In using PLS for feature selection, is directionality between X and Y necessarily implied?

Question

In systems epidemiology such as in metabolomics, sometimes we are interested in identifying putative biomarkers of intake e.g., intake of a food item. So we analyse the metabolome to investigate signatures/pertubations of intake. Expectedly, most metabolome datasets are n<<p. Partial least squares regression (PLS) and its variants (sPLS, PLSDA etc) are popular methods for selecting such features.

Short question:

In using PLS for feature selection, is directionality between X and Y (X -> Y) necessarily implied?

Long description:

Most PLS algorithms for feature selection require a matrix of metabolites as X and treat food intake as variable Y. Statistically, this seems okay for the purpose of variable selection, but when applied to some biological experiments, it doesnt seem consistent with biological relationship i.e., where metabolite matrix should be the response variable (Y) - because we are studying metabolome pertubations in response to intake of food item,which intuitively would be (X) in a normal regression model e.g., MLR.

So after reading many papers on PLS, and discussion here: Theory behind partial least squares regression these two questions remains a bit unclear:

a) In PLS, is directionality necessarily implied?

b) Technically, is it ok to have Y-variables anterior to X-variables?

After selecting features, inference will be made through other methods.

Many thanks!

Answer 1

I get your argument that the particular food eaten is what causes particular molecules to appear in your system. However, there is no statistical problem with using the effect to predict the cause. In fact, this is fairly routine: a criminal investigation uses the evidence to predict the perpetrator.

Consequently, I see no problem with using a blood sample to predict if someone ate carrots or chocolate lava cake with ice cream.

Explicitly, I would say that the answers to your questions are no and yes, respectively.