Group fairness definitions such as Demographic Parity and Equal Opportunity make assumptions about the underlying decision-problem that restrict them to classification problems. Prior work has translated these definitions to other machine learning environments, such as unsupervised learning and reinforcement learning, by implementing their closest mathematical equivalent. As a result, there are numerous bespoke interpretations of these definitions. Instead, we provide a generalized set of group fairness definitions that unambiguously extend to all machine learning environments while still retaining their original fairness notions. We derive two fairness principles that enable such a generalized framework. First, our framework measures outcomes in terms of utilities, rather than predictions, and does so for both the decision-algorithm and the individual. Second, our framework considers counterfactual outcomes, rather than just observed outcomes, thus preventing loopholes where fairness criteria are satisfied through self-fulfilling prophecies. We provide concrete examples of how our counterfactual utility fairness framework resolves known fairness issues in classification, clustering, and reinforcement learning problems. We also show that many of the bespoke interpretations of Demographic Parity and Equal Opportunity fit nicely as special cases of our framework.

We propose a system for determining properties of mathematical functions given an image of their graph representation. We demonstrate our approach for two-dimensional graphs (curves of single variable functions) and three-dimensional graphs (surfaces of two variable functions), studying the properties of convexity and symmetry. Our method uses a Convolutional Neural Network which classifies functions according to these properties, without using any hand-crafted features. We propose algorithms for randomly constructing functions with convexity or symmetry properties, and use the images generated by these algorithms to train our network. Our system achieves a high accuracy on this task, even for functions where humans find it difficult to determine the function's properties from its image.

Elicitation is the study of statistics or properties which are computable via empirical risk minimization. While several recent papers have approached the general question of which properties are elicitable, we suggest that this is the wrong question---all properties are elicitable by first eliciting the entire distribution or data set, and thus the important question is how elicitable. Specifically, what is the minimum number of regression parameters needed to compute the property?Building on previous work, we introduce a new notion of elicitation complexity and lay the foundations for a calculus of elicitation. We establish several general results and techniques for proving upper and lower bounds on elicitation complexity. These results provide tight bounds for eliciting the Bayes risk of any loss, a large class of properties which includes spectral risk measures and several new properties of interest.