March 2026

arXiv:2603.19804v1 Announce Type: cross Abstract: We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the sources of predictive uncertainty. Since the posterior predictive variance is fixed given the model, it represents a constant quantity that is conserved over these expansions. The terms in the expansions can be assessed in absolute or relative sense to […]

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arXiv:2603.19792v1 Announce Type: cross Abstract: Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to handle large-scale data. We address this issue by developing a novel coreset construction for multivariate conditional transformation models (MCTMs) to enhance their scalability and training efficiency. To the best of our knowledge, these are the first coresets for semi-parametric distributional models. […]

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arXiv:2603.19755v1 Announce Type: cross Abstract: Beckmann’s problem in optimal transport minimizes the total squared flux in a continuous transport problem from a source to a target distribution. In this article, the regularity theory for solutions to Beckmann’s problem in optimal transport is developed utilizing an unconstrained Lagrangian formulation and solving the variational first order optimality conditions. It turns out that the Lagrangian multiplier that enforces Beckmann’s divergence constraint fulfills a Poisson equation and the flux vector field is […]

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arXiv:2603.19648v1 Announce Type: cross Abstract: Stochastic approximation (SA) is a fundamental iterative framework with broad applications in reinforcement learning and optimization. Classical analyses typically rely on martingale difference or Markov noise with bounded second moments, but many practical settings, including finance and communications, frequently encounter heavy-tailed and long-range dependent (LRD) noise. In this work, we study SA for finding the root of a strongly monotone operator under these non-classical noise models. We establish the first finite-time moment bounds […]

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arXiv:2603.19633v1 Announce Type: cross Abstract: This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and backward iterations of the heat flow. The backward step was originally implemented by rejection sampling, whereas we directly simulate the dynamics. Unlike diffusion-based sampling methods that estimate scores via learned models or by invoking auxiliary samplers, our method treats the intermediate particle […]

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arXiv:2603.19331v1 Announce Type: cross Abstract: Boundary condition tuning is a fundamental step in patient-specific cardiovascular modeling. Despite an increase in offline training cost, recent methods in data-driven variational inference can efficiently estimate the joint posterior distribution of boundary conditions, with amortization of training efforts over clinical targets. However, even the most modern approaches fall short in two important scenarios: open-loop models with known mean flow and assumed waveform shapes, and anatomies affected by vascular lesions where segmentation influences […]

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arXiv:2603.19291v1 Announce Type: cross Abstract: As regression is a widely studied problem, many methods have been proposed to solve it, each of them often requiring setting different hyper-parameters. Therefore, selecting the proper method for a given application may be very difficult and relies on comparing their performances. Performance is usually measured using various metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), or R-squared (R${}^2$). These metrics provide a numerical summary of predictive accuracy by […]

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arXiv:2603.19899v1 Announce Type: new Abstract: Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and the label sequences, presenting two central research challenges: (1) designing neural architectures that model autocorrelation in history sequences, and (2) devising learning objectives that model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic […]

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arXiv:2603.19840v1 Announce Type: new Abstract: A major limitation of clustering approaches is their lack of explainability: methods rarely provide insight into which features drive the grouping of similar observations. To address this limitation, we propose an ensemble-based clustering framework that integrates bagging and feature dropout to generate feature importance scores, in analogy with feature importance mechanisms in supervised random forests. By leveraging multiple bootstrap resampling schemes and aggregating the resulting partitions, the method improves stability and robustness of […]

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arXiv:2603.19736v1 Announce Type: new Abstract: Finite-context models (FCMs) are widely used for compressing symbolic sequences such as DNA, where predictive performance depends critically on the context length k and smoothing parameter {alpha}. In practice, these hyperparameters are typically selected through exhaustive search, which is computationally expensive and scales poorly with model complexity. This paper proposes a statistically grounded two-step sequential approach for efficient hyperparameter selection in FCMs. The key idea is to decompose the joint optimization problem into […]

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