In interactive systems, actions are often correlated, presenting an opportunity for more sample-efficient off-policy evaluation (OPE) and learning (OPL) in large action spaces. We introduce a unified Bayesian framework to capture these correlations through structured and informative priors. In this framework, we propose sDM, a generic Bayesian approach designed for OPE and OPL, grounded in both algorithmic and theoretical foundations. Notably, sDM leverages action correlations without compromising computational efficiency. Moreover, inspired by online Bayesian bandits, we introduce Bayesian metrics that assess the average performance of algorithms across multiple problem instances, deviating from the conventional worst-case assessments. We analyze sDM in OPE and OPL, highlighting the benefits of leveraging action correlations. Empirical evidence showcases the strong performance of sDM.

We introduce a novel Information Criterion (IC), termed Learning under Singularity (LS), designed to enhance the functionality of the Widely Applicable Bayes Information Criterion (WBIC) and the Singular Bayesian Information Criterion (sBIC). LS is effective without regularity constraints and demonstrates stability. Watanabe defined a statistical model or a learning machine as regular if the mapping from a parameter to a probability distribution is one-to-one and its Fisher information matrix is positive definite. In contrast, models not meeting these conditions are termed singular. Over the past decade, several information criteria for singular cases have been proposed, including WBIC and sBIC. WBIC is applicable in non-regular scenarios but faces challenges with large sample sizes and redundant estimation of known learning coefficients. Conversely, sBIC is limited in its broader application due to its dependence on maximum likelihood estimates. LS addresses these limitations by enhancing the utility of both WBIC and sBIC. It incorporates the empirical loss from the Widely Applicable Information Criterion (WAIC) to represent the goodness of fit to the statistical model, along with a penalty term similar to that of sBIC. This approach offers a flexible and robust method for model selection, free from regularity constraints.

BlackJAX is a library implementing sampling and variational inference algorithms commonly used in Bayesian computation. It is designed for ease of use, speed, and modularity by taking a functional approach to the algorithms' implementation. BlackJAX is written in Python, using JAX to compile and run NumpPy-like samplers and variational methods on CPUs, GPUs, and TPUs. The library integrates well with probabilistic programming languages by working directly with the (un-normalized) target log density function. BlackJAX is intended as a collection of low-level, composable implementations of basic statistical 'atoms' that can be combined to perform well-defined Bayesian inference, but also provides high-level routines for ease of use. It is designed for users who need cutting-edge methods, researchers who want to create complex sampling methods, and people who want to learn how these work.

The American Statistical Association (ASA) statement on statistical significance and P-values \cite{wasserstein2016asa} cautioned statisticians against making scientific decisions solely on the basis of traditional P-values. The statement delineated key issues with P-values, including a lack of transparency, an inability to quantify evidence in support of the null hypothesis, and an inability to measure the size of an effect or the importance of a result. In this article, we demonstrate that the interval null hypothesis framework (instead of the point null hypothesis framework), when used in tandem with Bayes factor-based tests, is instrumental in circumnavigating the key issues of P-values. Further, we note that specifying prior densities for Bayes factors is challenging and has been a reason for criticism of Bayesian hypothesis testing in existing literature. We address this by adapting Bayes factors directly based on common test statistics. We demonstrate, through numerical experiments and real data examples, that the proposed Bayesian interval hypothesis testing procedures can be calibrated to ensure frequentist error control while retaining their inherent interpretability. Finally, we illustrate the improved flexibility and applicability of the proposed methods by providing coherent frameworks for competitive landscape analysis and end-to-end Bayesian hypothesis tests in the context of reporting clinical trial outcomes.

The integration of artificial intelligence (AI) into daily life, particularly through information retrieval and recommender systems, has necessitated advanced user modeling and profiling techniques to deliver personalized experiences. These techniques aim to construct accurate user representations based on the rich amounts of data generated through interactions with these systems. This paper presents a comprehensive survey of the current state, evolution, and future directions of user modeling and profiling research. We provide a historical overview, tracing the development from early stereotype models to the latest deep learning techniques, and propose a novel taxonomy that encompasses all active topics in this research area, including recent trends. Our survey highlights the paradigm shifts towards more sophisticated user profiling methods, emphasizing implicit data collection, multi-behavior modeling, and the integration of graph data structures. We also address the critical need for privacy-preserving techniques and the push towards explainability and fairness in user modeling approaches. By examining the definitions of core terminology, we aim to clarify ambiguities and foster a clearer understanding of the field by proposing two novel encyclopedic definitions of the main terms. Furthermore, we explore the application of user modeling in various domains, such as fake news detection, cybersecurity, and personalized education. This survey serves as a comprehensive resource for researchers and practitioners, offering insights into the evolution of user modeling and profiling and guiding the development of more personalized, ethical, and effective AI systems.

The typical phases of Bayesian network (BN) structured development include specification of purpose and scope, structure development, parameterisation and validation. Structure development is typically focused on qualitative issues and parameterisation quantitative issues, however there are qualitative and quantitative issues that arise in both phases. A common step that occurs after the initial structure has been developed is to perform a rough parameterisation that only captures and illustrates the intended qualitative behaviour of the model. This is done prior to a more rigorous parameterisation, ensuring that the structure is fit for purpose, as well as supporting later development and validation. In our collective experience and in discussions with other modellers, this step is an important part of the development process, but is under-reported in the literature. Since the practice focuses on qualitative issues, despite being quantitative in nature, we call this step qualitative parameterisation and provide an outline of its role in the BN development process.

Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete data, statistical dependencies between features must be estimated in a computationally tractable way, while also dealing with missing data. There is a need for a computationally tractable approach that considers the statistical dependencies between features and can handle missing values. We here develop a multivariate version of FLDA (MUDRA) to tackle this issue and describe an efficient expectation/conditional-maximization (ECM) algorithm to infer its parameters. We assess its predictive power on the "Articulary Word Recognition" data set and show its improvement over the state-of-the-art, especially in the case of missing data. MUDRA allows interpretable classification of data sets with large proportions of missing data, which will be particularly useful for medical or psychological data sets.

Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work, we propose a framework for integrating general forms of domain knowledge (i.e., any knowledge that can be represented by a loss function) into a BNN prior through variational inference, while enabling computationally efficient posterior inference and sampling. Specifically, our approach results in a prior over neural network weights that assigns high probability mass to models that better align with our domain knowledge, leading to posterior samples that also exhibit this behavior. We show that BNNs using our proposed domain knowledge priors outperform those with standard priors (e.g., isotropic Gaussian, Gaussian process), successfully incorporating diverse types of prior information such as fairness, physics rules, and healthcare knowledge and achieving better predictive performance. We also present techniques for transferring the learned priors across different model architectures, demonstrating their broad utility across various settings.

Abstract--Federated learning allows us to run machine learning algorithms on decentralized data when data sharing is not permitted due to privacy concerns. Ensemble-based learning works by training multiple (weak) classifiers whose output is aggregated. Federated ensembles are ensembles applied to a federated setting, where each classifier in the ensemble is trained on one data location. In this article, we explore the use of federated ensembles of Bayesian networks (FBNE) in a range of experiments and compare their performance with locally trained models and models trained with VertiBayes, a federated learning algorithm to train Bayesian networks from decentralized data. Our results show that FBNE outperforms local models and provides a significant increase in training speed compared with VertiBayes while maintaining a similar performance in most settings, among other advantages. We show that FBNE is a potentially useful tool within the federated learning toolbox, especially when local populations are heavily biased, or there is a strong imbalance in population size across parties. We discuss the advantages and disadvantages of this approach in terms of time complexity, model accuracy, privacy protection, and model interpretability.

Bayesian networks model relationships between random variables under uncertainty and can be used to predict the likelihood of events and outcomes while incorporating observed evidence. From an eXplainable AI (XAI) perspective, such models are interesting as they tend to be compact. Moreover, captured relations can be directly inspected by domain experts. In practice, data is often real-valued. Unless assumptions of normality can be made, discretization is often required. The optimal discretization, however, depends on the relations modelled between the variables. This complicates learning Bayesian networks from data. For this reason, most literature focuses on learning conditional dependencies between sets of variables, called structure learning. In this work, we extend an existing state-of-the-art structure learning approach based on the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) to jointly learn variable discretizations. The proposed Discretized Bayesian Network GOMEA (DBN-GOMEA) obtains similar or better results than the current state-of-the-art when tasked to retrieve randomly generated ground-truth networks. Moreover, leveraging a key strength of evolutionary algorithms, we can straightforwardly perform DBN learning multi-objectively. We show how this enables incorporating expert knowledge in a uniquely insightful fashion, finding multiple DBNs that trade-off complexity, accuracy, and the difference with a pre-determined expert network.