So the bias is an issue can be handled in a variety of ways, one which I know to work is to use weights on your rarer class when training. You could also use larger margins to make sure you definitely don't mis-classify the rare class at the cost of mislableling your dominant class — presuming you are ok with it. An example is when doctors order breast biopsies, it happens a lot more than the cancer itself and based on a noisy technique of physical exam.