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Subspace estimation in linear dimension reduction

Banff International Research Station for Mathematical Innovation and Discovery

In linear dimension reduction for a p-variate random vector x, the general idea is to find an orthogonal projection (matrix) P of rank k, k < p such that Px carries all or most of the information. In unsupervised dimension reduction this means that x|Px just presents (uninteresting) noise. In supervised dimension reduction for an interesting response variable y, x and y are conditionally independent, given Px, that is, the dependence of x on y is only through Px. In this talk we consider the problem of estimating the minimal subspace, that is, the corresponding unknown projection P with known or unknown dimension. Most of the linear (supervised and unsu- pervised) dimension reduction methods such as principal component analysis (PCA), fourth order blind identification (FOBI), Fisher’s linear discrimination subspace or sliced inverse regression (SIR) are based on a simultaneous diagonalization of two matrices S1 and S2. Asymptotic and robustness properties of the estimates of P can then be derived from those of the estimates of S1 and S2. We also discuss the tools for robustness studies as well as the possibility to robustify these approaches by replacing these matrices by their robust counterparts. The talk is based on the co-operation with several people.

Mathematics; Statistics

video/mp4

Author affiliation: University of Turku

2016-05-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58170

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/