January 2026

arXiv:2510.12639v2 Announce Type: replace Abstract: Entropy-regularized optimal transport, which has strong links to the Schr”odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed interest in this problem is the recent development of fast matrix-scaling algorithmstextemdash known as iterative proportional fitting or the Sinkhorn algorithmtextemdash for entropic optimal transport, which have favorable complexity over traditional approaches to the unregularized problem. Here, we take a perspective on […]

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arXiv:2506.17764v2 Announce Type: replace Abstract: Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for band-limited functions from noisy input-output measurements, by working in a Paley-Wiener reproducing kernel Hilbert space. Kernel norm bounds are tightened using a uniformly-randomized Hoeffding’s inequality for small samples and an empirical Bernstein bound for larger ones. We derive an approximate threshold, based […]

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arXiv:2504.11609v2 Announce Type: replace Abstract: Recent developments in generative artificial intelligence (AI) rely on machine learning techniques such as deep learning and generative modeling to achieve state-of-the-art performance across wide-ranging domains. These methods’ surprising performance is due in part to their ability to learn implicit “representations” of complex, multi-modal data. Unfortunately, deep neural networks are notoriously black boxes that obscure these representations, making them difficult to interpret or analyze. To resolve these difficulties, one approach is to build […]

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arXiv:2504.03097v2 Announce Type: replace Abstract: In this paper, we study the problem of multivariate shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we investigate the model $Y=tfrac{1}{sqrt{1+sigma^2}}(Pi_* X Q_* + sigma Z)$, where $X$ is an $n*d$ standard Gaussian design matrix, $Z$ is an $n*m$ Gaussian noise matrix, $Pi_*$ is an unknown $n*n$ permutation matrix, and $Q_*$ is an unknown $d*m$ on the Grassmanian manifold […]

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arXiv:2411.03384v2 Announce Type: replace Abstract: In this paper, we solve stochastic partial differential equations (SPDEs) numerically by using (possibly random) neural networks in the truncated Wiener chaos expansion of their corresponding solution. Moreover, we provide some approximation rates for learning the solution of SPDEs with additive and/or multiplicative noise. Finally, we apply our results in numerical examples to approximate the solution of three SPDEs: the stochastic heat equation, the Heath-Jarrow-Morton equation, and the Zakai equation.

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arXiv:2410.05263v2 Announce Type: replace Abstract: Reliable confidence measures of metrics derived from medical imaging reconstruction pipelines would improve the standard of decision-making in many clinical workflows. Conformal Prediction (CP) provides a robust framework for producing calibrated prediction intervals, but standard CP formulations face a critical challenge in the imaging pipeline: common mismatches between image reconstruction objectives and downstream metrics can introduce systematic prediction deviations from ground truth values, known as bias. These biases in turn compromise the efficiency […]

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arXiv:2110.07478v4 Announce Type: replace Abstract: It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower-dimensional coordinates without providing an estimate of the manifold or using the manifold to denoise the original data. This article proposes a new methodology to address these problems, allowing interpolation of the estimated manifold between the […]

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arXiv:2601.18788v1 Announce Type: cross Abstract: Unsupervised text segmentation is crucial because boundary labels are expensive, subjective, and often fail to transfer across domains and granularity choices. We propose Embed-KCPD, a training-free method that represents sentences as embedding vectors and estimates boundaries by minimizing a penalized KCPD objective. Beyond the algorithmic instantiation, we develop, to our knowledge, the first dependence-aware theory for KCPD under $m$-dependent sequences, a finite-memory abstraction of short-range dependence common in language. We prove an oracle […]

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arXiv:2601.18658v1 Announce Type: cross Abstract: When developing clinical prediction models, it can be challenging to balance between global models that are valid for all patients and personalized models tailored to individuals or potentially unknown subgroups. To aid such decisions, we propose a diagnostic tool for contrasting global regression models and patient-specific (local) regression models. The core utility of this tool is to identify where and for whom a global model may be inadequate. We focus on regression models […]

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arXiv:2601.18252v1 Announce Type: cross Abstract: Wireframe parsing aims to recover line segments and their junctions to form a structured geometric representation useful for downstream tasks such as Simultaneous Localization and Mapping (SLAM). Existing methods predict lines and junctions separately and reconcile them post-hoc, causing mismatches and reduced robustness. We present Co-PLNet, a point-line collaborative framework that exchanges spatial cues between the two tasks, where early detections are converted into spatial prompts via a Point-Line Prompt Encoder (PLP-Encoder), which […]

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