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arXiv:2603.22328v1 Announce Type: cross Abstract: Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue arises in scenarios where the likelihood of error inferred from learned representations follows a bimodal distribution, resulting from the coexistence of confident and ambiguous predictions. Standard regression approaches often struggle to adequately express this predictive uncertainty, as they implicitly assume unimodal Gaussian noise, leading […]

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arXiv:2603.22320v1 Announce Type: cross Abstract: While climate models provide insights for climate decision-making, their use is constrained by significant computational and technical demands. Although machine learning (ML) emulators offer a way to bypass the high computational costs, their effective use remains challenging. The hurdles are diverse, ranging from limited accessibility and a lack of specialized knowledge to a general mistrust of ML methods that are perceived as insufficiently physical. Here, we introduce a framework to overcome these barriers […]

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arXiv:2603.23305v1 Announce Type: new Abstract: We investigate contextual graph matching in the Gaussian setting, where both edge weights and node features are correlated across two networks. We derive precise information-theoretic thresholds for exact recovery, and identify conditions under which almost exact recovery is possible or impossible, in terms of graph and feature correlation strengths, the number of nodes, and feature dimension. Interestingly, whereas an all-or-nothing phase transition is observed in the standard graph-matching scenario, the additional contextual information […]

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arXiv:2603.23205v1 Announce Type: new Abstract: Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to local non-stationarity. We show that this adaptation induces a critical trade-off between the minimum attainable p-value and its stability. As importance weights localize to relevant calibration instances, the effective sample size decreases. This can render standard conformal p-values overly conservative for effective error control, […]

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arXiv:2603.23106v1 Announce Type: new Abstract: Characteristic functions of weighted sums of independent random variables exhibit low-rank structure in the quantized tensor train (QTT) representation, also known as matrix product states (MPS), enabling up to exponential compression of their fully non-Gaussian probability distributions. Under variable independence, the global characteristic function factorizes into local terms. Its low-rank QTT structure arises from intrinsic spectral smoothness in continuous models, or from spectral energy concentration as the number of components $D$ grows in […]

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arXiv:2603.22959v1 Announce Type: new Abstract: We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of trees built from copulas, where more complex latent dependence can be modeled with increasing number of trees. We propose to estimate the vine copula approximate posterior in a stepwise fashion, tree by tree along the vine structure. Further, […]

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arXiv:2603.22750v1 Announce Type: new Abstract: Active learning reduces labeling costs by selecting samples that maximize information gain. A dominant framework, Query-by-Committee (QBC), typically relies on perturbation-based diversity by inducing model disagreement through random feature subsetting or data blinding. While this approximates one notion of epistemic uncertainty, it sacrifices direct characterization of the plausible hypothesis space. We propose the complementary approach: Rashomon Ensembled Active Learning (REAL) which constructs a committee by exhaustively enumerating the Rashomon Set of all near-optimal […]

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arXiv:2603.22644v1 Announce Type: new Abstract: We consider a PAC-Bayes type learning rule for binary classification, balancing the training error of a randomized ”posterior” predictor with its KL divergence to a pre-specified ”prior”. This can be seen as an extension of a modified two-part-code Minimum Description Length (MDL) learning rule, to continuous priors and randomized predictions. With a balancing parameter of $lambda=1$ this learning rule recovers an (empirical) Bayes posterior and a modified variant recovers the profile posterior, linking […]

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arXiv:2603.22563v1 Announce Type: new Abstract: Preference-based fine-tuning has become an important component in training large language models, and the data used at this stage may contain sensitive user information. A central question is how to design a differentially private pipeline that is well suited to the distinct structure of reinforcement learning from human feedback. We propose a privacy-preserving framework that imposes differential privacy only on reward learning and derives the final policy from the resulting private reward model. […]

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arXiv:2603.22468v1 Announce Type: new Abstract: We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The posterior is represented as the invariant measure of a Langevin stochastic partial differential equation (SPDE) on a separable Hilbert space, which allows us to control posterior moments and obtain non-asymptotic concentration rates in Hilbert norms under various likelihood curvature and regularity […]

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