000205083 001__ 205083
000205083 005__ 20190317000108.0
000205083 037__ $$aREP_WORK
000205083 245__ $$aA Geometric View on Constrained M-Estimators
000205083 269__ $$a2015
000205083 260__ $$c2015
000205083 336__ $$aReports
000205083 520__ $$aWe study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the boundary of the constraint set (matched constraint), and where the true parameter is strictly in the constraint set (mismatched constraint) are considered. For both cases, we derive novel universal estimation error bounds for regression in a generalized linear model with the canonical link function. Our error bound for the mismatched constraint case is minimax optimal in terms of its dependence on the sample size, for Gaussian linear regression by the Lasso.
000205083 700__ $$0247574$$g221971$$aLi, Yen-Huan
000205083 700__ $$0249002$$g243846$$aHsieh, Ya-Ping
000205083 700__ $$g259392$$0(EPFLAUTH)259392$$aZerbib, Nissim
000205083 700__ $$aCevher, Volkan$$g199128$$0243957
000205083 8564_ $$uhttps://infoscience.epfl.ch/record/205083/files/constrained_estimation.pdf$$zPreprint$$s372492$$yPreprint
000205083 909C0 $$xU12179$$0252306$$pLIONS
000205083 909CO $$ooai:infoscience.tind.io:205083$$qGLOBAL_SET$$pSTI$$preport
000205083 917Z8 $$x221971
000205083 917Z8 $$x221971
000205083 917Z8 $$x221971
000205083 917Z8 $$x221971
000205083 937__ $$aEPFL-REPORT-205083
000205083 973__ $$aEPFL
000205083 980__ $$aREPORT