March 2026

arXiv:2603.24771v2 Announce Type: replace-cross Abstract: Missing data is a ubiquitous challenge in data analysis, often leading to biased and inaccurate results. Traditional imputation methods usually assume that the missingness mechanism is missing-at-random (MAR), where the missingness is independent of the missing values themselves. This assumption is frequently violated in real-world scenarios, prompted by recent advances in imputation methods using deep learning to address this challenge. However, these methods neglect the crucial issue of nonparametric identifiability in missing-not-at-random (MNAR) […]

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arXiv:2603.24763v2 Announce Type: replace-cross Abstract: Conditional independence is central to modern statistics, but beyond special parametric families it rarely admits an exact covariance characterization. We introduce the binary expansion group intersection network (BEGIN), a distribution-free graphical representation for multivariate binary data and bit-encoded multinomial variables. For arbitrary binary random vectors and bit representations of multinomial variables, we prove that conditional independence is equivalent to a sparse linear representation of conditional expectations, to a block factorization of the corresponding […]

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arXiv:2601.16195v2 Announce Type: replace-cross Abstract: Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to fulfill a number of physical laws exactly, from geometric symmetries to energy conservation. Evidence is mounting that relaxing some of these constraints can be beneficial to the efficiency and (somewhat surprisingly) accuracy of MLIPs, even though care should be taken to avoid qualitative failures […]

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arXiv:2510.03587v2 Announce Type: replace-cross Abstract: Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of algorithms require either perfect samplers or sequential samplers for complex models, which are often either not available, or suffer from poor mixing, especially in high dimensions. We develop a method that does not require perfect or sequential sampling, and can be applied to […]

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arXiv:2502.14950v2 Announce Type: replace-cross Abstract: Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization so that one can quickly discard impossible explanations. Via an explicit example, we demonstrate that, in general, symmetries cannot be exploited to reduce […]

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arXiv:2502.01557v3 Announce Type: replace-cross Abstract: Despite exceptional achievements, training neural networks remains computationally expensive and is often plagued by instabilities that can degrade convergence. While learning rate schedules can help mitigate these issues, finding optimal schedules is time-consuming and resource-intensive. This work explores theoretical issues concerning training stability in the constant-learning-rate (i.e., without schedule) and small-batch-size regime. Surprisingly, we show that the composition order of gradient updates affects stability and convergence in gradient-based optimizers. We illustrate this new […]

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arXiv:2412.04882v2 Announce Type: replace-cross Abstract: Global optimisation to optimise expensive-to-evaluate black-box functions without gradient information. Bayesian optimisation, one of the most well-known techniques, typically employs Gaussian processes as surrogate models, leveraging their probabilistic nature to balance exploration and exploitation. However, these processes become computationally prohibitive in high-dimensional spaces. Recent alternatives, based on inverse distance weighting (IDW) and radial basis functions (RBFs), offer competitive, computationally lighter solutions. Despite their efficiency, both traditional global and Bayesian optimisation strategies suffer from […]

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arXiv:2603.02460v4 Announce Type: replace Abstract: Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal prediction framework for graph-valued outputs, providing distribution-free coverage guarantees in structured output spaces. Our method defines nonconformity via the Z-Gromov-Wasserstein distance, instantiated in practice through Fused Gromov-Wasserstein (FGW), enabling permutation invariant comparison between predicted and candidate graphs. To obtain adaptive prediction sets, we introduce Score […]

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arXiv:2512.17374v3 Announce Type: replace Abstract: Given a probability distribution $mu$ in $mathbb{R}^d$ represented by data, we study in this paper the generative modeling of the corresponding conditional probability distributions on the level-sets of a collective variable $xi:mathbb{R}^d rightarrow mathbb{R}^k$, where $1 le k

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arXiv:2510.27643v2 Announce Type: replace Abstract: This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network’s geometry, we adopt Whittle-Mat’ern Gaussian process prior models defined via stochastic partial […]

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