  In the supervised high dimensional settings with a large number of variables
and a low number of individuals, one objective is to select the relevant
variables and thus to reduce the dimension. That subspace selection is often
managed with supervised tools. However, some data can be missing, compromising
the validity of the sub-space selection. We propose a Partial Least Square
(PLS) based method, called Multi-block Data-Driven sparse PLS mdd-sPLS,
allowing jointly variable selection and subspace estimation while training and
testing missing data imputation through a new algorithm called Koh-Lanta. This
method was challenged through simulations against existing methods such as mean
imputation, nipals, softImpute and imputeMFA. In the context of supervised
analysis of high dimensional data, the proposed method shows the lowest
prediction error of the response variables. So far this is the only method
combining data imputation and response variable prediction. The superiority of
the supervised multi-block mdd-sPLS method increases with the intra-block and
inter-block correlations. The application to a real data-set from a rVSV-ZEBOV
Ebola vaccine trial revealed interesting and biologically relevant results. The
method is implemented in a R-package available on the CRAN and a Python-package
available on pypi.
