我们严格地证明，如果目标函数具有组成结构，那么深层的过程先验可以超越高斯工艺先验。为此，我们研究了连续回归模型中高斯过程回归后收缩率的信息理论下限。我们表明，如果真实函数是广义的加性函数，那么基于任何平均零高斯过程的后验只能以严格慢的速率恢复真相，而该速率比最小值速率慢了，该因子在样品中多项式次优的因素。尺寸$ n $。

古典统计学习理论表示，拟合太多参数导致过度舒服和性能差。尽管大量参数矛盾，但是现代深度神经网络概括了这一发现，并构成了解释深度学习成功的主要未解决的问题。随机梯度下降（SGD）引起的隐式正规被认为是重要的，但其特定原则仍然是未知的。在这项工作中，我们研究了当地最小值周围的能量景观的局部几何学如何影响SGD的统计特性，具有高斯梯度噪声。我们争辩说，在合理的假设下，局部几何形状力强制SGD保持接近低维子空间，这会引起隐式正则化并导致深神经网络的泛化误差界定更严格的界限。为了获得神经网络的泛化误差界限，我们首先引入局部最小值周围的停滞迹象，并施加人口风险的局部基本凸性财产。在这些条件下，推导出SGD的下界，以保留在这些停滞套件中。如果发生停滞，我们会导出涉及权重矩阵的光谱规范的深神经网络的泛化误差的界限，但不是网络参数的数量。从技术上讲，我们的证据基于控制SGD中的参数值的变化以及基于局部最小值周围的合适邻域的熵迭代的参数值和局部均匀收敛。我们的工作试图通过统一收敛更好地连接非凸优化和泛化分析。

对于高维和非参数统计模型，速率最优估计器平衡平方偏差和方差是一种常见的现象。虽然这种平衡被广泛观察到，但很少知道是否存在可以避免偏差和方差之间的权衡的方法。我们提出了一般的策略，以获得对任何估计方差的下限，偏差小于预先限定的界限。这表明偏差差异折衷的程度是不可避免的，并且允许量化不服从其的方法的性能损失。该方法基于许多抽象的下限，用于涉及关于不同概率措施的预期变化以及诸如Kullback-Leibler或Chi-Sque-diversence的信息措施的变化。其中一些不平等依赖于信息矩阵的新概念。在该物品的第二部分中，将抽象的下限应用于几种统计模型，包括高斯白噪声模型，边界估计问题，高斯序列模型和高维线性回归模型。对于这些特定的统计应用，发生不同类型的偏差差异发生，其实力变化很大。对于高斯白噪声模型中集成平方偏置和集成方差之间的权衡，我们将较低界限的一般策略与减少技术相结合。这允许我们将原始问题与估计的估计器中的偏差折衷联动，以更简单的统计模型中具有额外的对称性属性。在高斯序列模型中，发生偏差差异的不同相位转换。虽然偏差和方差之间存在非平凡的相互作用，但是平方偏差的速率和方差不必平衡以实现最小估计速率。

Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to log nfactors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility in the network architecture, the tuning parameter is the sparsity of the network. Specifically, we consider large networks with number of potential network parameters exceeding the sample size. The analysis gives some insights into why multilayer feedforward neural networks perform well in practice. Interestingly, for ReLU activation function the depth (number of layers) of the neural network architectures plays an important role and our theory suggests that for nonparametric regression, scaling the network depth with the sample size is natural. It is also shown that under the composition assumption wavelet estimators can only achieve suboptimal rates.

Machine learning models are typically evaluated by computing similarity with reference annotations and trained by maximizing similarity with such. Especially in the bio-medical domain, annotations are subjective and suffer from low inter- and intra-rater reliability. Since annotations only reflect the annotation entity's interpretation of the real world, this can lead to sub-optimal predictions even though the model achieves high similarity scores. Here, the theoretical concept of Peak Ground Truth (PGT) is introduced. PGT marks the point beyond which an increase in similarity with the reference annotation stops translating to better Real World Model Performance (RWMP). Additionally, a quantitative technique to approximate PGT by computing inter- and intra-rater reliability is proposed. Finally, three categories of PGT-aware strategies to evaluate and improve model performance are reviewed.

Quaternion valued neural networks experienced rising popularity and interest from researchers in the last years, whereby the derivatives with respect to quaternions needed for optimization are calculated as the sum of the partial derivatives with respect to the real and imaginary parts. However, we can show that product- and chain-rule does not hold with this approach. We solve this by employing the GHRCalculus and derive quaternion backpropagation based on this. Furthermore, we experimentally prove the functionality of the derived quaternion backpropagation.

Neuromorphic systems require user-friendly software to support the design and optimization of experiments. In this work, we address this need by presenting our development of a machine learning-based modeling framework for the BrainScaleS-2 neuromorphic system. This work represents an improvement over previous efforts, which either focused on the matrix-multiplication mode of BrainScaleS-2 or lacked full automation. Our framework, called hxtorch.snn, enables the hardware-in-the-loop training of spiking neural networks within PyTorch, including support for auto differentiation in a fully-automated hardware experiment workflow. In addition, hxtorch.snn facilitates seamless transitions between emulating on hardware and simulating in software. We demonstrate the capabilities of hxtorch.snn on a classification task using the Yin-Yang dataset employing a gradient-based approach with surrogate gradients and densely sampled membrane observations from the BrainScaleS-2 hardware system.

Osteoarthritis (OA) is the most prevalent chronic joint disease worldwide, where knee OA takes more than 80% of commonly affected joints. Knee OA is not a curable disease yet, and it affects large columns of patients, making it costly to patients and healthcare systems. Etiology, diagnosis, and treatment of knee OA might be argued by variability in its clinical and physical manifestations. Although knee OA carries a list of well-known terminology aiming to standardize the nomenclature of the diagnosis, prognosis, treatment, and clinical outcomes of the chronic joint disease, in practice there is a wide range of terminology associated with knee OA across different data sources, including but not limited to biomedical literature, clinical notes, healthcare literacy, and health-related social media. Among these data sources, the scientific articles published in the biomedical literature usually make a principled pipeline to study disease. Rapid yet, accurate text mining on large-scale scientific literature may discover novel knowledge and terminology to better understand knee OA and to improve the quality of knee OA diagnosis, prevention, and treatment. The present works aim to utilize artificial neural network strategies to automatically extract vocabularies associated with knee OA diseases. Our finding indicates the feasibility of developing word embedding neural networks for autonomous keyword extraction and abstraction of knee OA.

Data-centric artificial intelligence (data-centric AI) represents an emerging paradigm emphasizing that the systematic design and engineering of data is essential for building effective and efficient AI-based systems. The objective of this article is to introduce practitioners and researchers from the field of Information Systems (IS) to data-centric AI. We define relevant terms, provide key characteristics to contrast the data-centric paradigm to the model-centric one, and introduce a framework for data-centric AI. We distinguish data-centric AI from related concepts and discuss its longer-term implications for the IS community.

Many real-world reinforcement learning tasks require control of complex dynamical systems that involve both costly data acquisition processes and large state spaces. In cases where the transition dynamics can be readily evaluated at specified states (e.g., via a simulator), agents can operate in what is often referred to as planning with a \emph{generative model}. We propose the AE-LSVI algorithm for best-policy identification, a novel variant of the kernelized least-squares value iteration (LSVI) algorithm that combines optimism with pessimism for active exploration (AE). AE-LSVI provably identifies a near-optimal policy \emph{uniformly} over an entire state space and achieves polynomial sample complexity guarantees that are independent of the number of states. When specialized to the recently introduced offline contextual Bayesian optimization setting, our algorithm achieves improved sample complexity bounds. Experimentally, we demonstrate that AE-LSVI outperforms other RL algorithms in a variety of environments when robustness to the initial state is required.