Author : Arnab Auddy
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Book Synopsis Large Dimensional Data Analysis Using Orthogonally Decomposable Tensors by : Arnab Auddy
Download or read book Large Dimensional Data Analysis Using Orthogonally Decomposable Tensors written by Arnab Auddy and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern data analysis requires the study of tensors, or multi-way arrays. We consider the case where the dimension d is large and the order p is fixed. For dimension reduction and for interpretability, one considers tensor decompositions, where a tensor T can be decomposed into a sum of rank one tensors. In this thesis, I will describe some recent work that illustrate why and how to use decompositions for orthogonally decomposable tensors. Our developments are motivated by statistical applications where the data dimension is large. The estimation procedures will therefore aim to be computationally tractable while providing error rates that depend optimally on the dimension. A tensor is said to be orthogonally decomposable if it can be decomposed into rank one tensors whose component vectors are orthogonal. A number of data analysis tasks can be recast as the problem of estimating the component vectors from a noisy observation of an orthogonally decomposable tensor. In our first set of results, we study this decompositionproblem and derive perturbation bounds.