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A probabilistic derivation of the partial least-squares algorithm.

M G Gustafsson1

  • 1Signal and Systems Group, Uppsala University, P.O. Box 528, 751 20 Uppsala, Sweden. Mats.Gustafsson@signal.uu.se

Journal of Chemical Information and Computer Sciences
|March 30, 2001
PubMed
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This study probabilistically derives the partial least-squares (PLS) algorithm, offering new insights into its steps for multivariate linear regression. The novel approach clarifies theoretical aspects of PLS, enhancing its application in chemistry.

Area of Science:

  • Multivariate statistics
  • Chemometrics
  • Machine learning

Background:

  • Partial Least-Squares (PLS) is a standard algorithm for ill-conditioned multivariate linear regression in chemistry.
  • Existing derivations are primarily matrix-based, lacking a probabilistic foundation.
  • The traditional approach often relies on latent variable models and 'inner relations'.

Purpose of the Study:

  • To derive the PLS algorithm probabilistically, providing a stochastic motivation for each step.
  • To perform the derivation for the general multiresponse case.
  • To analyze theoretical aspects of PLS without relying on latent variable models or inner relations.

Main Methods:

  • Probabilistic derivation of the PLS algorithm using stochastic variables.

Related Experiment Videos

  • Focus on sample estimates derived from data matrices.
  • General multiresponse regression framework.

    • Main Results:

    • A novel probabilistic derivation of the PLS algorithm is presented.
    • Each step of the algorithm is motivated probabilistically.
    • The derivation is applicable to multiresponse cases without latent variable models.

    Conclusions:

    • The probabilistic derivation offers a clearer theoretical understanding of the PLS algorithm.
    • It addresses complexities in traditional motivations, including 'inner relations' and prediction stages.
    • The approach provides a foundation for re-evaluating latent variable interpretations in PLS regression.