A Probabilistic Derivation of the Partial Least-Squares Algorithm.
Journal of Chemical Information and Computer Sciences,
vol.41, no.2, March-April 2001, pp. 288-294.
Traditionally the partial least-squares (PLS) algorithm, commonly
used in chemistry for ill-conditioned multivariate linear regression,
has been derived (motivated) and presented in terms of data matrices.
In this work the PLS algorithm is derived probabilistically in
terms of stochastic variables where sample estimates calculated
using data matrices are employed at the end. The derivation,
which offers a probabilistic motivation to each step of the
PLS algorithm, is performed for the general multiresponse
case and without reference to any latent variable model of the
response variable and also without any so-called
On the basis of the derivation, some theoretical
issues of the PLS algorithm are briefly considered: the complexity
of the original motivation of PLS regression which involves an
"inner relation"; the original motivation behind the prediction
stage of the PLS algorithm; the relationship between uncorrelated
and orthogonal latent variables; the limited possibilities to
make natural interpretations of the latent variables extracted.