Browsing by Author "Walk, Harro"
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- ItemDetecting ineffective features for pattern recognition(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Györfi, László; Walk, HarroFor a binary classification problem, the hypothesis testing is studied, that a component of the observation vector is not effective, i.e., that component carries no information for the classification. We introduce nearest neighbor and partitioning estimates of the Bayes error probability, which result in a strongly consistent test.
- ItemExact rate of convergence of k-nearest-neighbor classification rule(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Györfi, László; Döring, Maik; Walk, HarroA binary classification problem is considered. The excess error probability of the k-nearest neighbor classification rule according to the error probability of the Bayes decision is revisited by a decomposition of the excess error probability into approximation and estimation error. Under a weak margin condition and under a modified Lipschitz condition, tight upper bounds are presented such that one avoids the condition that the feature vector is bounded.
- ItemRate of convergence of the density estimation of regression residual(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Györfi, Lásló; Walk, HarroConsider the regression problem with a response variable Y and with a d-dimensional feature vector X. For the regression function m(x) = E{Y|X = x}, this paper investigates methods for estimating the density of the residual Y - m(X) from independent and identically distributed data. If the density is twice differentiable and has compact support then we bound the rate of convergence of the kernel density estimate. It turns out that for d <_ 3 and for partitioning regression estimates, the regression estimation error has no influence in the rate of convergence of the density estimate.
- ItemStrongly consistent density estimation of regression residual(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Györfi, Lásló; Walk, HarroConsider the regression problem with a response variable Y and with a d-dimensional feature vector X. For the regression function m(x) = E {Y|X} = xg, this paper investigates methods for estimating the density of the residual Y - m(X) from independent and identically distributed data. For heteroscedastic regression, we prove the strong universal (density-free) L1-consistency of a recursive and a nonrecursive kernel density estimate based on a regression estimate.