Set estimation is a problem that arises in myriad applications where a region of interest needs to be estimated based on a finite number of observations. This can involve identifying the support of a function, where a function exceeds a certain level, or where a function exhibits a discontinuity or changepoint. Furthermore, set estimation arises as a subproblem in other learning problems. For example, classification and piecewise-smooth regression require identification of subregions called decision sets over which the classification label is constant or the regression function is homogeneously smooth. This thesis addresses some open theoretical questions in nonparametric learning using level sets and decision sets. It also discusses applications of set estimation to inference problems in neuroimaging and wireless sensor networks.Chapter 2 Adaptive Hausdorff Estimation of Density Level Sets Consider the problem of estimating the 7- level set G* = {x : f(x) agt; 7} of an unknown d- dimensional density function / based on n independent observations X\ , . . . , Xn from theanbsp;...

Title | : | Nonparametric Set Estimation Problems in Statistical Inference and Learning |

Author | : | Aarti Singh |

Publisher | : | ProQuest - 2008 |

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