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SUMMARY:Linear regression with unmatched data: a deconvolution perspective
  - Mona Azadkia (London School of Economics)
DTSTART:20230303T140000Z
DTEND:20230303T150000Z
UID:TALK194908@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Consider the regression problem where the response Y∈ℝ and
  the covariate X∈ℝd for d≥1 are \\textit{unmatched}. Under this scen
 ario\, we do not have access to pairs of observations from the distributio
 n of (X\,Y)\, but instead\, we have separate datasets {Yi}ni=1 and {Xj}mj=
 1\, possibly collected from different sources. We study this problem assum
 ing that the regression function is linear and the noise distribution is k
 nown or can be estimated. We introduce an estimator of the regression vect
 or based on deconvolution and demonstrate its consistency and asymptotic n
 ormality under an identifiability assumption. In the general case\, we sho
 w that our estimator (DLSE: Deconvolution Least Squared Estimator) is cons
 istent in terms of an extended ℓ2 norm. Using this observation\, we devi
 se a method for semi-supervised learning\, i.e.\, when we have access to a
  small sample of matched pairs (Xk\,Yk). Several applications with synthet
 ic and real datasets are considered to illustrate the theory.\n\nhttps://a
 rxiv.org/abs/2207.06320
LOCATION:MR12\, Centre for Mathematical Sciences
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