Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some limitations of probabilistic models for dimension-reduction:
  illustration in the case of one particular probabilistic formulation of PLS   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 $x\in\mathbb{R}^p$ and $y\in\mathbb{R}^q$, with $p\geq 1, q\geq 1$.
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).

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
2
The categories of this paper are: math
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con