Pitch ownership models allow many types of analysis in soccer and provide valuable assistance to tactical analysts in understanding the game's dynamics. The novelty they provide over event-based analysis is that tracking data incorporates context that event-based data does not possess, like player positioning. This paper proposes a novel approach to building pitch ownership models in soccer games using the K-Nearest Neighbors (KNN) algorithm. Our approach provides a fast inference mechanism that can model different approaches to pitch control using the same algorithm. Despite its flexibility, it uses only three hyperparameters to tune the model, facilitating the tuning process for different player skill levels. The flexibility of the approach allows for the emulation of different methods available in the literature by adjusting a small number of parameters, including adjusting for different levels of uncertainty. In summary, the proposed model provides a new and more flexible strategy for building pitch ownership models, extending beyond just replicating existing algorithms, and can provide valuable insights for tactical analysts and open up new avenues for future research. We thoroughly visualize several examples demonstrating the presented models' strengths and weaknesses. The code is available at github.com/nvsclub/KNNPitchControl.

Alzheimer's disease (AD) progresses through distinct stages, from early mild cognitive impairment (EMCI) to late mild cognitive impairment (LMCI) and eventually to AD. Accurate identification of these stages, especially distinguishing LMCI from EMCI, is crucial for developing pre-dementia treatments but remains challenging due to subtle and overlapping imaging features. This study proposes a minimal-feature machine learning framework that leverages structural MRI data, focusing on the hippocampus and amygdala as regions of interest. The framework addresses the curse of dimensionality through feature selection, utilizes region-specific voxel information, and implements innovative data organization to enhance classification performance by reducing noise. The methodology integrates dimensionality reduction techniques such as PCA and t-SNE with state-of-the-art classifiers, achieving the highest accuracy of 88.46%. This framework demonstrates the potential for efficient and accurate staging of AD progression while providing valuable insights for clinical applications.

The growing demand for halal cosmetic products has exposed significant challenges, especially in Muslim-majority countries. Recently, various machine learning-based strategies, e.g., image-based methods, have shown remarkable success in predicting the halal status of cosmetics. However, these methods mainly focus on analyzing the discrete and specific ingredients within separate cosmetics, which ignore the high-order and complex relations between cosmetics and ingredients. To address this problem, we propose a halal cosmetic recommendation framework, namely HaCKG, that leverages a knowledge graph of cosmetics and their ingredients to explicitly model and capture the relationships between cosmetics and their components. By representing cosmetics and ingredients as entities within the knowledge graph, HaCKG effectively learns the high-order and complex relations between entities, offering a robust method for predicting halal status. Specifically, we first construct a cosmetic knowledge graph representing the relations between various cosmetics, ingredients, and their properties. We then propose a pre-trained relational graph attention network model with residual connections to learn the structural relation between entities in the knowledge graph. The pre-trained model is then fine-tuned on downstream cosmetic data to predict halal status. Extensive experiments on the cosmetic dataset over halal prediction tasks demonstrate the superiority of our model over state-of-the-art baselines.

Nowadays, there are many similar services available on the internet, making Quality of Service (QoS) a key concern for users. Since collecting QoS values for all services through user invocations is impractical, predicting QoS values is a more feasible approach. Matrix factorization is considered an effective prediction method. However, most existing matrix factorization algorithms focus on capturing global similarities between users and services, overlooking the local similarities between users and their similar neighbors, as well as the non-interactive effects between users and services. This paper proposes a matrix factorization approach based on user information entropy and region bias, which utilizes a similarity measurement method based on fuzzy information entropy to identify similar neighbors of users. Simultaneously, it integrates the region bias between each user and service linearly into matrix factorization to capture the non-interactive features between users and services. This method demonstrates improved predictive performance in more realistic and complex network environments. Additionally, numerous experiments are conducted on real-world QoS datasets. The experimental results show that the proposed method outperforms some of the state-of-the-art methods in the field at matrix densities ranging from 5% to 20%.

In this paper, we consider an unconstrained stochastic optimization problem where the objective function exhibits high-order smoothness. Specifically, we propose a new stochastic first-order method (SFOM) with multi-extrapolated momentum, in which multiple extrapolations are performed in each iteration, followed by a momentum update based on these extrapolations. We demonstrate that the proposed SFOM can accelerate optimization by exploiting the high-order smoothness of the objective function $f$. Assuming that the $p$th-order derivative of $f$ is Lipschitz continuous for some $p\ge2$, and under additional mild assumptions, we establish that our method achieves a sample complexity of $\widetilde{\mathcal{O}}(\epsilon^{-(3p+1)/p})$ for finding a point $x$ such that $\mathbb{E}[\|\nabla f(x)\|]\le\epsilon$. To the best of our knowledge, this is the first SFOM to leverage arbitrary-order smoothness of the objective function for acceleration, resulting in a sample complexity that improves upon the best-known results without assuming the mean-squared smoothness condition. Preliminary numerical experiments validate the practical performance of our method and support our theoretical findings.

Neural operators are aiming at approximating operators mapping between Banach spaces of functions, achieving much success in the field of scientific computing. Compared to certain deep learning-based solvers, such as Physics-Informed Neural Networks (PINNs), Deep Ritz Method (DRM), neural operators can solve a class of Partial Differential Equations (PDEs). Although much work has been done to analyze the approximation and generalization error of neural operators, there is still a lack of analysis on their training error. In this work, we conduct the convergence analysis of gradient descent for the wide shallow neural operators and physics-informed shallow neural operators within the framework of Neural Tangent Kernel (NTK). The core idea lies on the fact that over-parameterization and random initialization together ensure that each weight vector remains near its initialization throughout all iterations, yielding the linear convergence of gradient descent. In this work, we demonstrate that under the setting of over-parametrization, gradient descent can find the global minimum regardless of whether it is in continuous time or discrete time.

This paper provides an in-depth analysis of Wave Network, a novel token representation method derived from the Wave Network, designed to capture both global and local semantics of input text through wave-inspired complex vectors. In complex vector token representation, each token is represented with a magnitude component, capturing the global semantics of the entire input text, and a phase component, encoding the relationships between individual tokens and the global semantics. Building on prior research that demonstrated the effectiveness of wave-like operations, such as interference and modulation, during forward propagation, this study investigates the convergence behavior, backpropagation characteristics, and embedding independence within the Token2Wave framework. A detailed computational complexity analysis shows that Token2Wave can significantly reduce video memory usage and training time compared to BERT. Gradient comparisons for the [CLS] token, total input text, and classifier parameters further highlight Token2Wave's unique characteristics. This research offers new insights into wave-based token representations, demonstrating their potential to enable efficient and computationally friendly language model architectures.

By employing superstatistical methods and machine learning, we analyze time series data of water quality indicators for the River Thames, with a specific focus on the dynamics of dissolved oxygen. After detrending, the probability density functions of dissolved oxygen fluctuations exhibit heavy tails that are effectively modeled using $q$-Gaussian distributions. Our findings indicate that the multiplicative Empirical Mode Decomposition method stands out as the most effective detrending technique, yielding the highest log-likelihood in nearly all fittings. We also observe that the optimally fitted width parameter of the $q$-Gaussian shows a negative correlation with the distance to the sea, highlighting the influence of geographical factors on water quality dynamics. In the context of same-time prediction of dissolved oxygen, regression analysis incorporating various water quality indicators and temporal features identify the Light Gradient Boosting Machine as the best model. SHapley Additive exPlanations reveal that temperature, pH, and time of year play crucial roles in the predictions. Furthermore, we use the Transformer to forecast dissolved oxygen concentrations. For long-term forecasting, the Informer model consistently delivers superior performance, achieving the lowest MAE and SMAPE with the 192 historical time steps that we used. This performance is attributed to the Informer's ProbSparse self-attention mechanism, which allows it to capture long-range dependencies in time-series data more effectively than other machine learning models. It effectively recognizes the half-life cycle of dissolved oxygen, with particular attention to key intervals. Our findings provide valuable insights for policymakers involved in ecological health assessments, aiding in accurate predictions of river water quality and the maintenance of healthy aquatic ecosystems.

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the influence of predefined kernels on model performance; (ii) the difficulty of preserving the original manifold structures in the nonlinear space; (iii) the dependency of spectral-type strategies on the ideal block diagonal structure of the affinity matrix. This paper presents DKLM, a novel paradigm for kernel-induced nonlinear subspace clustering. DKLM provides a data-driven approach that directly learns the kernel from the data's self-representation, ensuring adaptive weighting and satisfying the multiplicative triangle inequality constraint, which enhances the robustness of the learned kernel. By leveraging this learned kernel, DKLM preserves the local manifold structure of data in a nonlinear space while promoting the formation of an optimal block-diagonal affinity matrix. A thorough theoretical examination of DKLM reveals its relationship with existing clustering paradigms. Comprehensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method.

We study the statistical complexity of offline Nevertheless, learning good policies from offline data decision-making with function approximation, presents a unique challenge not present in online decisionmaking: establishing (near) minimax-optimal rates for distributional shift. In essence, the policy that stochastic contextual bandits and Markov decision interacts with the environment and collects data differs from processes. The performance limits are captured by the target policy we aim to learn. This challenge becomes the pseudo-dimension of the (value) function class more pronounced in real-world problems with large state and a new characterization of the behavior policy spaces, where it necessitates function approximation to generalize that strictly subsumes all the previous notions of from observed states to unseen ones.