Using low coverage predictors in models? The conventional wisdom I run up against is to drop predictors with low coverage without given them much consideration.
By low coverage predictors: I meant predictors whose values are mostly missing. So, say we have values for only 1% or say 0.1% of the exemplars.
To me one -- I would tend to think -- that the low coverage predictors might have a high degree of leverage in say a boosting learner.
Does this line of argument hold any water -- if it does, is there a method one can employ to make such a case.
 A: The conventional wisdom here is very flawed.
You should not be in the habit of thinking about missing values as one concept.  Indeed, values can be missing from your data for many, many qualitatively different reasons.
It could be that values missing at random, for example, some cosmic rays bombarded your storage mechanism and destroyed bits at random, these clearly have no predictive or inferential power.  They also may be missing systematically, i.e. someone who believes they are earning much lower than their potential may be wary to report their income, which is something you should want a model to account for.
Furthermore, just because a variable has low coverage, it may still be highly predictive, especially if its true effect size is large.  Think about drunk driving; not many people are that irresponsible, but if they are, they are much, much more risky of a driver.  If you dropped an indicator for past drunk driving because of low coverage, you would be depriving yourself of a powerful and important predictor.
