Neural networks often assume independence among input data samples,
disregarding correlations arising from inherent clustering patterns in
real-world datasets (e.g., due to different sites or repeated measurements).
Recently, mixed effects neural networks (MENNs) which separate cluster-specific
'random effects' from cluster-invariant 'fixed effects' have been proposed to
improve generalization and interpretability for clustered data. However,
existing methods only allow for approximate quantification of cluster effects
and are limited to regression and binary targets with only one clustering
feature. We present MC-GMENN, a novel approach employing Monte Carlo methods to
train Generalized Mixed Effects Neural Networks. We empirically demonstrate
that MC-GMENN outperforms existing mixed effects deep learning models in terms
of generalization performance, time complexity, and quantification of
inter-cluster variance. Additionally, MC-GMENN is applicable to a wide range of
datasets, including multi-class classification tasks with multiple
high-cardinality categorical features. For these datasets, we show that
MC-GMENN outperforms conventional encoding and embedding methods,
simultaneously offering a principled methodology for interpreting the effects
of clustering patterns.

MC-GMENN 是一种新颖的方法，使用蒙特卡罗方法训练广义混合效应神经网络，证明在泛化性能、时间复杂度和簇间差异量化方面优于现有的混合效应深度学习模型，适用于包括多类别分类任务在内的各种数据集，并提供了一种解释聚类模式效果的原则方法。

利用蒙特卡罗方法实现混合效应神经网络对多样化，集群数据的支持

Enabling Mixed Effects Neural Networks for Diverse, Clustered Data Using  Monte Carlo Methods

To ensure unbiased and ethical automated predictions, fairness must be a core
principle in machine learning applications. Fairness in machine learning aims
to mitigate biases present in the training data and model imperfections that
could lead to discriminatory outcomes. This is achieved by preventing the model
from making decisions based on sensitive characteristics like ethnicity or
sexual orientation. A fundamental assumption in machine learning is the
independence of observations. However, this assumption often does not hold true
for data describing social phenomena, where data points are often clustered
based. Hence, if the machine learning models do not account for the cluster
correlations, the results may be biased. Especially high is the bias in cases
where the cluster assignment is correlated to the variable of interest. We
present a fair mixed effects support vector machine algorithm that can handle
both problems simultaneously. With a reproducible simulation study we
demonstrate the impact of clustered data on the quality of fair machine
learning predictions.

机器学习中的公平性与聚类数据对公平机器学习预测的影响，以及一种能够同时处理这两个问题的公平混合效应支持向量机算法。

公平混合效应支持向量机

Fair Mixed Effects Support Vector Machine

We propose an $\ell_1$-penalized estimation procedure for high-dimensional
linear mixed-effects models. The models are useful whenever there is a grouping
structure among high-dimensional observations, i.e. for clustered data. We
prove a consistency and an oracle optimality result and we develop an algorithm
with provable numerical convergence. Furthermore, we demonstrate the
performance of the method on simulated and a real high-dimensional data set.

本研究提出了一种针对高维线性混合效应模型的 $\ell_1$- 惩罚估计过程，该模型对于高维观测中存在分组结构的数据非常有用。我们证明了一致性和优化性结果，并开发了一种具有可证明数值收敛性的算法。此外，我们还在模拟和实际高维数据集上展示了该方法的性能。