Not all real-world data are labeled, and when labels are not available, it is
often costly to obtain them. Moreover, as many algorithms suffer from the curse
of dimensionality, reducing the features in the data to a smaller set is often
of great utility. Unsupervised feature selection aims to reduce the number of
features, often using feature importance scores to quantify the relevancy of
single features to the task at hand. These scores can be based only on the
distribution of variables and the quantification of their interactions. The
previous literature, mainly investigating anomaly detection and clusters, fails
to address the redundancy-elimination issue. We propose an evaluation of
correlations among features to compute feature importance scores representing
the contribution of single features in explaining the dataset's structure.
Based on Coalitional Game Theory, our feature importance scores include a
notion of redundancy awareness making them a tool to achieve redundancy-free
feature selection. We show that the deriving features' selection outperforms
competing methods in lowering the redundancy rate while maximizing the
information contained in the data. We also introduce an approximated version of
the algorithm to reduce the complexity of Shapley values' computations.

本文提出了一种基于博弈理论、计算特征重要性的方法，用于无监督特征选择并消除冗余，结果表明该方法在降低冗余率的同时最大化数据信息。同时，本文还介绍了一种计算 Shapley 值的算法的近似版本，使其能够降低复杂度。

基于集合博弈理论的无监督分类数据特征排序

Unsupervised Features Ranking via Coalitional Game Theory for  Categorical Data

Federated learning is a setting where agents, each with access to their own
data source, combine models from local data to create a global model. If agents
are drawing their data from different distributions, though, federated learning
might produce a biased global model that is not optimal for each agent. This
means that agents face a fundamental question: should they choose the global
model or their local model? We show how this situation can be naturally
analyzed through the framework of coalitional game theory.
We propose the following game: there are heterogeneous players with different
model parameters governing their data distribution and different amounts of
data they have noisily drawn from their own distribution. Each player's goal is
to obtain a model with minimal expected mean squared error (MSE) on their own
distribution. They have a choice of fitting a model based solely on their own
data, or combining their learned parameters with those of some subset of the
other players. Combining models reduces the variance component of their error
through access to more data, but increases the bias because of the
heterogeneity of distributions.
Here, we derive exact expected MSE values for problems in linear regression
and mean estimation. We then analyze the resulting game in the framework of
hedonic game theory; we study how players might divide into coalitions, where
each set of players within a coalition jointly construct model(s). We analyze
three methods of federation, modeling differing degrees of customization. In
uniform federation, the agents collectively produce a single model. In
coarse-grained federation, each agent can weight the global model together with
their local model. In fine-grained federation, each agent can flexibly combine
models from all other agents in the federation. For each method, we analyze the
stable partitions of players into coalitions.

本文介绍了在联邦学习中，面临着全局模型与本地模型的选择困境，运用博弈论的框架进行自然分析，提出了基于博弈论的联邦学习模型，探讨了均衡的选手分区问题，并分别分析了三种联邦模式的稳定分区。

模型共享游戏：自愿参与下联邦学习的分析

Model-sharing Games: Analyzing Federated Learning Under Voluntary  Participation

Understanding the influence of features in machine learning is crucial to
interpreting models and selecting the best features for classification. In this
work we propose the use of principles from coalitional game theory to reason
about importance of features. In particular, we propose the use of the Banzhaf
power index as a measure of influence of features on the outcome of a
classifier. We show that features having Banzhaf power index of zero can be
losslessly pruned without damage to classifier accuracy. Computing the power
indices does not require having access to data samples. However, if samples are
available, the indices can be empirically estimated. We compute Banzhaf power
indices for a neural network classifier on real-life data, and compare the
results with gradient-based feature saliency, and coefficients of a logistic
regression model with $L_1$ regularization.

本研究提出利用集合博弈理论的原则来解释和选择分类器最佳特征，并使用 Banzhaf power index 测量特征对分类器结果的影响，结果表明 Banzhaf power index 为零的特征可被无损剪枝以提高分类器性能，无需访问数据样本。