Fair GLASSO：估计具有无偏统计行为的公平图模型
Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior
AI总结：
针对图结构数据中敏感节点属性导致的统计歧视，本文提出 Fair GLASSO 及近端梯度算法，估计群体间无偏依赖的稀疏 Gaussian 精度矩阵，并给出准确性—公平性权衡、复杂度与实证验证。
摘要：
我们提出估计关于敏感节点属性公平的 Gaussian graphical models（GGM，高斯图模型）。许多现实世界模型由于数据中的偏差而表现出不公平的歧视行为。众所周知，当数据具有以图编码的成对关系时，这种歧视会加剧。此外，有偏数据对图模型的影响在很大程度上仍未得到充分研究。因此，我们以两个偏差指标的形式引入图模型的公平性，以促进具有不同敏感属性的节点群体之间统计相似性的平衡。利用这些指标，我们提出 Fair GLASSO，这是一种正则化 graphical lasso 方法，用于获得稀疏 Gaussian 精度矩阵，并在各群体之间具有无偏统计依赖。我们还提出一种高效的近端梯度算法来获得估计值。在理论上，我们表述了公平与准确估计的精度矩阵之间的权衡。关键在于，这包括证明在存在公平正则化项时何时能够保持准确性。在此基础上，我们研究 Fair GLASSO 的复杂性，并证明我们的算法具有快速收敛速率。我们的实证验证包括合成仿真和现实世界仿真，这些仿真说明了所提出优化问题和迭代算法的价值与有效性。
英文摘要：
We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes. Many real-world models exhibit unfair discriminatory behavior due to biases in data. Such discrimination is known to be exacerbated when data is equipped with pairwise relationships encoded in a graph. Additionally, the effect of biased data on graphical models is largely underexplored. We thus introduce fairness for graphical models in the form of two bias metrics to promote balance in statistical similarities across nodal groups with different sensitive attributes. Leveraging these metrics, we present Fair GLASSO, a regularized graphical lasso approach to obtain sparse Gaussian precision matrices with unbiased statistical dependencies across groups. We also propose an efficient proximal gradient algorithm to obtain the estimates. Theoretically, we express the tradeoff between fair and accurate estimated precision matrices. Critically, this includes demonstrating when accuracy can be preserved in the presence of a fairness regularizer. On top of this, we study the complexity of Fair GLASSO and demonstrate that our algorithm enjoys a fast convergence rate. Our empirical validation includes synthetic and real-world simulations that illustrate the value and effectiveness of our proposed optimization problem and iterative algorithm.
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