January 2026

arXiv:2601.11897v1 Announce Type: cross Abstract: Fairness-aware machine learning has recently attracted various communities to mitigate discrimination against certain societal groups in data-driven tasks. For fair supervised learning, particularly in pre-processing, there have been two main categories: data fairness and task-tailored fairness. The former directly finds an intermediate distribution among the groups, independent of the type of the downstream model, so a learned downstream classification/regression model returns similar predictive scores to individuals inputting the same covariates irrespective of their […]

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arXiv:2601.11701v1 Announce Type: cross Abstract: Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm’s output is to small changes in the training data. Stability plays a crucial role in understanding generalization, robustness, and replicability, and a variety of stability notions have been proposed in different learning settings. However, while stability entails desirable properties, it is typically not sufficient on its own for statistical learning — and indeed, it may be […]

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arXiv:2601.11638v1 Announce Type: cross Abstract: Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems by embedding physical laws into the learning process. However, rigorously quantifying how well a PINN captures the complete dynamical behavior of the system, beyond simple trajectory prediction, remains a challenge. This paper proposes a novel experimental framework to address this by employing Fisher information for differentiable dynamical systems, denoted $g_F^C$. This Fisher information, distinct from […]

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arXiv:2601.14031v1 Announce Type: new Abstract: Intermittent time series, characterised by the presence of a significant amount of zeros, constitute a large percentage of inventory items in supply chain. Probabilistic forecasts are needed to plan the inventory levels; the predictive distribution should cover non-negative values, have a mass in zero and a long upper tail. Intermittent time series are commonly forecast using local models, which are trained individually on each time series. In the last years global models, which […]

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arXiv:2601.13642v1 Announce Type: new Abstract: Average-reward reinforcement learning offers a principled framework for long-term decision-making by maximizing the mean reward per time step. Although Q-learning is a widely used model-free algorithm with established sample complexity in discounted and finite-horizon Markov decision processes (MDPs), its theoretical guarantees for average-reward settings remain limited. This work studies a simple but effective Q-learning algorithm for average-reward MDPs with finite state and action spaces under the weakly communicating assumption, covering both single-agent and […]

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arXiv:2601.13436v1 Announce Type: new Abstract: Linearly parametrized models are widely used in control and signal processing, with the least-squares (LS) estimate being the archetypical solution. When the input is insufficiently exciting, the LS problem may be unsolvable or numerically unstable. This issue can be resolved through regularization, typically with ridge regression. Although regularized estimators reduce the variance error, it remains important to quantify their estimation uncertainty. A possible approach for linear regression is to construct confidence ellipsoids with […]

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arXiv:2601.13191v1 Announce Type: new Abstract: In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected empirical risk subject to an $f$-divergence constraint are established. The proposed approach extends applicability to a broader class of $f$-divergences than previously reported and yields theoretical results that recover previously known results. Additionally, the difference between the expected empirical […]

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arXiv:2601.12587v1 Announce Type: new Abstract: We address the following question: given a collection ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$ of independent $d times d$ random matrices drawn from a common distribution $mathbb{P}$, what is the probability that the centralizer of ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$ is trivial? We provide lower bounds on this probability in terms of the sample size $N$ and the dimension $d$ for several families of random matrices which arise from the discretization of linear Schr”odinger operators with random potentials. […]

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arXiv:2601.12023v1 Announce Type: new Abstract: Semi-implicit variational inference (SIVI) enhances the expressiveness of variational families through hierarchical semi-implicit distributions, but the intractability of their densities makes standard ELBO-based optimization biased. Recent score-matching approaches to SIVI (SIVI-SM) address this issue via a minimax formulation, at the expense of an additional lower-level optimization problem. In this paper, we propose kernel semi-implicit variational inference (KSIVI), a principled and tractable alternative that eliminates the lower-level optimization by leveraging kernel methods. We show […]

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arXiv:2601.11790v1 Announce Type: new Abstract: Global sensitivity analysis of complex numerical simulators is often limited by the small number of model evaluations that can be afforded. In such settings, surrogate models built from a limited set of simulations can substantially reduce the computational burden, provided that the design of computer experiments is enriched efficiently. In this context, we propose an active learning approach that, for a fixed evaluation budget, targets the most informative regions of the input space […]

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