  Zero-inflated explanatory variables are common in fields such as ecology and
finance. In this paper we address the problem of having excess of zero values
in some explanatory variables which are subject to multioutcome
lasso-regularized variable selection. Briefly, the problem results from the
failure of the lasso-type of shrinkage methods to recognize any difference
between zero value occurring either in the regression coefficient or in the
corresponding value of the explanatory variable. This kind of confounding will
obviously increase number of false positives - all non-zero regression
coefficients do not necessarily represent real outcome effects.
  We present here the adaptive LAD-lasso for multiple outcomes which extends
the earlier work of multivariate LAD-lasso with adaptive penalization. In
addition of well known property of having less biased regression coefficients,
we show here how the adaptivity improves also method's ability to recover from
influences of excess of zero values measured in continuous covariates.
