TY - THES A1 - Zadorozhnyi, Oleksandr T1 - Contributions to the theoretical analysis of the algorithms with adversarial and dependent data N2 - 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). KW - Machine learning KW - nonparametric regression KW - kernel methods KW - regularisation KW - concentration inequalities KW - learning rates KW - sequential learning KW - multi-armed bandits KW - Sobolev spaces Y1 - 2021 ER - TY - BOOK A1 - Kempe, Wolfram T1 - Das Arbeitsangebot verheirateter Frauen in den neuen und alten Bundesländern N2 - In diesem Beitrag wird eine Regressionsanalyse vorgestellt, die die Einflüsse auf die Entscheidung verheirateter deutscher Frauen untersucht, eine Erwerbstätigkeit aufzunehmen. Um Differenzen im Verhalten von ost- und westdeutschen Frauen zu ermitteln, erfolgte die Untersuchung getrennt in zwei Datensätzen. Zur Vermeidung von Annahmen über die Art des Zusammenhanges wurde das Generalisierte Additive Modell (GAM) gewählt, 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 Schätz verfahren, dem Backfitting. Seit etwa einem Jahr gibt es neue Ansätze, in dieser Modellform zu schätzen. Die analytischen Eigenschaften des neuen Schätzers lassen sich leichter bestimmen. Mit dieser Schätzung konnten Unterschiede zwischen Ost und West genau herausgearbeitet werden und die funktionalen Zusammenhänge zwischen Einflußvariablen und Antwortvariable untersucht werden. Die Analyse brachte deutliche Unterschiede im Erwerbsverhalten zwischen der Frauen beider Landesteile zum Vorschein. N2 - This paper will focus on the regression analysis of labor supply decisions of married German women. In order to determine differences East and West German women were compared seperately. To avoid assumptions about the functional type of correlation the Generalized Additive Model, a semiparametric regression model, was chosen. So far, this pattern consisting of nonparametric and parametric methods has not found acceptance in practical application. Reason for that is the backfitting-estimator. One year ago new ideas for the estimation by GAM were found. The analytical features of the new estimator are easier to determine. Using this method differences between East and West were discovered in detail and functional correlations between endogenous and exogenous variables were investigated. This analysis unveiled significant differences of labor supply behavior among East and West Germany. T3 - Statistische Diskussionsbeiträge - 02 KW - Arbeitsangebot KW - Frauenerwerbstätigkeit KW - nichtparametrische Regression KW - GAM KW - Integrationsschätzer KW - female labor supply KW - nonparametric regression KW - GAM KW - Integration estimator Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-37719 ER - TY - INPR A1 - Blanchard, Gilles A1 - Krämer, Nicole T1 - Convergence rates of kernel conjugate gradient for random design regression N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 8 KW - nonparametric regression KW - reproducing kernel Hilbert space KW - conjugate gradient KW - partial least squares KW - minimax convergence rates Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-94195 SN - 2193-6943 VL - 5 IS - 8 PB - Universitätsverlag Potsdam CY - Potsdam ER -