Equalized odds -- where the true positive rates and false positive rates are equal across groups (e.g. racial groups) -- is a common quantitative measure of fairness. Equalized outcomes -- where the difference in predicted outcomes between groups is less than the difference observed in the training data -- is more contentious, because it is incompatible with perfectly accurate predictions. We formalize and quantify the relationship between these two important but seemingly distinct notions of fairness. We show that under realistic assumptions, equalized odds implies partially equalized outcomes. We prove a comparable result for approximately equalized odds. In addition, we generalize a well-known previous result about the incompatibility of equalized odds and another definition of fairness known as calibration, by showing that partially equalized outcomes implies non-calibration. Our results highlight the risks of using trends observed across groups to make predictions about individuals.

No abstract available.

Machine learning algorithms are increasingly used to make or support important decisions about people's lives. This has led to interest in the problem of fair classification, which involves learning to make decisions that are non-discriminatory with respect to a sensitive variable such as race or gender. Several methods have been proposed to solve this problem, including fair representation learning, which cleans the input data used by the algorithm to remove information about the sensitive variable. We show that using fair representation learning as an intermediate step in fair classification incurs a cost compared to directly solving the problem, which we refer to as thecost of mistrust. We show that fair representation learning in fact addresses a different problem, which is of interest when the data user is not trusted to access the sensitive variable. We quantify the benefits of fair representation learning, by showing that any subsequent use of the cleaned data will not be too unfair. The benefits we identify result from restricting the decisions of adversarial data users, while the costs are due to applying those same restrictions to other data users.

This paper describes the design and fabrication of MOD (Mo- bile Object for Drawing)-a portable instrument for combining analog and digital drawing. MOD is intended for live performance and content creation efforts that mix common analog drawing interfaces (i.e. paper, transparency, pencil, marker) with digital cameras (webcams, scientific imaging cameras, digital magnifiers and microscopes), custom software (for keying, thresholding, looping, layer) and digital projectors. The iteration of the instrument described here combines all of these components into a single portable battery powered pack- age that embeds the computation on a small linux computer, includes a small laser projector, and integrates custom tac- tile controllers. The intended uses of this instrument include experimental performance and rapid content creation; the instrument is intended to be suitable for formal (concert hall, theater) and informal (street performance, busking, parade, protest) settings, classrooms and maker spaces.

A popular machine learning strategy is the transfer of a representation (i.e. a feature extraction function) learned on a source task to a target task. Examples include the re-use of neural network weights or word embeddings. We develop sufficient conditions for the success of this approach. If the representation learned from the source task is fixed, we identify conditions on how the tasks relate to obtain an upper bound on target task risk via a VC dimension-based argument. We then consider using the representation from the source task to construct a prior, which is fine-tuned using target task data. We give a PAC-Bayes target task risk bound in this setting under suitable conditions. We show examples of our bounds using feedforward neural networks. Our results motivate a practical approach to weight transfer, which we validate with experiments.