@unpublished{BlanchardKraemer2016,
  author    = {Blanchard, Gilles and Kr{\"a}mer, Nicole},
  title     = {Convergence rates of kernel conjugate gradient for random design regression},
  volume    = {5},
  number    = {8},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94195},
  pages     = {31},
  year      = {2016},
  abstract  = {We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.},
  language  = {en}
}
@book{Kempe1996,
  author    = {Kempe, Wolfram},
  title     = {Das Arbeitsangebot verheirateter Frauen in den neuen und alten Bundesl{\"a}ndern},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-37719},
  publisher      = {Universit{\"a}t Potsdam},
  year      = {1996},
  abstract  = {In diesem Beitrag wird eine Regressionsanalyse vorgestellt, die die Einfl{\"u}sse auf die Entscheidung verheirateter deutscher Frauen untersucht, eine Erwerbst{\"a}tigkeit aufzunehmen. Um Differenzen im Verhalten von ost- und westdeutschen Frauen zu ermitteln, erfolgte die Untersuchung getrennt in zwei Datens{\"a}tzen. Zur Vermeidung von Annahmen {\"u}ber die Art des Zusammenhanges wurde das Generalisierte Additive Modell (GAM) gew{\"a}hlt, ein semiparametrisches Regressionsmodell. Diese Modellform, die nichtparametrische und parametrische Regressionsmethoden in sich vereint, hat bisher wenig Verbreitung in der Praxis gefunden. Dies lag vor allem am Sch{\"a}tz verfahren, dem Backfitting. Seit etwa einem Jahr gibt es neue Ans{\"a}tze, in dieser Modellform zu sch{\"a}tzen. Die analytischen Eigenschaften des neuen Sch{\"a}tzers lassen sich leichter bestimmen. Mit dieser Sch{\"a}tzung konnten Unterschiede zwischen Ost und West genau herausgearbeitet werden und die funktionalen Zusammenh{\"a}nge zwischen Einflußvariablen und Antwortvariable untersucht werden. Die Analyse brachte deutliche Unterschiede im Erwerbsverhalten zwischen der Frauen beider Landesteile zum Vorschein.},
  language  = {de}
}
@phdthesis{Zadorozhnyi2021,
  author    = {Zadorozhnyi, Oleksandr},
  title     = {Contributions to the theoretical analysis of the algorithms with adversarial and dependent data},
  school      = {Universit{\"a}t Potsdam},
  pages     = {144},
  year      = {2021},
  abstract  = {In this work I present the concentration inequalities of Bernstein's type for the norms of Banach-valued random sums under a general functional weak-dependency assumption (the so-called \$\cC-\$mixing). The latter is then used to prove, in the asymptotic framework, excess risk upper bounds of the regularised Hilbert valued statistical learning rules under the τ-mixing assumption on the underlying training sample. These results (of the batch statistical setting) are then supplemented with the regret analysis over the classes of Sobolev balls of the type of kernel ridge regression algorithm in the setting of online nonparametric regression with arbitrary data sequences. Here, in particular, a question of robustness of the kernel-based forecaster is investigated. Afterwards, in the framework of sequential learning, the multi-armed bandit problem under \$\cC-\$mixing assumption on the arm's outputs is considered and the complete regret analysis of a version of Improved UCB algorithm is given. Lastly, probabilistic inequalities of the first part are extended to the case of deviations (both of Azuma-Hoeffding's and of Burkholder's type) to the partial sums of real-valued weakly dependent random fields (under the type of projective dependence condition).},
  language  = {en}
}