ed.KLqp VI seems to have trouble with small parameters with sparse data

When I try out the logistic regression sample code which only involves Bernoulli distribution, I am able to get excellent recovery of the simulation parameter values as long as the data is not sparse or if the parameters values are not very small (1st decimal place, not 2nd). But when the data is sparse, the larger parameters still come out close, but the smaller parameters all get bumped by an order of magnitude, so that they become in 1st decimal place. This is true even if I keep adding on more sample data to 10’s of thousands. Is this a known weakness for VI?