Due to the increasing use of Machine Learning models in high stakes decision
making settings, it has become increasingly important to have tools to
understand how models arrive at decisions. Assuming a trained Supervised
Classification model, explanations can be obtained via counterfactual analysis:
a counterfactual explanation of an instance indicates how this instance should
be minimally modified so that the perturbed instance is classified in the
desired class by the Machine Learning classification model. Most of the
Counterfactual Analysis literature focuses on the single-instance
single-counterfactual setting, in which the analysis is done for one single
instance to provide one single explanation. Taking a stakeholder's perspective,
in this paper we introduce the so-called collective counterfactual
explanations. By means of novel Mathematical Optimization models, we provide a
counterfactual explanation for each instance in a group of interest, so that
the total cost of the perturbations is minimized under some linking
constraints. Making the process of constructing counterfactuals collective
instead of individual enables us to detect the features that are critical to
the entire dataset to have the individuals classified in the desired class. Our
methodology allows for some instances to be treated individually, performing
the collective counterfactual analysis for a fraction of records of the group
of interest. This way, outliers are identified and handled appropriately. Under
some assumptions on the classifier and the space in which counterfactuals are
sought, finding collective counterfactuals is reduced to solving a convex
quadratic linearly constrained mixed integer optimization problem, which, for
datasets of moderate size, can be solved to optimality using existing solvers.
The performance of our approach is illustrated on real-world datasets,
demonstrating its usefulness.

利用数学优化模型，通过集体反事实解释为给定组内各实例提供一个反事实解释，以使扰动实例的总成本在一定约束下最小化，从而检测对整个数据集都至关重要的特征，验证了该方法的实用性。

通过数学优化在基于得分的分类中生成集体反事实解释

Generating collective counterfactual explanations in score-based  classification via mathematical optimization

Decision-making problems can be represented as mathematical optimization
models, finding wide applications in fields such as economics, engineering and
manufacturing, transportation, and health care. Optimization models are
mathematical abstractions of the problem of making the best decision while
satisfying a set of requirements or constraints. One of the primary barriers to
deploying these models in practice is the challenge of helping practitioners
understand and interpret such models, particularly when they are infeasible,
meaning no decision satisfies all the constraints. Existing methods for
diagnosing infeasible optimization models often rely on expert systems,
necessitating significant background knowledge in optimization. In this paper,
we introduce OptiChat, a first-of-its-kind natural language-based system
equipped with a chatbot GUI for engaging in interactive conversations about
infeasible optimization models. OptiChat can provide natural language
descriptions of the optimization model itself, identify potential sources of
infeasibility, and offer suggestions to make the model feasible. The
implementation of OptiChat is built on GPT-4, which interfaces with an
optimization solver to identify the minimal subset of constraints that render
the entire optimization problem infeasible, also known as the Irreducible
Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought,
key-retrieve, and sentiment prompts to enhance OptiChat's reliability. Our
experiments demonstrate that OptiChat assists both expert and non-expert users
in improving their understanding of the optimization models, enabling them to
quickly identify the sources of infeasibility.

OptiChat 是基于 GPT-4 的自然语言系统，具有聊天机器人图形用户界面，可以通过互动对话提供关于无法实现的优化模型的自然语言描述，识别潜在的无法实现原因，并提供使模型可行的建议，实验证明 OptiChat 可以帮助专家和非专家用户改善对优化模型的理解，快速识别无法实现的原因。