Achieving non-discrimination in prediction

Discrimination-aware classification is receiving an increasing attention in data science fields. The pre-process methods for constructing a discrimination-free classifier first remove discrimination from the training data, and then learn the classifier from the cleaned data. However, they lack a theoretical guarantee for the potential discrimination when the classifier is deployed for prediction. In this paper, we fill this gap by mathematically bounding the probability of the discrimination in prediction being within a given interval in terms of the training data and classifier. We adopt the causal model for modeling the data generation mechanism, and formally defining discrimination in population, in a dataset, and in prediction. We obtain two important theoretical results: (1) the discrimination in prediction can still exist even if the discrimination in the training data is completely removed; and (2) not all pre-process methods can ensure non-discrimination in prediction even though they can achieve non-discrimination in the modified training data. Based on the results, we develop a two-phase framework for constructing a discrimination-free classifier with a theoretical guarantee. The experiments demonstrate the theoretical results and show the effectiveness of our two-phase framework

Close-packed dimers on nonorientable surfaces

The problem of enumerating dimers on an M x N net embedded on non-orientable surfaces is considered. We solve both the Moebius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary weights simplifies the analysis, and as a result we obtain new compact solutions in the form of double products. The compact expressions also permit us to establish a general reciprocity theorem.Comment: 13 pages, 1 figure, typo corrected to the version published in Phys. Lett. A 293, 235 (2002