While many models have been developed that can produce such probabilistic predictions, it is often the case that predictions are required for multiple related tasks, such that it would be desirable to have a probabilistic model that can make rapid predictions on new tasks without the need for task-specific training. Such is the case in the probabilistic meta-learning paradigm. While meta-learning has received an abundance of attention from the research community over the last decade (Finn et al., 2017; Gordon et al., 2019; Hospedales et al., 2022), the most notable class of probabilistic meta-model is, without doubt, the neural process family (NP; Garnelo et al., 2018a,b; Dubois et al., 2020). Recent advances in NPs have led them to reach astonishing heights in performance, representing the state-of-the-art in data-based approaches to weather and climate modeling (Bodnar et al., 2024; Allen et al., 2025; Ashman et al., 2024b), for example. Despite such impressive performance, industry practitioners seldom opt for deep learning models owing to their inherent lack of interpretability (Li et al., 2022), and instead prefer more traditional approaches such as kernel methods (Hofmann et al., 2008) that are easier to explain to non-technical stakeholders, even if they are incapable of meta-learning. Perhaps the most ubiquitous probabilistic model that practitioners turn to is the Gaussian process (GP; Rasmussen and Williams, 2005). With GPs, users can leverage their domain expertise to specify meaningful priors with which to bias predictions, any free parameters tend to have clear interpretations, and schemes such as automatic relevance T. Rochussen & V. Fortuin.

Discrete diffusion is a promising framework for modeling and generating discrete data. In this work, we present Target Concrete Score Matching (TCSM), a novel and versatile objective for training and fine-tuning discrete diffusion models. TCSM provides a general framework with broad applicability. It supports pre-training discrete diffusion models directly from data samples, and many existing discrete diffusion approaches naturally emerge as special cases of our more general TCSM framework. Furthermore, the same TCSM objective extends to post-training of discrete diffusion models, including fine-tuning using reward functions or preference data, and distillation of knowledge from pre-trained autoregressive models. These new capabilities stem from the core idea of TCSM, estimating the concrete score of the target distribution, which resides in the original (clean) data space. This allows seamless integration with reward functions and pre-trained models, which inherently only operate in the clean data space rather than the noisy intermediate spaces of diffusion processes. Our experiments on language modeling tasks demonstrate that TCSM matches or surpasses current methods. Additionally, TCSM is versatile, applicable to both pre-training and post-training scenarios, offering greater flexibility and sample efficiency.

--We propose an automated approach to bug assignment to developers in large open-source software projects. This way, we assist human bug triagers who are in charge of finding the best developer with the right level of expertise in a particular area to be assigned to a newly reported issue. Our approach is based on the history of software development as documented in the issue tracking systems. Our approach works based on the bug reports' features, such as the corresponding products and components, as well as their priority and severity levels. We sort developers based on their experience with specific combinations of new reports. The evaluation is performed using T op-k accuracy, and the results are compared with the reported results in prior work, namely T opicMiner MTM, BUGZIE, Bug triaging via deep Reinforcement Learning BT -RL, and LDA-SVM. The evaluation data come from various Eclipse and Mozilla projects, such as JDT, Firefox, and Thunderbird. Large open-source projects offer an issue tracking system or open bug repository, where developers and users can report the software defects they find or any new feature requests they may have. These reports are called bug reports or issues . In some cases, developers can volunteer to work on the reported issues they find interesting or relevant to their field of expertise. Additionally, they sometimes report issues and assign them to themselves. However, in many cases, particularly in large open-source projects, a group of developers, called bug triagers, decide who should process and fix a newly reported issue.

This paper presents a performance benchmarking study of a Gradient-Optimized Fuzzy Inference System (GF) classifier against several state-of-the-art machine learning models, including Random Forest, XGBoost, Logistic Regression, Support Vector Machines, and Neural Networks. The evaluation was conducted across five datasets from the UCI Machine Learning Repository, each chosen for their diversity in input types, class distributions, and classification complexity. Unlike traditional Fuzzy Inference Systems that rely on derivative-free optimization methods, the GF leverages gradient descent to significantly improving training efficiency and predictive performance. Results demonstrate that the GF model achieved competitive, and in several cases superior, classification accuracy while maintaining high precision and exceptionally low training times. In particular, the GF exhibited strong consistency across folds and datasets, underscoring its robustness in handling noisy data and variable feature sets. These findings support the potential of gradient optimized fuzzy systems as interpretable, efficient, and adaptable alternatives to more complex deep learning models in supervised learning tasks.

Energy-based models (EBMs) are a powerful class of probabilistic generative models due to their flexibility and interpretability. However, relationships between potential flows and explicit EBMs remain underexplored, while contrastive divergence training via implicit Markov chain Monte Carlo (MCMC) sampling is often unstable and expensive in high-dimensional settings. In this paper, we propose Variational Potential Flow Bayes (VPFB), a new energy-based generative framework that eliminates the need for implicit MCMC sampling and does not rely on auxiliary networks or cooperative training. VPFB learns an energy-parameterized potential flow by constructing a flow-driven density homotopy that is matched to the data distribution through a variational loss minimizing the Kullback-Leibler divergence between the flow-driven and marginal homotopies. This principled formulation enables robust and efficient generative modeling while preserving the interpretability of EBMs. Experimental results on image generation, interpolation, out-of-distribution detection, and compositional generation confirm the effectiveness of VPFB, showing that our method performs competitively with existing approaches in terms of sample quality and versatility across diverse generative modeling tasks. 1 1 Introduction

We develop a methodology for constructing confidence sets for parameters of statistical models via a reduction to sequential prediction. Our key observation is that for any generalized linear model (GLM), one can construct an associated game of sequential probability assignment such that achieving low regret in the game implies a high-probability upper bound on the excess likelihood of the true parameter of the GLM. This allows us to develop a scheme that we call online-to-confidence-set conversions, which effectively reduces the problem of proving the desired statistical claim to an algorithmic question. We study two varieties of this conversion scheme: 1) analytical conversions that only require proving the existence of algorithms with low regret and provide confidence sets centered at the maximum-likelihood estimator 2) algorithmic conversions that actively leverage the output of the online algorithm to construct confidence sets (and may be centered at other, adaptively constructed point estimators). The resulting methodology recovers all state-of-the-art confidence set constructions within a single framework, and also provides several new types of confidence sets that were previously unknown in the literature.

Class imbalance occurs when data used for training classification models has a different number of observations or samples within each category or class. Models built on such data can be biased towards the majority class and have poor predictive performance and generalisation for the minority class. We propose a Bayesian weighted-likelihood (power-likelihood) approach to deal with class imbalance: each observation's likelihood is raised to a weight inversely proportional to its class proportion, with weights normalized to sum to the number of samples. This embeds cost-sensitive learning directly into Bayesian updating and is applicable to binary, multinomial and ordered logistic prediction models. Example models are implemented in Stan, PyMC, and Turing.jl, and all code and reproducible scripts are archived on Github: https://github.com/stanlazic/weighted_likelihoods. This approach is simple to implement and extends naturally to arbitrary error-cost matrices.

We propose a new framework for Bayesian estimation of differential privacy, incorporating evidence from multiple membership inference attacks (MIA). Bayesian estimation is carried out via a Markov chain Monte Carlo (MCMC) algorithm, named MCMC-DP-Est, which provides an estimate of the full posterior distribution of the privacy parameter (e.g., instead of just credible intervals). Critically, the proposed method does not assume that privacy auditing is performed with the most powerful attack on the worst-case (dataset, challenge point) pair, which is typically unrealistic. Instead, MCMC-DP-Est jointly estimates the strengths of MIAs used and the privacy of the training algorithm, yielding a more cautious privacy analysis. We also present an economical way to generate measurements for the performance of an MIA that is to be used by the MCMC method to estimate privacy. We present the use of the methods with numerical examples with both artificial and real data.

In this article, we address the inconsistency of a system of max-min fuzzy relational equations by minimally modifying the matrix governing the system in order to achieve consistency. Our method yields consistent systems that approximate the original inconsistent system in the following sense: the right-hand side vector of each consistent system is that of the inconsistent system, and the coefficients of the matrix governing each consistent system are obtained by modifying, exactly and minimally, the entries of the original matrix that must be corrected to achieve consistency, while leaving all other entries unchanged. To obtain a consistent system that closely approximates the considered inconsistent system, we study the distance (in terms of a norm among $L_1$, $L_2$ or $L_\infty$) between the matrix of the inconsistent system and the set formed by the matrices of consistent systems that use the same right-hand side vector as the inconsistent system. We show that our method allows us to directly compute matrices of consistent systems that use the same right-hand side vector as the inconsistent system whose distance in terms of $L_\infty$ norm to the matrix of the inconsistent system is minimal (the computational costs are higher when using $L_1$ norm or $L_2$ norm). We also give an explicit analytical formula for computing this minimal $L_\infty$ distance. Finally, we translate our results for systems of min-max fuzzy relational equations and present some potential applications.

This paper presents a fault-tolerant control for the trajectory tracking of autonomous underwater vehicles (AUVs) against thruster failures. We formulate faults in AUV thrusters as discrete switching events during a UAV mission, and develop a soft-switching approach in facilitating shift of control strategies across fault scenarios. We mathematically define AUV thruster fault scenarios, and develop the fault-tolerant control that captures the fault scenario via Bayesian approach. Particularly, when the AUV fault type switches from one to another, the developed control captures the fault states and maintains the control by a linear quadratic tracking controller. With the captured fault states by Bayesian approach, we derive the control law by aggregating the control outputs for individual fault scenarios weighted by their Bayesian posterior probability. The developed fault-tolerant control works in an adaptive way and guarantees soft-switching across fault scenarios, and requires no complicated fault detection dedicated to different type of faults. The entailed soft-switching ensures stable AUV trajectory tracking when fault type shifts, which otherwise leads to reduced control under hard-switching control strategies. We conduct numerical simulations with diverse AUV thruster fault settings. The results demonstrate that the proposed control can provide smooth transition across thruster failures, and effectively sustain AUV trajectory tracking control in case of thruster failures and failure shifts.