Recent studies have highlighted the benefits of generating multiple synthetic
datasets for supervised learning, from increased accuracy to more effective
model selection and uncertainty estimation. These benefits have clear empirical
support, but the theoretical understanding of them is currently very light. We
seek to increase the theoretical understanding by deriving bias-variance
decompositions for several settings of using multiple synthetic datasets. Our
theory predicts multiple synthetic datasets to be especially beneficial for
high-variance downstream predictors, and yields a simple rule of thumb to
select the appropriate number of synthetic datasets in the case of mean-squared
error and Brier score. We investigate how our theory works in practice by
evaluating the performance of an ensemble over many synthetic datasets for
several real datasets and downstream predictors. The results follow our theory,
showing that our insights are also practically relevant.

通过推导多个合成数据集使用的偏差 - 方差分解，我们的理论预测多个合成数据集对于高方差的下游预测器特别有益，并给出了在均方误差和 Brier 得分情况下选择合适数量合成数据集的简单经验法则。在多个真实数据集和下游预测器上评估集成的性能，结果符合我们的理论，表明我们的洞察力在实践中也具有相关性。

多个合成数据集上集成模型的偏差 - 方差分解

A Bias-Variance Decomposition for Ensembles over Multiple Synthetic  Datasets

Fair representation learning is an attractive approach that promises fairness
of downstream predictors by encoding sensitive data. Unfortunately, recent work
has shown that strong adversarial predictors can still exhibit unfairness by
recovering sensitive attributes from these representations. In this work, we
present Fair Normalizing Flows (FNF), a new approach offering more rigorous
fairness guarantees for learned representations. Specifically, we consider a
practical setting where we can estimate the probability density for sensitive
groups. The key idea is to model the encoder as a normalizing flow trained to
minimize the statistical distance between the latent representations of
different groups. The main advantage of FNF is that its exact likelihood
computation allows us to obtain guarantees on the maximum unfairness of any
potentially adversarial downstream predictor. We experimentally demonstrate the
effectiveness of FNF in enforcing various group fairness notions, as well as
other attractive properties such as interpretability and transfer learning, on
a variety of challenging real-world datasets.

本文提出了公平正则流 (FNF) 的方法来保证公平性，FNF 模型将敏感信息通过对编码器进行归一化流建模的方法来区分不同的群体，从而提供更严格的公平保障与最大不公平性的保障，并证明了其在各种具有挑战性的实际数据集上的有效性。