Postitive event but unsure when it occurred in time
This is referred to as "interval censoring": that is to say, you know the event occurred within an interval, but not exactly where in that interval. 

I don't think there has been a lot of attention in the ML community for interval censored data (or any, really). However, there has been a reasonable amount in the statistical community, myself included. As such, I've written the R package icenReg for interval censored regression models. Regression models certainly can be used as ML tool, although these don't yet have all the bells and whistles that are more typical for ML problems (i.e. no penalized regression a la elastic net etc.). 

However, icenReg at least contains a tool for generalized cross validation, although it is hidden from the public. It can be extracted by icenReg:::icenReg_cv.