贝叶斯深度学习提供了一种原则性的方法来训练神经网络，以说明造成这种不确定性和认知不确定性。在各种推理中，先验通常是在权重参数上指定的，但它们并未捕获大型和复杂的神经网络体系结构中的真实先验知识。我们提出了一种简单的方法，以结合有关贝叶斯神经网络（BNN）中预测概率（例如Sigmoid或SoftMax评分）输出的摘要信息。可用的摘要信息被合并为增强数据，并以Dirichlet过程进行建模，我们得出相应的\ emph {摘要证据下限}。我们展示了该方法如何为模型提供有关任务难度或班级失衡的信息。广泛的经验实验表明，在可忽略的计算开销中，提出的方法产生了BNN，并具有更好的不确定性校准。

尽管扩散模型在图像生成中表现出了巨大的成功，但它们的噪声生成过程并未明确考虑图像的结构，例如它们固有的多尺度性质。受扩散模型的启发和粗到精细建模的可取性，我们提出了一个新模型，该模型通过迭代反转热方程式生成图像，当在图像的2D平面上运行时，PDE局部删除了细尺度信息。在我们的新方法中，正向热方程的解被解释为有向图形模型中的变异近似。我们展示了有希望的图像质量，并指出了在扩散模型中未见的新兴定性特性，例如在神经网络可解释性的图像和各个方面的整体颜色和形状分解。对自然图像的光谱分析将我们的模型定位为扩散模型的一种双重偶，并揭示了其中的隐式感应偏见。

贝叶斯神经网络（BNNS）通过提供认知不确定性的原则概率表示，有望在协变量转移下改善概括。但是，基于重量的BNN通常会在大规模体系结构和数据集的高计算复杂性上挣扎。基于节点的BNN最近被引入了可扩展的替代方案，该替代方案通过将每个隐藏节点乘以潜在的随机变量来诱导认知不确定性，同时学习权重的点刻度。在本文中，我们将这些潜在的噪声变量解释为训练过程中简单和域 - 不合时宜数据扰动的隐式表示，从而产生了由于输入损坏而导致协变量转移的BNN。我们观察到，隐性腐败的多样性取决于潜在变量的熵，并提出了一种直接的方法来增加训练期间这些变量的熵。我们评估了分布外图像分类基准测试的方法，并显示出由于输入扰动而导致的协变量转移下基于节点的BNN的不确定性估计。作为副作用，该方法还提供了针对嘈杂训练标签的鲁棒性。

图加高斯进程（GGPS）在图形结构域提供数据有效解决方案。现有方法专注于静态结构，而许多实际图表数据代表动态结构，限制了GGP的应用。克服这一点，我们提出了不断发展的图形高斯过程（E-GGPS）。该方法能够通过邻域内核随时间学习图形顶点的转换函数来模拟顶点之间的连接和交互变化。我们评估我们对时间序列回归问题的方法的性能随着时间的推移而演变的。我们展示了E-GGP对静态图高斯工艺方法的益处。

最近的机器学习进展已直接从数据中直接提出了对未知连续时间系统动力学的黑盒估计。但是，较早的作品基于近似ODE解决方案或点估计。我们提出了一种新型的贝叶斯非参数模型，该模型使用高斯工艺直接从数据中直接从数据中推断出未知ODE系统的后代。我们通过脱钩的功能采样得出稀疏的变异推断，以表示矢量场后代。我们还引入了一种概率的射击增强，以从任意长的轨迹中有效推断。该方法证明了计算矢量场后代的好处，预测不确定性得分优于多个ODE学习任务的替代方法。

In recent years, several metrics have been developed for evaluating group fairness of rankings. Given that these metrics were developed with different application contexts and ranking algorithms in mind, it is not straightforward which metric to choose for a given scenario. In this paper, we perform a comprehensive comparative analysis of existing group fairness metrics developed in the context of fair ranking. By virtue of their diverse application contexts, we argue that such a comparative analysis is not straightforward. Hence, we take an axiomatic approach whereby we design a set of thirteen properties for group fairness metrics that consider different ranking settings. A metric can then be selected depending on whether it satisfies all or a subset of these properties. We apply these properties on eleven existing group fairness metrics, and through both empirical and theoretical results we demonstrate that most of these metrics only satisfy a small subset of the proposed properties. These findings highlight limitations of existing metrics, and provide insights into how to evaluate and interpret different fairness metrics in practical deployment. The proposed properties can also assist practitioners in selecting appropriate metrics for evaluating fairness in a specific application.

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

Classically, the development of humanoid robots has been sequential and iterative. Such bottom-up design procedures rely heavily on intuition and are often biased by the designer's experience. Exploiting the non-linear coupled design space of robots is non-trivial and requires a systematic procedure for exploration. We adopt the top-down design strategy, the V-model, used in automotive and aerospace industries. Our co-design approach identifies non-intuitive designs from within the design space and obtains the maximum permissible range of the design variables as a solution space, to physically realise the obtained design. We show that by constructing the solution space, one can (1) decompose higher-level requirements onto sub-system-level requirements with tolerance, alleviating the "chicken-or-egg" problem during the design process, (2) decouple the robot's morphology from its controller, enabling greater design flexibility, (3) obtain independent sub-system level requirements, reducing the development time by parallelising the development process.

Recent diffusion-based AI art platforms are able to create impressive images from simple text descriptions. This makes them powerful tools for concept design in any discipline that requires creativity in visual design tasks. This is also true for early stages of architectural design with multiple stages of ideation, sketching and modelling. In this paper, we investigate how applicable diffusion-based models already are to these tasks. We research the applicability of the platforms Midjourney, DALL-E 2 and StableDiffusion to a series of common use cases in architectural design to determine which are already solvable or might soon be. We also analyze how they are already being used by analyzing a data set of 40 million Midjourney queries with NLP methods to extract common usage patterns. With this insights we derived a workflow to interior and exterior design that combines the strengths of the individual platforms.

With the rise of AI and automation, moral decisions are being put into the hands of algorithms that were formerly the preserve of humans. In autonomous driving, a variety of such decisions with ethical implications are made by algorithms for behavior and trajectory planning. Therefore, we present an ethical trajectory planning algorithm with a framework that aims at a fair distribution of risk among road users. Our implementation incorporates a combination of five essential ethical principles: minimization of the overall risk, priority for the worst-off, equal treatment of people, responsibility, and maximum acceptable risk. To the best of the authors' knowledge, this is the first ethical algorithm for trajectory planning of autonomous vehicles in line with the 20 recommendations from the EU Commission expert group and with general applicability to various traffic situations. We showcase the ethical behavior of our algorithm in selected scenarios and provide an empirical analysis of the ethical principles in 2000 scenarios. The code used in this research is available as open-source software.