Fair Top-k Ranking (FA*IR)
We present a formal problem definition and an algorithm to solve the Fair Top-k Ranking problem. The problem consists of creating a ranking of k elements out of a pool of n >> k candidates. The objective is to maximize utility, and maximization is subject to a ranked group fairness constraint. Our definition of ranked group fairness uses the standard notion of protected group to extend the concept of group fairness. It ensures that every prefix of the rank contains a number of protected candidates that is statistically indistinguishable from a given target proportion, or exceeds it. The utility objective favors rankings in which every candidate included in the ranking is more qualified than any candidate not included, and rankings in which candidates are sorted by decreasing qualifications. We describe an efficient algorithm for this problem, which is tested on a series of existing datasets, as well as new datasets. Experimentally, this approach yields a ranking that is similar to the so-called ‘color-blind’ ranking, while respecting the fairness criteria. To the best of our knowledge, FA*IR is the first algorithm grounded in statistical tests that can be used to mitigate biases in ranking against an under-represented group. …

Sequential Deactivation (SDA)
We introduce a new neural network model, together with a tractable and monotone online learning algorithm. Our model describes feed-forward networks for classification, with one output node for each class. The only nonlinear operation is rectification using a ReLU function with a bias. However, there is a rectifier on every edge rather than at the nodes of the network. There are also weights, but these are positive, static, and associated with the nodes. Our ‘rectified wire’ networks are able to represent arbitrary Boolean functions. Only the bias parameters, on the edges of the network, are learned. Another departure in our approach, from standard neural networks, is that the loss function is replaced by a constraint. This constraint is simply that the value of the output node associated with the correct class should be zero. Our model has the property that the exact norm-minimizing parameter update, required to correctly classify a training item, is the solution to a quadratic program that can be computed with a few passes through the network. We demonstrate a training algorithm using this update, called sequential deactivation (SDA), on MNIST and some synthetic datasets. Upon adopting a natural choice for the nodal weights, SDA has no hyperparameters other than those describing the network structure. Our experiments explore behavior with respect to network size and depth in a family of sparse expander networks. …

Zipf’s Law
Zipf’s law, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. …

Association Rule Mining
➘ “Association Rule Learning” …