  The article proposes and theoretically analyses a \emph{computationally
efficient} multi-task learning (MTL) extension of popular principal component
analysis (PCA)-based supervised learning schemes
\cite{barshan2011supervised,bair2006prediction}. The analysis reveals that (i)
by default learning may dramatically fail by suffering from \emph{negative
transfer}, but that (ii) simple counter-measures on data labels avert negative
transfer and necessarily result in improved performances.
  Supporting experiments on synthetic and real data benchmarks show that the
proposed method achieves comparable performance with state-of-the-art MTL
methods but at a \emph{significantly reduced computational cost}.
