From Fairness to Infinity: Outcome-Indistinguishable (Omni)Prediction in Evolving Graphs

TL;DR

This paper develops online algorithms for evolving graphs that produce outcome-indistinguishable and omnipredictive edge formation predictions, enabling fair and efficient structural interventions in professional networks.

Contribution

It introduces novel online algorithms combining the online K29 star method with kernel methods to achieve outcome-indistinguishability and omniprediction in evolving graphs.

Findings

Algorithms provide multicalibrated edge formation predictions.

Guarantees improve upon existing methods.

Enable simultaneous optimization of multiple social welfare metrics.

Abstract

Professional networks provide invaluable entree to opportunity through referrals and introductions. A rich literature shows they also serve to entrench and even exacerbate a status quo of privilege and disadvantage. Hiring platforms, equipped with the ability to nudge link formation, provide a tantalizing opening for beneficial structural change. We anticipate that key to this prospect will be the ability to estimate the likelihood of edge formation in an evolving graph. Outcome-indistinguishable prediction algorithms ensure that the modeled world is indistinguishable from the real world by a family of statistical tests. Omnipredictors ensure that predictions can be post-processed to yield loss minimization competitive with respect to a benchmark class of predictors for many losses simultaneously, with appropriate post-processing. We begin by observing that, by combining a slightly modified form of the online K29 star algorithm of Vovk (2007) with basic facts from the theory of reproducing kernel Hilbert spaces, one can derive simple and efficient online algorithms satisfying outcome indistinguishability and omniprediction, with guarantees that improve upon, or are complementary to, those currently known. This is of independent interest. We apply these techniques to evolving graphs, obtaining online outcome-indistinguishable omnipredictors for rich -- possibly infinite -- sets of distinguishers that capture properties of pairs of nodes, and their neighborhoods. This yields, inter alia, multicalibrated predictions of edge formation with respect to pairs of demographic groups, and the ability to simultaneously optimize loss as measured by a variety of social welfare functions.