Gaussian-Bernoulli restricted Boltzmann machines (GBRBMs) are often used for
semi-supervised anomaly detection, where they are trained using only normal
data points. In GBRBM-based anomaly detection, normal and anomalous data are
classified based on a score that is identical to an energy function of the
marginal GBRBM. However, the classification threshold is difficult to set to an
appropriate value, as this score cannot be interpreted. In this study, we
propose a measure that improves score's interpretability based on its
cumulative distribution, and establish a guideline for setting the threshold
using the interpretable measure. The results of numerical experiments show that
the guideline is reasonable when setting the threshold solely using normal data
points. Moreover, because identifying the measure involves computationally
infeasible evaluation of the minimum score value, we also propose an evaluation
method for the minimum score based on simulated annealing, which is widely used
for optimization problems. The proposed evaluation method was also validated
using numerical experiments.

基于高斯 - 伯努利受限玻尔兹曼机的异常检测中，通过基于累积分布的可解释度测量，提出了用于设置分类阈值的准则。同时，通过模拟退火方法对最小得分进行评估，验证了该评估方法的可行性。

基于高斯伯努利受限玻尔兹曼机的异常检测分数解释性的改进

Improving Interpretability of Scores in Anomaly Detection Based on  Gaussian-Bernoulli Restricted Boltzmann Machine

Credit scoring has been catalogued by the European Commission and the
Executive Office of the US President as a high-risk classification task, a key
concern being the potential harms of making loan approval decisions based on
models that would be biased against certain groups. To address this concern,
recent credit scoring research has considered a range of fairness-enhancing
techniques put forward by the machine learning community to reduce bias and
unfair treatment in classification systems. While the definition of fairness or
the approach they follow to impose it may vary, most of these techniques,
however, disregard the robustness of the results. This can create situations
where unfair treatment is effectively corrected in the training set, but when
producing out-of-sample classifications, unfair treatment is incurred again.
Instead, in this paper, we will investigate how to apply Distributionally
Robust Optimisation (DRO) methods to credit scoring, thereby empirically
evaluating how they perform in terms of fairness, ability to classify
correctly, and the robustness of the solution against changes in the marginal
proportions. In so doing, we find DRO methods to provide a substantial
improvement in terms of fairness, with almost no loss in performance. These
results thus indicate that DRO can improve fairness in credit scoring, provided
that further advances are made in efficiently implementing these systems. In
addition, our analysis suggests that many of the commonly used fairness metrics
are unsuitable for a credit scoring setting, as they depend on the choice of
classification threshold.

应用分布鲁棒优化方法 (DRO) 研究信用评分，评估其在公平性、正确分类能力和解决边际比例变动时解决方案的稳健性方面的表现，结果显示 DRO 方法在公平性方面有显著改进，并且几乎不损失性能。但需要进一步完善有效实施这些系统。研究还指出，在信用评分环境中，许多常用的公平性指标并不适用，因为它们依赖于分类阈值的选择。

公平信用评分的分布鲁棒优化方法

A Distributionally Robust Optimisation Approach to Fair Credit Scoring

Demographic parity is the most widely recognized measure of group fairness in
machine learning, which ensures equal treatment of different demographic
groups. Numerous works aim to achieve demographic parity by pursuing the
commonly used metric $\Delta DP$. Unfortunately, in this paper, we reveal that
the fairness metric $\Delta DP$ can not precisely measure the violation of
demographic parity, because it inherently has the following drawbacks:
\textit{i)} zero-value $\Delta DP$ does not guarantee zero violation of
demographic parity, \textit{ii)} $\Delta DP$ values can vary with different
classification thresholds. To this end, we propose two new fairness metrics,
\textsf{A}rea \textsf{B}etween \textsf{P}robability density function
\textsf{C}urves (\textsf{ABPC}) and \textsf{A}rea \textsf{B}etween
\textsf{C}umulative density function \textsf{C}urves (\textsf{ABCC}), to
precisely measure the violation of demographic parity in distribution level.
The new fairness metrics directly measure the difference between the
distributions of the prediction probability for different demographic groups.
Thus our proposed new metrics enjoy: \textit{i)} zero-value
\textsf{ABCC}/\textsf{ABPC} guarantees zero violation of demographic parity;
\textit{ii)} \textsf{ABCC}/\textsf{ABPC} guarantees demographic parity while
the classification threshold adjusted. We further re-evaluate the existing fair
models with our proposed fairness metrics and observe different fairness
behaviors of those models under the new metrics.

该研究提出两种新的公平度量标准，ABPC 和 ABCC，用于精确量化分布级别的人口平等破坏。新的公平性指标直接衡量不同人口群体的预测概率分布之间的差异，并且在分类阈值调整时保证人口平等。