creator A5078564922 @default.
• W2912142320 creator A5082704866 @default.
• W2912142320 date "2019-02-01" @default.
• W2912142320 modified "2023-10-07" @default.
• W2912142320 title "Challenges with EM in application to weakly identifiable mixture models." @default.
• W2912142320 cites W1509689762 @default.
• W2912142320 cites W1546851689 @default.
• W2912142320 cites W1981367467 @default.
• W2912142320 cites W1993463265 @default.
• W2912142320 cites W2011277999 @default.
• W2912142320 cites W2049633694 @default.
• W2912142320 cites W2053742104 @default.
• W2912142320 cites W2055218217 @default.
• W2912142320 cites W2101522492 @default.
• W2912142320 cites W2107106142 @default.
• W2912142320 cites W2119537322 @default.
• W2912142320 cites W2126100478 @default.
• W2912142320 cites W2134199473 @default.
• W2912142320 cites W2171208486 @default.
• W2912142320 cites W2496316373 @default.
• W2912142320 cites W2509532045 @default.
• W2912142320 cites W2769553966 @default.
• W2912142320 cites W2893999069 @default.
• W2912142320 cites W2911742394 @default.
• W2912142320 cites W2962737134 @default.
• W2912142320 cites W2964337236 @default.
• W2912142320 hasPublicationYear "2019" @default.
• W2912142320 type Work @default.
• W2912142320 sameAs 2912142320 @default.
• W2912142320 citedByCount "5" @default.
• W2912142320 countsByYear W29121423202018 @default.
• W2912142320 countsByYear W29121423202020 @default.
• W2912142320 countsByYear W29121423202021 @default.
• W2912142320 countsByYear W29121423202022 @default.
• W2912142320 crossrefType "posted-content" @default.
• W2912142320 hasAuthorship W2912142320A5023047996 @default.
• W2912142320 hasAuthorship W2912142320A5029523984 @default.
• W2912142320 hasAuthorship W2912142320A5038379562 @default.
• W2912142320 hasAuthorship W2912142320A5049812527 @default.
• W2912142320 hasAuthorship W2912142320A5078564922 @default.
• W2912142320 hasAuthorship W2912142320A5082704866 @default.
• W2912142320 hasConcept C10138342 @default.
• W2912142320 hasConcept C105795698 @default.
• W2912142320 hasConcept C106487976 @default.
• W2912142320 hasConcept C11413529 @default.
• W2912142320 hasConcept C114614502 @default.
• W2912142320 hasConcept C121332964 @default.
• W2912142320 hasConcept C129782007 @default.
• W2912142320 hasConcept C134567657 @default.
• W2912142320 hasConcept C158693339 @default.
• W2912142320 hasConcept C159985019 @default.
• W2912142320 hasConcept C161584116 @default.
• W2912142320 hasConcept C162324750 @default.
• W2912142320 hasConcept C177384507 @default.
• W2912142320 hasConcept C178650346 @default.
• W2912142320 hasConcept C182081679 @default.
• W2912142320 hasConcept C182306322 @default.
• W2912142320 hasConcept C185142706 @default.
• W2912142320 hasConcept C192562407 @default.
• W2912142320 hasConcept C199163554 @default.
• W2912142320 hasConcept C2524010 @default.
• W2912142320 hasConcept C33676613 @default.
• W2912142320 hasConcept C33923547 @default.
• W2912142320 hasConcept C49781872 @default.
• W2912142320 hasConcept C62520636 @default.
• W2912142320 hasConceptScore W2912142320C10138342 @default.
• W2912142320 hasConceptScore W2912142320C105795698 @default.
• W2912142320 hasConceptScore W2912142320C106487976 @default.
• W2912142320 hasConceptScore W2912142320C11413529 @default.
• W2912142320 hasConceptScore W2912142320C114614502 @default.
• W2912142320 hasConceptScore W2912142320C121332964 @default.
• W2912142320 hasConceptScore W2912142320C129782007 @default.
• W2912142320 hasConceptScore W2912142320C134567657 @default.
• W2912142320 hasConceptScore W2912142320C158693339 @default.
• W2912142320 hasConceptScore W2912142320C159985019 @default.
• W2912142320 hasConceptScore W2912142320C161584116 @default.
• W2912142320 hasConceptScore W2912142320C162324750 @default.
• W2912142320 hasConceptScore W2912142320C177384507 @default.
• W2912142320 hasConceptScore W2912142320C178650346 @default.
• W2912142320 hasConceptScore W2912142320C182081679 @default.
• W2912142320 hasConceptScore W2912142320C182306322 @default.
• W2912142320 hasConceptScore W2912142320C185142706 @default.
• W2912142320 hasConceptScore W2912142320C192562407 @default.
• W2912142320 hasConceptScore W2912142320C199163554 @default.
• W2912142320 hasConceptScore W2912142320C2524010 @default.
• W2912142320 hasConceptScore W2912142320C33676613 @default.
• W2912142320 hasConceptScore W2912142320C33923547 @default.
• W2912142320 hasConceptScore W2912142320C49781872 @default.
• W2912142320 hasConceptScore W2912142320C62520636 @default.
• W2912142320 hasLocation W29121423201 @default.
• W2912142320 hasOpenAccess W2912142320 @default.
• W2912142320 hasPrimaryLocation W29121423201 @default.
• W2912142320 hasRelatedWork W1516765225 @default.
• W2912142320 hasRelatedWork W1978271759 @default.

• next