A Unified Framework to Study the Properties of the PLS Vector of Regression Coefficients

  • Mélanie BlazèreEmail author
  • Fabrice Gamboa
  • Jean-Michel Loubes
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 173)


In this paper we propose a new approach to study the properties of the Partial Least Squares (PLS) vector of regression coefficients. This approach relies on the link between PLS and discrete orthogonal polynomials. In fact many important PLS objects can be expressed in terms of some specific discrete orthogonal polynomials, called the residual polynomials. Based on the explicit analytical expression we have stated for these polynomials in terms of signal and noise, we provide a new framework for the study of PLS. We show that this approach allows to simplify and retrieve independent proofs of many classical results (proved earlier by different authors using various approaches and tools). This general and unifying approach also sheds light on PLS and helps to gain insight on its properties.


Partial least squares regression (PLSR) Orthogonal polynomial Krylov subspaces 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mélanie Blazère
    • 1
    Email author
  • Fabrice Gamboa
    • 1
  • Jean-Michel Loubes
    • 1
  1. 1.Institut de mathématiques de ToulouseToulouseFrance

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