This paper focuses on the impact of rule representation in Michigan-style Learning Fuzzy-Classifier Systems (LFCSs) on its classification performance. A well-representation of the rules in an LFCS is crucial for improving its performance. However, conventional rule representations frequently need help addressing problems with unknown data characteristics. To address this issue, this paper proposes a supervised LFCS (i.e., Fuzzy-UCS) with a self-adaptive rule representation mechanism, entitled Adaptive-UCS. Adaptive-UCS incorporates a fuzzy indicator as a new rule parameter that sets the membership function of a rule as either rectangular (i.e., crisp) or triangular (i.e., fuzzy) shapes. The fuzzy indicator is optimized with evolutionary operators, allowing the system to search for an optimal rule representation. Results from extensive experiments conducted on continuous space problems demonstrate that Adaptive-UCS outperforms other UCSs with conventional crisp-hyperrectangular and fuzzy-hypertrapezoidal rule representations in classification accuracy. Additionally, Adaptive-UCS exhibits robustness in the case of noisy inputs and real-world problems with inherent uncertainty, such as missing values, leading to stable classification performance.

Causal discovery in multi-omic datasets is crucial for understanding the bigger picture of gene regulatory mechanisms, but remains challenging due to high dimensionality, differentiation of direct from indirect relationships, and hidden confounders. We introduce GENESIS (GEne Network inference from Expression SIgnals and SNPs), a constraint-based algorithm that leverages the natural causal precedence of genotypes to infer ancestral relationships in transcriptomic data. Unlike traditional causal discovery methods that start with a fully connected graph, GENESIS initialises an empty ancestrality matrix and iteratively populates it with direct, indirect or non-causal relationships using a series of provably sound marginal and conditional independence tests. By integrating genotypes as fixed causal anchors, GENESIS provides a principled ``head start'' to classical causal discovery algorithms, restricting the search space to biologically plausible edges. We test GENESIS on synthetic and real-world genomic datasets. This framework offers a powerful avenue for uncovering causal pathways in complex traits, with promising applications to functional genomics, drug discovery, and precision medicine.

Federated Learning (FL) has emerged as a promising paradigm for collaborative model training while preserving data privacy across decentralized participants. As FL adoption grows, numerous techniques have been proposed to tackle its practical challenges. However, the lack of standardized evaluation across key dimensions hampers systematic progress and fair comparison of FL methods. In this work, we introduce ATR-Bench, a unified framework for analyzing federated learning through three foundational dimensions: Adaptation, Trust, and Reasoning. We provide an in-depth examination of the conceptual foundations, task formulations, and open research challenges associated with each theme. We have extensively benchmarked representative methods and datasets for adaptation to heterogeneous clients and trustworthiness in adversarial or unreliable environments. Due to the lack of reliable metrics and models for reasoning in FL, we only provide literature-driven insights for this dimension. ATR-Bench lays the groundwork for a systematic and holistic evaluation of federated learning with real-world relevance. We will make our complete codebase publicly accessible and a curated repository that continuously tracks new developments and research in the FL literature.

Asymmetric, non-Gaussian probability distributions are often observed in the analysis of natural and engineering datasets. The lognormal distribution is a standard model for data with skewed frequency histograms and fat tails. However, the lognormal law severely restricts the asymptotic dependence of the probability density and the hazard function for high values. Herein we present a family of three-parameter non-Gaussian probability density functions that are based on generalized kappa-exponential and kappa-logarithm functions and investigate its mathematical properties. These kappa-lognormal densities represent continuous deformations of the lognormal with lighter right tails, controlled by the parameter kappa. In addition, bimodal distributions are obtained for certain parameter combinations. We derive closed-form analytic expressions for the main statistical functions of the kappa-lognormal distribution. For the moments, we derive bounds that are based on hypergeometric functions as well as series expansions. Explicit expressions for the gradient and Hessian of the negative log-likelihood are obtained to facilitate numerical maximum-likelihood estimates of the kappa-lognormal parameters from data. We also formulate a joint probability density function for kappa-lognormal stochastic processes by applying Jacobi's multivariate theorem to a latent Gaussian process. Estimation of the kappa-lognormal distribution based on synthetic and real data is explored. Furthermore, we investigate applications of kappa-lognormal processes with different covariance kernels in time series forecasting and spatial interpolation using warped Gaussian process regression. Our results are of practical interest for modeling skewed distributions in various scientific and engineering fields.

In electromyogram (EMG)-based motion recognition, a subject-specific classifier is typically trained with sufficient labeled data. However, this process demands extensive data collection over extended periods, burdening the subject. To address this, utilizing information from pre-training on multiple subjects for the training of the target subject could be beneficial. This paper proposes an inter-subject variance transfer learning method based on a Bayesian approach. This method is founded on the simple hypothesis that while the means of EMG features vary greatly across subjects, their variances may exhibit similar patterns. Our approach transfers variance information, acquired through pre-training on multiple source subjects, to a target subject within a Bayesian updating framework, thereby allowing accurate classification using limited target calibration data. A coefficient was also introduced to adjust the amount of information transferred for efficient transfer learning. Experimental evaluations using two EMG datasets demonstrated the effectiveness of our variance transfer strategy and its superiority compared to existing methods.

Off-policy evaluation (OPE) and off-policy learning (OPL) for contextual bandit policies leverage historical data to evaluate and optimize a target policy. Most existing OPE/OPL methods--based on importance weighting or imputation--assume common support between the target and logging policies. When this assumption is violated, these methods typically require unstable extrapolation, truncation, or conservative strategies for individuals outside the common support assumption. However, such approaches can be inadequate in settings where explicit evaluation or optimization for such individuals is required. To address this issue, we propose DOLCE: Decomposing Off-policy evaluation/learning into Lagged and Current Effects, a novel estimator that leverages contextual information from multiple time points to decompose rewards into lagged and current effects. By incorporating both past and present contexts, DOLCE effectively handles individuals who violate the common support assumption. We show that the proposed estimator is unbiased under two assumptions--local correctness and conditional independence. Our experiments demonstrate that DOLCE achieves substantial improvements in OPE and OPL, particularly as the proportion of individuals outside the common support assumption increases.

In statistical learning, models are classified as regular or singular depending on whether the mapping from parameters to probability distributions is injective. Most models with hierarchical structures or latent variables are singular, for which conventional criteria such as the Akaike Information Criterion and the Bayesian Information Criterion are inapplicable due to the breakdown of normal approximations for the likelihood and posterior. To address this, the Widely Applicable Information Criterion (WAIC) and the Widely Applicable Bayesian Information Criterion (WBIC) have been proposed. Since WAIC and WBIC are computed using posterior distributions at different temperature settings, separate posterior sampling is generally required. In this paper, we theoretically derive an asymptotic equation that links WAIC and WBIC, despite their dependence on different posteriors. This equation yields an asymptotically unbiased expression of WAIC in terms of the posterior distribution used for WBIC. The result clarifies the structural relationship between these criteria within the framework of singular learning theory, and deepens understanding of their asymptotic behavior. This theoretical contribution provides a foundation for future developments in the computational efficiency of model selection in singular models.

We revisit the classical problem of Bayesian ensembles and address the challenge of learning optimal combinations of Bayesian models in an online, continual learning setting. To this end, we reinterpret existing approaches such as Bayesian model averaging (BMA) and Bayesian stacking through a novel empirical Bayes lens, shedding new light on the limitations and pathologies of BMA. Further motivated by insights from online optimization, we propose Online Bayesian Stacking (OBS), a method that optimizes the log-score over predictive distributions to adaptively combine Bayesian models. A key contribution of our work is establishing a novel connection between OBS and portfolio selection, bridging Bayesian ensemble learning with a rich, well-studied theoretical framework that offers efficient algorithms and extensive regret analysis. We further clarify the relationship between OBS and online BMA, showing that they optimize related but distinct cost functions. Through theoretical analysis and empirical evaluation, we identify scenarios where OBS outperforms online BMA and provide principled guidance on when practitioners should prefer one approach over the other.

Causal inference determines cause-and-effect relationships between variables and has broad applications across disciplines. Traditional time-series methods often reveal causal links only in a time-averaged sense, while ensemble-based information transfer approaches detect the time evolution of short-term causal relationships but are typically limited to low-dimensional systems. In this paper, a new causal inference framework, called assimilative causal inference (ACI), is developed. Fundamentally different from the state-of-the-art methods, ACI uses a dynamical system and a single realization of a subset of the state variables to identify instantaneous causal relationships and the dynamic evolution of the associated causal influence range (CIR). Instead of quantifying how causes influence effects as done traditionally, ACI solves an inverse problem via Bayesian data assimilation, thus tracing causes backward from observed effects with an implicit Bayesian hypothesis. Causality is determined by assessing whether incorporating the information of the effect variables reduces the uncertainty in recovering the potential cause variables. ACI has several desirable features. First, it captures the dynamic interplay of variables, where their roles as causes and effects can shift repeatedly over time. Second, a mathematically justified objective criterion determines the CIR without empirical thresholds. Third, ACI is scalable to high-dimensional problems by leveraging computationally efficient Bayesian data assimilation techniques. Finally, ACI applies to short time series and incomplete datasets. Notably, ACI does not require observations of candidate causes, which is a key advantage since potential drivers are often unknown or unmeasured. The effectiveness of ACI is demonstrated by complex dynamical systems showcasing intermittency and extreme events.

Recently, large language models (LLMs) have significantly advanced text-attributed graph (TAG) learning. However, existing methods inadequately handle data uncertainty in open-world scenarios, especially concerning limited labeling and unknown-class nodes. Prior solutions typically rely on isolated semantic or structural approaches for unknown-class rejection, lacking effective annotation pipelines. To address these limitations, we propose Open-world Graph Assistant (OGA), an LLM-based framework that combines adaptive label traceability, which integrates semantics and topology for unknown-class rejection, and a graph label annotator to enable model updates using newly annotated nodes. Comprehensive experiments demonstrate OGA's effectiveness and practicality.