There is growing research interest in measuring the statistical heterogeneity of clients' local datasets. Such measurements are used to estimate the suitability for collaborative training of personalized federated learning (PFL) models. Currently, these research endeavors are taking place in silos and there is a lack of a unified benchmark to provide a fair and convenient comparison among various approaches in common settings. We aim to bridge this important gap in this paper. The proposed benchmarking framework currently includes six representative approaches. Extensive experiments have been conducted to compare these approaches under five standard non-IID FL settings, providing much needed insights into which approaches are advantageous under which settings. The proposed framework offers useful guidance on the suitability of various data divergence measures in FL systems. It is beneficial for keeping related research activities on the right track in terms of: (i) designing PFL schemes, (ii) selecting appropriate data heterogeneity evaluation approaches for specific FL application scenarios, and (iii) addressing fairness issues in collaborative model training.

In the current era of social media and generative AI, an ability to automatically assess the credibility of online social media content is of tremendous importance. Credibility assessment is fundamentally based on aggregating credibility signals, which refer to small units of information, such as content factuality, bias, or a presence of persuasion techniques, into an overall credibility score. Credibility signals provide a more granular, more easily explainable and widely utilizable information in contrast to currently predominant fake news detection, which utilizes various (mostly latent) features. A growing body of research on automatic credibility assessment and detection of credibility signals can be characterized as highly fragmented and lacking mutual interconnections. This issue is even more prominent due to a lack of an up-to-date overview of research works on automatic credibility assessment. In this survey, we provide such systematic and comprehensive literature review of 175 research papers while focusing on textual credibility signals and Natural Language Processing (NLP), which undergoes a significant advancement due to Large Language Models (LLMs). While positioning the NLP research into the context of other multidisciplinary research works, we tackle with approaches for credibility assessment as well as with 9 categories of credibility signals (we provide a thorough analysis for 3 of them, namely: 1) factuality, subjectivity and bias, 2) persuasion techniques and logical fallacies, and 3) claims and veracity). Following the description of the existing methods, datasets and tools, we identify future challenges and opportunities, while paying a specific attention to recent rapid development of generative AI.

Descriptions of the Galactic Center using Fermi gamma-ray data have so far modeled the Galactic Center Excess (GCE) as a template with fixed spatial morphology or as a linear combination of such templates. Although these templates are informed by various physical expectations, the morphology of the excess is a priori unknown. For the first time, we describe the GCE using a flexible, non-parametric machine learning model -- the Gaussian process (GP). We assess our model's performance on synthetic data, demonstrating that the model can recover the templates used to generate the data. We then fit the \Fermi data with our model in a single energy bin from 2-20 GeV (leaving a spectral GP analysis of the GCE for future work) using a variety of template models of diffuse gamma-ray emission to quantify our fits' systematic uncertainties associated with diffuse emission modeling. We interpret our best-fit GP in terms of GCE templates consisting of an NFW squared template and a bulge component to determine which bulge models can best describe the fitted GP and to what extent the best-fit GP is described better by an NFW squared template versus a bulge template. The best-fit GP contains morphological features that are typically not associated with traditional GCE studies. These include a localized bright source at around $(\ell,b) = (20^{\circ}, 0^{\circ})$ and a diagonal arm extending Northwest from the Galactic Center. In spite of these novel features, the fitted GP is explained best by a template-based model consisting of the bulge presented in Coleman et al. (2020) and a squared NFW component. Our results suggest that the physical interpretation of the GCE in terms of stellar bulge and NFW-like components is highly sensitive to the assumed morphologies, background models, and the region of the sky used for inference.

Nonlocal, integral operators have become an efficient surrogate for bottom-up homogenization, due to their ability to represent long-range dependence and multiscale effects. However, the nonlocal homogenized model has unavoidable discrepancy from the microscale model. Such errors accumulate and propagate in long-term simulations, making the resultant prediction unreliable. To develop a robust and reliable bottom-up homogenization framework, we propose a new framework, which we coin Embedded Nonlocal Operator Regression (ENOR), to learn a nonlocal homogenized surrogate model and its structural model error. This framework provides discrepancy-adaptive uncertainty quantification for homogenized material response predictions in long-term simulations. The method is built on Nonlocal Operator Regression (NOR), an optimization-based nonlocal kernel learning approach, together with an embedded model error term in the trainable kernel. Then, Bayesian inference is employed to infer the model error term parameters together with the kernel parameters. To make the problem computationally feasible, we use a multilevel delayed acceptance Markov chain Monte Carlo (MLDA-MCMC) method, enabling efficient Bayesian model calibration and model error estimation. We apply this technique to predict long-term wave propagation in a heterogeneous one-dimensional bar, and compare its performance with additive noise models. Owing to its ability to capture model error, the learned ENOR achieves improved estimation of posterior predictive uncertainty.

Discovering the underlying Directed Acyclic Graph (DAG) from time series observational data is highly challenging due to the dynamic nature and complex nonlinear interactions between variables. Existing methods often struggle with inefficiency and the handling of high-dimensional data. To address these research gap, we propose LOCAL, a highly efficient, easy-to-implement, and constraint-free method for recovering dynamic causal structures. LOCAL is the first attempt to formulate a quasi-maximum likelihood-based score function for learning the dynamic DAG equivalent to the ground truth. On this basis, we propose two adaptive modules for enhancing the algebraic characterization of acyclicity with new capabilities: Asymptotic Causal Mask Learning (ACML) and Dynamic Graph Parameter Learning (DGPL). ACML generates causal masks using learnable priority vectors and the Gumbel-Sigmoid function, ensuring the creation of DAGs while optimizing computational efficiency. DGPL transforms causal learning into decomposed matrix products, capturing the dynamic causal structure of high-dimensional data and enhancing interpretability. Extensive experiments on synthetic and real-world datasets demonstrate that LOCAL significantly outperforms existing methods, and highlight LOCAL's potential as a robust and efficient method for dynamic causal discovery. Our code will be available soon.

This study explores the limitations of image-based structural health monitoring (SHM) techniques in detecting structural damage. Leveraging machine learning and computer vision, image-based SHM offers a scalable and efficient alternative to manual inspections. However, its reliability is impacted by challenges such as false positives, false negatives, and environmental variability, particularly in low base rate damage scenarios. The Base Rate Bias plays a significant role, as low probabilities of actual damage often lead to misinterpretation of positive results. This study uses both Bayesian analysis and a frequentist approach to evaluate the precision of damage detection systems, revealing that even highly accurate models can yield misleading results when the occurrence of damage is rare. Strategies for mitigating these limitations are discussed, including hybrid systems that combine multiple data sources, human-in-the-loop approaches for critical assessments, and improving the quality of training data. These findings provide essential insights into the practical applicability of image-based SHM techniques, highlighting both their potential and their limitations for real-world infrastructure monitoring.

Exemplar-Free Class Incremental Learning (EFCIL) tackles the problem of training a model on a sequence of tasks without access to past data. Existing state-of-the-art methods represent classes as Gaussian distributions in the feature extractor's latent space, enabling Bayes classification or training the classifier by replaying pseudo features. However, we identify two critical issues that compromise their efficacy when the feature extractor is updated on incremental tasks. First, they do not consider that classes' covariance matrices change and must be adapted after each task. Second, they are susceptible to a task-recency bias caused by dimensionality collapse occurring during training. In this work, we propose AdaGauss -- a novel method that adapts covariance matrices from task to task and mitigates the task-recency bias owing to the additional anti-collapse loss function. AdaGauss yields state-of-the-art results on popular EFCIL benchmarks and datasets when training from scratch or starting from a pre-trained backbone. The code is available at: https://github.com/grypesc/AdaGauss.

Bayesian Additive Regression Trees (BART) is a nonparametric Bayesian regression technique of rising fame. It is a sum-of-decision-trees model, and is in some sense the Bayesian version of boosting. In the limit of infinite trees, it becomes equivalent to Gaussian process (GP) regression. This limit is known but has not yet led to any useful analysis or application. For the first time, I derive and compute the exact BART prior covariance function. With it I implement the infinite trees limit of BART as GP regression. Through empirical tests, I show that this limit is worse than standard BART in a fixed configuration, but also that tuning the hyperparameters in the natural GP way yields a competitive method, although a properly tuned BART is still superior. The advantage of using a GP surrogate of BART is the analytical likelihood, which simplifies model building and sidesteps the complex BART MCMC. More generally, this study opens new ways to understand and develop BART and GP regression. The implementation of BART as GP is available in the Python package https://github.com/Gattocrucco/lsqfitgp .

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence class, necessitating interventional data to learn the complete causal graph. Most works in the literature design causal discovery policies with perfect interventions, i.e., they have access to infinite interventional samples. This study considers a Bayesian approach for learning causal graphs with limited interventional samples, mirroring real-world scenarios where such samples are usually costly to obtain. By leveraging the recent result of Wien\"obst et al. (2023) on uniform DAG sampling in polynomial time, we can efficiently enumerate all the cut configurations and their corresponding interventional distributions of a target set, and further track their posteriors. Given any number of interventional samples, our proposed algorithm randomly intervenes on a set of target vertices that cut all the edges in the graph and returns a causal graph according to the posterior of each target set. When the number of interventional samples is large enough, we show theoretically that our proposed algorithm will return the true causal graph with high probability. We compare our algorithm against various baseline methods on simulated datasets, demonstrating its superior accuracy measured by the structural Hamming distance between the learned DAG and the ground truth. Additionally, we present a case study showing how this algorithm could be modified to answer more general causal questions without learning the whole graph. As an example, we illustrate that our method can be used to estimate the causal effect of a variable that cannot be intervened.

Over the past few years, several approaches utilizing score-based diffusion have been proposed to sample from probability distributions, that is without having access to exact samples and relying solely on evaluations of unnormalized densities. In practice, the performance of these methods heavily depends on key hyperparameters that require ground truth samples to be accurately tuned. Our work aims to highlight and address this fundamental issue, focusing in particular on multimodal distributions, which pose significant challenges for existing sampling methods. Building on existing approaches, we introduce Learned Reference-based Diffusion Sampler (LRDS), a methodology specifically designed to leverage prior knowledge on the location of the target modes in order to bypass the obstacle of hyperparameter tuning. LRDS proceeds in two steps by (i) learning a reference diffusion model on samples located in high-density space regions and tailored for multimodality, and (ii) using this reference model to foster the training of a diffusion-based sampler. We experimentally demonstrate that LRDS best exploits prior knowledge on the target distribution compared to competing algorithms on a variety of challenging distributions. We consider the problem of sampling from a probability density known up to a normalizing constant. In particular, we are interested in sampling from multimodal distributions, i.e., distributions whose density admits multiple local maxima, called modes. Finding the modes of such distributions is a notoriously hard problem, yet, maybe surprisingly, even if the location of the modes is known, sampling π remains a very challenging problem (Noé et al., 2019; Pompe et al., 2020; Grenioux et al., 2023). In this work, we aim to address this specific issue and will assume that we have access to the location of the modes as prior information on π. However, we do not assume to have access a priori to ground truth samples from π. Annealed MCMC. Markov Chain Monte Carlo (MCMC) samplers are among the most popular approaches for sampling. In particular, gradient-based methods based on discretizations of Langevin or Hamiltonian dynamics (Roberts & Tweedie, 1996; Neal, 2012; Hoffman & Gelman, 2014) are guaranteed to be efficient for high-dimensional target distributions that are log-concave or satisfy or functional inequalities (Dalalyan, 2017; Durmus & Moulines, 2017).