Matches in SemOpenAlex for { <https://semopenalex.org/work/W4312342020> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W4312342020 abstract "We consider the problem of recovering a k-sparse signal β0∈Rp from noisy observations y=Xβ0+w∈Rn. One of the most popular approaches is the l1-regularized least squares, also known as LASSO. We analyze the mean square error of LASSO in the case of random designs in which each row of X is drawn from distribution N(0,Σ) with general Σ. We first derive the asymptotic risk of LASSO for w≠0 in the limit of n,p→∞ with n∕p→δ∈[0,∞). We then examine conditions on n, p, and k for LASSO to exactly reconstruct β0 in the noiseless case w=0. A phase boundary δc=δ(ϵ) is precisely established in the phase space defined by 0≤δ,ϵ≤1, where ϵ=k∕p. Above this boundary, LASSO perfectly recovers β0 with high probability. Below this boundary, LASSO fails to recover β0 with high probability. While the values of the non-zero elements of β0 do not have any effect on the phase transition curve, our analysis shows that δc does depend on the signed pattern of the nonzero values of β0 for general Σ≠Ip×p. This is in sharp contrast to the previous phase transition results derived in i.i.d. case with Σ= Ip×p where δc is completely determined by ϵ regardless of the distribution of β0. Underlying our formalism is a recently developed efficient algorithm called approximate message passing (AMP) algorithm. We generalize the state evolution of AMP from i.i.d. case to general case with Σ≠Ip×p. Extensive computational experiments confirm that our theoretical predictions are consistent with simulation results on moderate size system." @default.
- W4312342020 created "2023-01-04" @default.
- W4312342020 creator A5018496840 @default.
- W4312342020 date "2022-01-01" @default.
- W4312342020 modified "2023-10-01" @default.
- W4312342020 title "LASSO risk and phase transition under dependence" @default.
- W4312342020 cites W1974755392 @default.
- W4312342020 cites W2018429487 @default.
- W4312342020 cites W2051275493 @default.
- W4312342020 cites W2067038358 @default.
- W4312342020 cites W2082029531 @default.
- W4312342020 cites W2103539935 @default.
- W4312342020 cites W2123202508 @default.
- W4312342020 cites W2144006746 @default.
- W4312342020 cites W2163916252 @default.
- W4312342020 cites W2164595191 @default.
- W4312342020 cites W2166670884 @default.
- W4312342020 cites W2332658360 @default.
- W4312342020 cites W2566505556 @default.
- W4312342020 cites W2918745211 @default.
- W4312342020 cites W2963064298 @default.
- W4312342020 cites W2963072996 @default.
- W4312342020 cites W2963278901 @default.
- W4312342020 cites W2963639053 @default.
- W4312342020 cites W2963765569 @default.
- W4312342020 cites W2963791198 @default.
- W4312342020 cites W2965497096 @default.
- W4312342020 cites W3098848552 @default.
- W4312342020 cites W3100706365 @default.
- W4312342020 cites W3121195152 @default.
- W4312342020 doi "https://doi.org/10.1214/22-ejs2092" @default.
- W4312342020 hasPublicationYear "2022" @default.
- W4312342020 type Work @default.
- W4312342020 citedByCount "0" @default.
- W4312342020 crossrefType "journal-article" @default.
- W4312342020 hasAuthorship W4312342020A5018496840 @default.
- W4312342020 hasBestOaLocation W43123420201 @default.
- W4312342020 hasConcept C11413529 @default.
- W4312342020 hasConcept C114614502 @default.
- W4312342020 hasConcept C118615104 @default.
- W4312342020 hasConcept C134306372 @default.
- W4312342020 hasConcept C136764020 @default.
- W4312342020 hasConcept C28826006 @default.
- W4312342020 hasConcept C33923547 @default.
- W4312342020 hasConcept C37616216 @default.
- W4312342020 hasConcept C41008148 @default.
- W4312342020 hasConcept C62354387 @default.
- W4312342020 hasConceptScore W4312342020C11413529 @default.
- W4312342020 hasConceptScore W4312342020C114614502 @default.
- W4312342020 hasConceptScore W4312342020C118615104 @default.
- W4312342020 hasConceptScore W4312342020C134306372 @default.
- W4312342020 hasConceptScore W4312342020C136764020 @default.
- W4312342020 hasConceptScore W4312342020C28826006 @default.
- W4312342020 hasConceptScore W4312342020C33923547 @default.
- W4312342020 hasConceptScore W4312342020C37616216 @default.
- W4312342020 hasConceptScore W4312342020C41008148 @default.
- W4312342020 hasConceptScore W4312342020C62354387 @default.
- W4312342020 hasIssue "2" @default.
- W4312342020 hasLocation W43123420201 @default.
- W4312342020 hasLocation W43123420202 @default.
- W4312342020 hasOpenAccess W4312342020 @default.
- W4312342020 hasPrimaryLocation W43123420201 @default.
- W4312342020 hasRelatedWork W1978042415 @default.
- W4312342020 hasRelatedWork W1994109492 @default.
- W4312342020 hasRelatedWork W2094362282 @default.
- W4312342020 hasRelatedWork W2145767695 @default.
- W4312342020 hasRelatedWork W2158471709 @default.
- W4312342020 hasRelatedWork W2191654806 @default.
- W4312342020 hasRelatedWork W2351859806 @default.
- W4312342020 hasRelatedWork W4239376463 @default.
- W4312342020 hasRelatedWork W4307299127 @default.
- W4312342020 hasRelatedWork W4362499101 @default.
- W4312342020 hasVolume "16" @default.
- W4312342020 isParatext "false" @default.
- W4312342020 isRetracted "false" @default.
- W4312342020 workType "article" @default.