公平性约束有助于结构化预测中的精确推理
Fairness constraints can help exact inference in structured prediction
摘要：
结构化预测中的许多推理问题可以建模为在标签空间上最大化得分函数，其中图是将总分数分解为一元（节点）和成对（边缘）分数之和的自然表示。给定具有无向连接图$G$和二进制标签的真实向量的生成模型，先前已经示出，当$G$具有良好的扩展属性时，例如完全图或$d$ -正则扩展器，可以从每个边缘和节点的单个噪声观察中精确地恢复真实标签（具有高概率并且在多项式时间内）。我们在统计奇偶性的概念下分析了以前研究过的生成模型，由Globerson等人（2015）。也就是说，给定一个公平的二进制节点标记，我们问的问题是，是否有可能恢复公平的分配，以高概率和多项式时间，从单一的边缘和节点的意见。我们发现，与公知的公平性和模型性能之间的权衡相比，公平性约束的加入提高了准确恢复的概率。我们有效地解释了这一现象，并经验性地展示了具有较差扩展特性的图形（如网格）现在如何能够以高概率实现精确恢复。最后，作为我们的分析的副产品，我们提供了一个更严格的最小特征值界比外尔不等式。
英文摘要：
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.
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