Correcting sample selection bias in maximum entropy density estimation

We study the problem of maximum entropy density estimation in the presence of known sample selection bias. We propose three bias correction approaches. The first one takes advantage of unbiased sufficient statistics which can be obtained from biased samples. The second one estimates the biased distribution and then factors the bias out. The third one approximates the second by only using samples from the sampling distribution. We provide guarantees for the first two approaches and evaluate the performance of all three approaches in synthetic experiments and on real data from species habitat modeling, where maxent has been successfully applied and where sample selection bias is a significant problem.