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This work introduces a novel cause-effect relation in Markov decision processes using the probability-raising principle. Initially, sets of states as causes and effects are considered, which is subsequently extended to regular path properties as effects and then as causes. The paper lays the mathematical foundations and analyzes the algorithmic properties of these cause-effect relations. This includes algorithms for checking cause conditions given an effect and deciding the existence of probability-raising causes. As the definition allows for sub-optimal coverage properties, quality measures for causes inspired by concepts of statistical analysis are studied. These include recall, coverage ratio and f-score. The computational complexity for finding optimal causes with respect to these measures is analyzed.

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or free energy function or equivalently normalized divisively by its partition function. Both subtractive and divisive normalizers are strictly convex and smooth functions inducing pairs of Bregman and Jensen divergences. It is well-known that skewed Bhattacharryya distances between probability densities of an exponential family amounts to skewed Jensen divergences induced by the cumulant function between their corresponding natural parameters, and in limit cases that the sided Kullback-Leibler divergences amount to reverse-sided Bregman divergences. In this paper, we first show that the $\alpha$-divergences between unnormalized densities of an exponential family amounts to scaled $\alpha$-skewed Jensen divergences induced by the partition function. We then show how comparative convexity with respect to a pair of quasi-arithmetic means allows to deform both convex functions and their arguments, and thereby define dually flat spaces with corresponding divergences when ordinary convexity is preserved.

As the capabilities of large language models (LLMs) continue to advance, evaluating their performance becomes increasingly crucial and challenging. This paper aims to bridge this gap by introducing CMMLU, a comprehensive Chinese benchmark that covers various subjects, including natural science, social sciences, engineering, and humanities. We conduct a thorough evaluation of 18 advanced multilingual- and Chinese-oriented LLMs, assessing their performance across different subjects and settings. The results reveal that most existing LLMs struggle to achieve an average accuracy of 50%, even when provided with in-context examples and chain-of-thought prompts, whereas the random baseline stands at 25%. This highlights significant room for improvement in LLMs. Additionally, we conduct extensive experiments to identify factors impacting the models' performance and propose directions for enhancing LLMs. CMMLU fills the gap in evaluating the knowledge and reasoning capabilities of large language models within the Chinese context.

Network time series are becoming increasingly relevant in the study of dynamic processes characterised by a known or inferred underlying network structure. Generalised Network Autoregressive (GNAR) models provide a parsimonious framework for exploiting the underlying network, even in the high-dimensional setting. We extend the GNAR framework by introducing the $\textit{community}$-$\alpha$ GNAR model that exploits prior knowledge and/or exogenous variables for identifying and modelling dynamic interactions across communities in the underlying network. We further analyse the dynamics of $\textit{Red, Blue}$ and $\textit{Swing}$ states throughout presidential elections in the USA. Our analysis shows that dynamics differ among the state-wise clusters.

Pairwise comparison models are used for quantitatively evaluating utility and ranking in various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the number of subjects diverges, which is currently lacking in the literature except in a few special instances. This paper addresses this gap by establishing an asymptotic normality result for the maximum likelihood estimator in a broad class of pairwise comparison models. The key idea lies in identifying the Fisher information matrix as a weighted graph Laplacian matrix which can be studied via a meticulous spectral analysis. Our findings provide the first unified theory for performing statistical inference in a wide range of pairwise comparison models beyond the Bradley--Terry model, benefiting practitioners with a solid theoretical guarantee for their use. Simulations utilizing synthetic data are conducted to validate the asymptotic normality result, followed by a hypothesis test using a tennis competition dataset.

Quantum communications are based on the law of physics for information security and the implications for this form of future information security enabled by quantum science has to be studied. Physics-based vulnerabilities may exist due to the inherent physics properties and behavior of quantum technologies such as Quantum Key Distribution (QKD), thus resulting in new threats that may emerge with attackers exploiting the physics-based vulnerabilities. There were many studies and experiments done to demonstrate the threat of physics-based attacks on quantum links. However, there is a lack of a framework that provides a common language to communicate about the threats and type of adversaries being dealt with for physics-based attacks. This paper is a review of physics-based attacks that were being investigated and attempt to initialize a framework based on the attack objectives and methodologies, referencing the concept from the well-established MITRE ATT&CK, therefore pioneering the classification of Indicator of Compromises (IoCs) for physics-based attacks. This paper will then pave the way for future work in the development of a forensic tool for the different classification of IoCs, with the methods of evidence collections and possible points of extractions for analysis being further investigated.

Sparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the statistical tools for model discovery are well established in the context of linear regression, their generalization to nonlinear regression in material modeling is highly problem-specific and insufficiently understood. Here we explore the potential of neural networks for automatic model discovery and induce sparsity by a hybrid approach that combines two strategies: regularization and physical constraints. We integrate the concept of Lp regularization for subset selection with constitutive neural networks that leverage our domain knowledge in kinematics and thermodynamics. We train our networks with both, synthetic and real data, and perform several thousand discovery runs to infer common guidelines and trends: L2 regularization or ridge regression is unsuitable for model discovery; L1 regularization or lasso promotes sparsity, but induces strong bias; only L0 regularization allows us to transparently fine-tune the trade-off between interpretability and predictability, simplicity and accuracy, and bias and variance. With these insights, we demonstrate that Lp regularized constitutive neural networks can simultaneously discover both, interpretable models and physically meaningful parameters. We anticipate that our findings will generalize to alternative discovery techniques such as sparse and symbolic regression, and to other domains such as biology, chemistry, or medicine. Our ability to automatically discover material models from data could have tremendous applications in generative material design and open new opportunities to manipulate matter, alter properties of existing materials, and discover new materials with user-defined properties.

For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.

The generative paradigm has become increasingly important in machine learning and deep learning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a base distribution through diffeomorphic transformations. Extending the normalizing flow framework to handle time-indexed flows gave dynamic normalizing flows, a powerful tool to model time series, stochastic processes, and neural stochastic differential equations (SDEs). In this work, we propose a novel variant of dynamic normalizing flows, a Time Changed Normalizing Flow (TCNF), based on time deformation of a Brownian motion which constitutes a versatile and extensive family of Gaussian processes. This approach enables us to effectively model some SDEs, that cannot be modeled otherwise, including standard ones such as the well-known Ornstein-Uhlenbeck process, and generalizes prior methodologies, leading to improved results and better inference and prediction capability.

A key challenge in analyzing the behavior of change-plane estimators is that the objective function has multiple minimizers. Two estimators are proposed to deal with this non-uniqueness. For each estimator, an n-rate of convergence is established, and the limiting distribution is derived. Based on these results, we provide a parametric bootstrap procedure for inference. The validity of our theoretical results and the finite sample performance of the bootstrap are demonstrated through simulation experiments. We illustrate the proposed methods to latent subgroup identification in precision medicine using the ACTG175 AIDS study data.