现有的可解释AI和可解释的ML的方法无法解释统计单元的输出变量值的变化，以说明输入值的变化以及“机制”的变化（将输入转换为输出的函数）的变化。我们提出了两种基于反事实的方法，用于使用游戏理论中的沙普利值的概念来解释各种输入粒度的单位级变化。这些方法满足了对任何单位级别更改归因方法所需的两个关键公理。通过模拟，我们研究了所提出方法的可靠性和可扩展性。我们从案例研究中获得了明智的结果，该案例研究确定了美国个人收入变化的驱动力。

我们介绍了Dowhy Python库的扩展Dowhy-GCM，该库利用图形因果模型。与现有的因果关系库（主要关注效应估计问题）不同，使用Dowhy-GCM，用户可以提出各种其他因果问题，例如确定异常值的根本原因和分布变化的根本原因，因果结构学习，归因于因果关系，以及因果影响，以及归因于因果关系因果结构的诊断。为此，Dowhy-GCM用户通过图形因果模型在研究系统中的变量之间的首次模型导致关系效果关系，符合接下来变量的因果机制，然后提出因果问题。所有这些步骤仅在Dowhy-GCM中采用几行代码。该库可在https://github.com/py-why/dowhy上找到。

我们基于从多个数据集的合并信息介绍了一种反事实推断的方法。我们考虑了统计边际问题的因果重新重新制定：鉴于边际结构因果模型（SCM）的集合在不同但重叠的变量集上，请确定与边际相反一致的关节SCMS集。我们使用响应函数配方对分类SCM进行了形式化这种方法，并表明它降低了允许的边际和关节SCM的空间。因此，我们的工作通过其他变量突出了一种通过其他变量的新模式，与统计数据相反。

尽管预测方法的相关性越来越高，但这些算法的因果影响仍然很大程度上是未开发的。这与考虑到，即使在简化因果充足之类的假设下，模型的统计风险也可能与其\ Textit {因果风险}有显着差异。在这里，我们研究了*因果概括* - 从观察到介入分布的概括 - 预测。我们的目标是找到问题的答案：自回归（var）模型在预测统计协会方面的疗效如何与其在干预措施下预测的能力相比？为此，我们介绍了*因果学习理论*预测的框架。使用此框架，我们获得了统计和因果风险之间差异的表征，这有助于识别它们之间的分歧源。在因果充足之下，因果概括的因果概括金额与额外的结构（限制介入介入分配）。该结构允许我们获得统一的收敛界面对VAR模型类的因果概括性。据我们所知，这是第一个为时序设置中因果概念提供理论保障的工作。

由于没有理由更喜欢另一个，因此原因不足（PIR）的原则为随机实验的每种替代方案分配相同的概率。最大熵原理（MaxEnt）将PIR推广到给出期望等预期的统计信息。众所周知，这两种原则都会导致矛盾的概率更新，用于导致和效果的联合分布。这是因为在条件p（效果）上的约束导致p（原因）的变化为导致的原因的值较高的概率，这些值为效果提供更多选项，表明“有意行为”。因此，早期的工作根据因果秩序顺序地最大化（条件）熵，但除了玩具例子的合理性之外，没有进一步的理由。我们通过将限制分离为从原因产生效果的机制的原因和限制的限制来证明PIR和Maxent的因果修改。我们进一步描绘了原因PIR的原因也需要“信息几何因果推理”。我们简要讨论了概括最大值的原因版本到任意因果表达的问题。

我们提出了一个新的因果贡献的概念，它描述了在DAG中目标节点上的节点的“内在”部分。我们显示，在某些情况下，现有的因果量化方法无法完全捕获此概念。通过以上游噪声术语递归地将每个节点写入每个节点，我们将每个节点添加的内部信息分开从其祖先所获得的每个节点添加的内部信息。要将内在信息解释为因果贡献，我们考虑“结构保留干预”，该介绍每个节点随机化，以一种模仿通常依赖父母的方式，也不会扰乱观察到的联合分布。为了获得跨越节点的任意排序的措施，我们提出了基于福利的对称化。我们描述了对方差和熵的贡献分析，但可以类似地定义对其他目标度量的贡献。

可以培训生成模型以模拟复杂的经验数据，但它们是有用的，可以在先前未观察到的环境的上下文中进行预测吗？促进这种外推能力的直观思想是具有这种模型的架构反映真实数据生成过程的因果图，使得可以独立于其他节点介入每个节点。然而，该图的节点通常是不可观察的，导致过度公开表化和缺乏因果结构的可识别性。通过定义机制独立原则，我们制定理论框架来解决这一具有挑战性的情况，以解决较弱的可识别性。我们在玩具例子上展示了经典随机梯度下降可以阻碍模型的外推能力，建议在培训期间明确地强制执行机制的独立性。关于现实世界数据培训的深度生成模型的实验支持这些见解，并说明如何利用这些模型的外推能力。

The analysis of network structure is essential to many scientific areas, ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO based approach that only needs number-of-nodes many qubits and is represented by a QUBO-matrix as sparse as the input graph's adjacency matrix. The substantial improvement on the sparsity of the QUBO-matrix, which is typically very dense in related work, is achieved through the novel concept of separation-nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which -- upon its removal from the graph -- yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept. This work hence displays a promising approach to NISQ ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large scale, real world problem instances.

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, also a novel primal-dual Langevin algorithm for sampling from non-smooth distributions is introduced in this work.

Machine learning (ML) on graph-structured data has recently received deepened interest in the context of intrusion detection in the cybersecurity domain. Due to the increasing amounts of data generated by monitoring tools as well as more and more sophisticated attacks, these ML methods are gaining traction. Knowledge graphs and their corresponding learning techniques such as Graph Neural Networks (GNNs) with their ability to seamlessly integrate data from multiple domains using human-understandable vocabularies, are finding application in the cybersecurity domain. However, similar to other connectionist models, GNNs are lacking transparency in their decision making. This is especially important as there tend to be a high number of false positive alerts in the cybersecurity domain, such that triage needs to be done by domain experts, requiring a lot of man power. Therefore, we are addressing Explainable AI (XAI) for GNNs to enhance trust management by exploring combining symbolic and sub-symbolic methods in the area of cybersecurity that incorporate domain knowledge. We experimented with this approach by generating explanations in an industrial demonstrator system. The proposed method is shown to produce intuitive explanations for alerts for a diverse range of scenarios. Not only do the explanations provide deeper insights into the alerts, but they also lead to a reduction of false positive alerts by 66% and by 93% when including the fidelity metric.