Year: 2020
Type: preprint
Abstract: We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each data set individually, whereas the proposed method exploits similarities between tasks, without any related information being known in advance. First, for each data set, similar or neighboring means are determined from the data by multiple testing. Then each naive estimator is shrunk towards the local average of its neighbors. We prove theoretically that this approach provides a reduction in mean squared error. This improvement can be significant when the dimension of the input space is large, demonstrating a "blessing of dimensionality" phenomenon. An application of this approach is the estimation of multiple kernel mean embeddings, which plays an important role in many modern applications. The theoretical results are verified on artificial and real world data.
Source: arXiv (Cornell University)
Institutions: University of Potsdam, Technische Universität Berlin, École Normale Supérieure de Rennes, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay, DATASHAPE: Comprendre la forme des données
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W3099588916