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- W4287777147 abstract "Partial Least Squares (PLS) refer to a class of dimension-reduction techniques aiming at the identification of two sets of components with maximal covariance, in order to model the relationship between two sets of observed variables $xinmathbb{R}^p$ and $yinmathbb{R}^q$, with $pgeq 1, qgeq 1$. El Bouhaddani et al. (2017) have recently proposed a probabilistic formulation of PLS. Under the constraints they consider for the parameters of their model, this latter can be seen as a probabilistic formulation of one version of PLS, namely the PLS-SVD. However, we establish that these constraints are too restrictive as they define a very particular subset of distributions for $(x,y)$ under which, roughly speaking, components with maximal covariance (solutions of PLS-SVD), are also necessarily of respective maximal variances (solutions of the principal components analyses of $x$ and $y$, respectively). Then, we propose a simple extension of el Bouhaddani et al.'s model, which corresponds to a more general probabilistic formulation of PLS-SVD, and which is no longer restricted to these particular distributions. We present numerical examples to illustrate the limitations of the original model of el Bouhaddani et al. (2017)." @default.
- W4287777147 created "2022-07-26" @default.
- W4287777147 creator A5060396702 @default.
- W4287777147 creator A5082073306 @default.
- W4287777147 date "2020-05-19" @default.
- W4287777147 modified "2023-09-24" @default.
- W4287777147 title "On some limitations of probabilistic models for dimension-reduction: illustration in the case of one particular probabilistic formulation of PLS" @default.
- W4287777147 doi "https://doi.org/10.48550/arxiv.2005.09498" @default.
- W4287777147 hasPublicationYear "2020" @default.
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