Fairness constraints can help exact inference in structured prediction

TL;DR

This paper demonstrates that incorporating fairness constraints in structured prediction models can enhance the likelihood of exact label recovery, especially on graphs with poor expansion properties, and provides theoretical and empirical insights into this phenomenon.

Contribution

It shows that fairness constraints can improve exact inference in structured prediction, challenging the usual trade-offs and extending results to graphs with poor expansion.

Findings

Fairness constraints increase the probability of exact recovery.

Graphs with poor expansion, like grids, can achieve high-probability exact recovery.

A tighter minimum-eigenvalue bound is derived.

Abstract

Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges) scores. Given a generative model with an undirected connected graph $G$ and true vector of binary labels, it has been previously shown that when $G$ has good expansion properties, such as complete graphs or $d$-regular expanders, one can exactly recover the true labels (with high probability and in polynomial time) from a single noisy observation of each edge and node. We analyze the previously studied generative model by Globerson et al. (2015) under a notion of statistical parity. That is, given a fair binary node labeling, we ask the question whether it is possible to recover the fair assignment, with high probability and in polynomial time, from single edge and node observations. We find that, in contrast to the known trade-offs between fairness and model performance, the addition of the fairness constraint improves the probability of exact recovery. We effectively explain this phenomenon and empirically show how graphs with poor expansion properties, such as grids, are now capable to achieve exact recovery with high probability. Finally, as a byproduct of our analysis, we provide a tighter minimum-eigenvalue bound than that of Weyl's inequality.