mailitics

Category: cs.NA

  • Estimation of instrument and noise parameters for inverse problem based on prior diffusion model

    Estimation of instrument and noise parameters for inverse problem based on prior diffusion model arXiv:2602.11711v1 Announce Type: new Abstract: This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…

  • Radon–Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions

    Radon–Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions arXiv:2602.05227v1 Announce Type: new Abstract: Gradient flows of the Kullback–Leibler (KL) divergence, such as the Fokker–Planck equation and Stein Variational Gradient Descent, evolve a distribution toward a target density known only up to a normalizing constant. We introduce new gradient flows of the KL divergence with…

  • Error Analysis of Bayesian Inverse Problems with Generative Priors

    Error Analysis of Bayesian Inverse Problems with Generative Priors arXiv:2601.17374v1 Announce Type: new Abstract: Data-driven methods for the solution of inverse problems have become widely popular in recent years thanks to the rise of machine learning techniques. A popular approach concerns the training of a generative model on additional data to learn a bespoke prior…

  • Distributional Computational Graphs: Error Bounds

    Distributional Computational Graphs: Error Bounds arXiv:2601.16250v1 Announce Type: new Abstract: We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the…

  • Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions

    Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions arXiv:2601.14515v1 Announce Type: new Abstract: Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The method minimizes a Dirichlet energy defined on a (discrete) graph…

  • Inference-Time Alignment for Diffusion Models via Doob’s Matching

    Inference-Time Alignment for Diffusion Models via Doob’s Matching arXiv:2601.06514v1 Announce Type: new Abstract: Inference-time alignment for diffusion models aims to adapt a pre-trained diffusion model toward a target distribution without retraining the base score network, thereby preserving the generative capacity of the base model while enforcing desired properties at the inference time. A central mechanism…

  • Constrained Density Estimation via Optimal Transport

    Constrained Density Estimation via Optimal Transport arXiv:2601.06830v1 Announce Type: new Abstract: A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of functions adopts or exceeds given values. The framework…

  • Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference

    Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference arXiv:2601.00038v1 Announce Type: new Abstract: This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are explainable, computationally…

  • Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics

    Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics arXiv:2512.11090v1 Announce Type: new Abstract: Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we propose WeldNet: Windowed Encoders for Learning Dynamics, a data-driven nonlinear model reduction framework to build…

  • Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels

    Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels arXiv:2512.10256v1 Announce Type: new Abstract: We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of…

  • Provable Diffusion Posterior Sampling for Bayesian Inversion

    Provable Diffusion Posterior Sampling for Bayesian Inversion arXiv:2512.08022v1 Announce Type: new Abstract: This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a warm-start strategy to initialize the particles. To approximate the posterior score, we…

  • Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework

    Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework arXiv:2511.06235v1 Announce Type: new Abstract: This paper presents a comprehensive analysis of hyperparameter estimation within the empirical Bayes framework (EBF) for sparse learning. By studying the influence of hyperpriors on the solution of EBF, we establish a theoretical connection between the choice of…

  • Data-driven Learning of Interaction Laws in Multispecies Particle Systems with Gaussian Processes: Convergence Theory and Applications

    Data-driven Learning of Interaction Laws in Multispecies Particle Systems with Gaussian Processes: Convergence Theory and Applications arXiv:2511.02053v1 Announce Type: new Abstract: We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic interaction rules generate complex…

  • Score-based constrained generative modeling via Langevin diffusions with boundary conditions

    Score-based constrained generative modeling via Langevin diffusions with boundary conditions arXiv:2510.23985v1 Announce Type: new Abstract: Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative model using kinetic (underdamped) Langevin dynamics with specular reflection of velocity…

  • Enhanced Cyclic Coordinate Descent Methods for Elastic Net Penalized Linear Models

    Enhanced Cyclic Coordinate Descent Methods for Elastic Net Penalized Linear Models arXiv:2510.19999v1 Announce Type: new Abstract: We present a novel enhanced cyclic coordinate descent (ECCD) framework for solving generalized linear models with elastic net constraints that reduces training time in comparison to existing state-of-the-art methods. We redesign the CD method by performing a Taylor expansion…

  • Extreme Event Aware ($eta$-) Learning

    Extreme Event Aware ($eta$-) Learning arXiv:2510.19161v1 Announce Type: new Abstract: Quantifying and predicting rare and extreme events persists as a crucial yet challenging task in understanding complex dynamical systems. Many practical challenges arise from the infrequency and severity of these events, including the considerable variance of simple sampling methods and the substantial computational cost of…

  • Adaptive randomized pivoting and volume sampling

    Adaptive randomized pivoting and volume sampling arXiv:2510.02513v1 Announce Type: new Abstract: Adaptive randomized pivoting (ARP) is a recently proposed and highly effective algorithm for column subset selection. This paper reinterprets the ARP algorithm by drawing connections to the volume sampling distribution and active learning algorithms for linear regression. As consequences, this paper presents new analysis…

  • PBPK-iPINNs : Inverse Physics-Informed Neural Networks for Physiologically Based Pharmacokinetic Brain Models

    PBPK-iPINNs : Inverse Physics-Informed Neural Networks for Physiologically Based Pharmacokinetic Brain Models arXiv:2509.12666v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) leverage machine learning with differential equations to solve direct and inverse problems, ensuring predictions follow physical laws. Physiologically based pharmacokinetic (PBPK) modeling advances beyond classical compartmental approaches by using a mechanistic, physiology focused framework.…

  • Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning

    Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning arXiv:2509.11070v1 Announce Type: new Abstract: We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which admit discrete spectral decompositions, and (ii) diagonal kernels of the form $K(x,x’)=k(x,x’)T$, where $k$…

  • Cryo-EM as a Stochastic Inverse Problem

    Cryo-EM as a Stochastic Inverse Problem arXiv:2509.05541v1 Announce Type: new Abstract: Cryo-electron microscopy (Cryo-EM) enables high-resolution imaging of biomolecules, but structural heterogeneity remains a major challenge in 3D reconstruction. Traditional methods assume a discrete set of conformations, limiting their ability to recover continuous structural variability. In this work, we formulate cryo-EM reconstruction as a stochastic…

  • Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations

    Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations arXiv:2509.05186v1 Announce Type: new Abstract: In-context operator networks (ICON) are a class of operator learning methods based on the novel architectures of foundation models. Trained on a diverse set of datasets of initial and boundary conditions paired with corresponding solutions to…

  • Scale-Adaptive Generative Flows for Multiscale Scientific Data

    Scale-Adaptive Generative Flows for Multiscale Scientific Data arXiv:2509.02971v1 Announce Type: new Abstract: Flow-based generative models can face significant challenges when modeling scientific data with multiscale Fourier spectra, often producing large errors in fine-scale features. We address this problem within the framework of stochastic interpolants, via principled design of noise distributions and interpolation schedules. The key…

  • The Nondecreasing Rank

    The Nondecreasing Rank arXiv:2509.00265v1 Announce Type: new Abstract: In this article the notion of the nondecreasing (ND) rank of a matrix or tensor is introduced. A tensor has an ND rank of r if it can be represented as a sum of r outer products of vectors, with each vector satisfying a monotonicity constraint. It…

  • Underdamped Langevin MCMC with third order convergence

    Underdamped Langevin MCMC with third order convergence arXiv:2508.16485v1 Announce Type: new Abstract: In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein distance when the $d$-dimensional target distribution $p(x)propto e^{-f(x)}$ is strongly log-concave and has varying degrees of…

  • Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factors

    Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factors arXiv:2508.14234v1 Announce Type: cross Abstract: We give a proof of the conjecture of Nelson and Nguyen [FOCS 2013] on the optimal dimension and sparsity of oblivious subspace embeddings, up to sub-polylogarithmic factors: For any $ngeq d$ and $epsilongeq d^{-O(1)}$, there is a random $tilde O(d/epsilon^2)times…

  • On computing and the complexity of computing higher-order $U$-statistics, exactly

    On computing and the complexity of computing higher-order $U$-statistics, exactly arXiv:2508.12627v1 Announce Type: new Abstract: Higher-order $U$-statistics abound in fields such as statistics, machine learning, and computer science, but are known to be highly time-consuming to compute in practice. Despite their widespread appearance, a comprehensive study of their computational complexity is surprisingly lacking. This paper…

  • Distributional Sensitivity Analysis: Enabling Differentiability in Sample-Based Inference

    Distributional Sensitivity Analysis: Enabling Differentiability in Sample-Based Inference arXiv:2508.09347v1 Announce Type: new Abstract: We present two analytical formulae for estimating the sensitivity — namely, the gradient or Jacobian — at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula interprets this sensitivity as partial derivatives of the inverse…

  • Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theory

    Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theory arXiv:2508.05764v1 Announce Type: new Abstract: We consider matrices $boldsymbol{A}(boldsymboltheta)inmathbb{R}^{mtimes m}$ that depend, possibly nonlinearly, on a parameter $boldsymboltheta$ from a compact parameter space $Theta$. We present a Monte Carlo estimator for minimizing $text{trace}(boldsymbol{A}(boldsymboltheta))$ over all $boldsymbolthetainTheta$, and determine the sampling amount so that…

  • Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks

    Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks arXiv:2508.00247v1 Announce Type: new Abstract: The Kolmogorov-Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single variable functions. Subsequent simplifications of this representation involve expressing these functions as parameterized sums of a smaller number of unique monotonic functions. These…

  • Hybrid least squares for learning functions from highly noisy data

    Hybrid least squares for learning functions from highly noisy data arXiv:2507.02215v1 Announce Type: new Abstract: Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are powerful in the small noise regime are suboptimal when large noise is present. We propose…

  • A generative modeling / Physics-Informed Neural Network approach to random differential equations

    A generative modeling / Physics-Informed Neural Network approach to random differential equations arXiv:2507.01687v1 Announce Type: new Abstract: The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertainty in complex systems.…

  • Forward Reverse Kernel Regression for the Schr”{o}dinger bridge problem

    Forward Reverse Kernel Regression for the Schr”{o}dinger bridge problem arXiv:2507.00640v1 Announce Type: new Abstract: In this paper, we study the Schr”odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin–endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure to approximate the Schr”odinger potentials in a nonparametric way.…

  • Gaussian Processes and Reproducing Kernels: Connections and Equivalences

    Gaussian Processes and Reproducing Kernels: Connections and Equivalences arXiv:2506.17366v1 Announce Type: new Abstract: This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences…

  • Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling

    Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling arXiv:2505.18327v1 Announce Type: new Abstract: Constrained stochastic nonlinear optimization problems have attracted significant attention for their ability to model complex real-world scenarios in physics, economics, and biology. As datasets continue to grow, online inference methods have become crucial for enabling real-time decision-making without the need…

  • On the expressivity of deep Heaviside networks

    On the expressivity of deep Heaviside networks arXiv:2505.00110v1 Announce Type: new Abstract: We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We provide lower and upper bounds for the Vapnik-Chervonenkis (VC) dimensions and approximation rates of these network…

  • A Dictionary of Closed-Form Kernel Mean Embeddings

    A Dictionary of Closed-Form Kernel Mean Embeddings arXiv:2504.18830v1 Announce Type: new Abstract: Kernel mean embeddings — integrals of a kernel with respect to a probability distribution — are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference based on the maximum mean discrepancy. These methods…

  • Physics-informed features in supervised machine learning

    Physics-informed features in supervised machine learning arXiv:2504.17112v1 Announce Type: new Abstract: Supervised machine learning involves approximating an unknown functional relationship from a limited dataset of features and corresponding labels. The classical approach to feature-based machine learning typically relies on applying linear regression to standardized features, without considering their physical meaning. This may limit model explainability,…

  • Physics-Informed Inference Time Scaling via Simulation-Calibrated Scientific Machine Learning

    Physics-Informed Inference Time Scaling via Simulation-Calibrated Scientific Machine Learning arXiv:2504.16172v1 Announce Type: cross Abstract: High-dimensional partial differential equations (PDEs) pose significant computational challenges across fields ranging from quantum chemistry to economics and finance. Although scientific machine learning (SciML) techniques offer approximate solutions, they often suffer from bias and neglect crucial physical insights. Inspired by inference-time…

  • Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems

    Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems arXiv:2504.13320v1 Announce Type: new Abstract: We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for…

  • On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces

    On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces arXiv:2504.13623v1 Announce Type: new Abstract: We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the input data. We first prove…

  • Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems

    Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems arXiv:2503.18190v1 Announce Type: new Abstract: The reconstruction of tensor-valued signals from corrupted measurements, known as tensor regression, has become essential in many multi-modal applications such as hyperspectral image reconstruction and medical imaging. In this work, we address the tensor linear system problem $mathcal{A} mathcal{X}=mathcal{B}$, where $mathcal{A}$ is…

  • Data-Driven Approximation of Binary-State Network Reliability Function: Algorithm Selection and Reliability Thresholds for Large-Scale Systems

    Data-Driven Approximation of Binary-State Network Reliability Function: Algorithm Selection and Reliability Thresholds for Large-Scale Systems arXiv:2503.15545v1 Announce Type: cross Abstract: Network reliability assessment is pivotal for ensuring the robustness of modern infrastructure systems, from power grids to communication networks. While exact reliability computation for binary-state networks is NP-hard, existing approximation methods face critical tradeoffs between…

  • Exploring specialization and sensitivity of convolutional neural networks in the context of simultaneous image augmentations

    Exploring specialization and sensitivity of convolutional neural networks in the context of simultaneous image augmentations arXiv:2503.03283v1 Announce Type: new Abstract: Drawing parallels with the way biological networks are studied, we adapt the treatment–control paradigm to explainable artificial intelligence research and enrich it through multi-parametric input alterations. In this study, we propose a framework for investigating…

  • Weighted quantization using MMD: From mean field to mean shift via gradient flows

    Weighted quantization using MMD: From mean field to mean shift via gradient flows arXiv:2502.10600v1 Announce Type: new Abstract: Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a finite weighted mixture of Dirac measures that best approximates…

  • Online Covariance Matrix Estimation in Sketched Newton Methods

    Online Covariance Matrix Estimation in Sketched Newton Methods arXiv:2502.07114v1 Announce Type: new Abstract: Given the ubiquity of streaming data, online algorithms have been widely used for parameter estimation, with second-order methods particularly standing out for their efficiency and robustness. In this paper, we study an online sketched Newton method that leverages a randomized sketching technique…

  • Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond

    Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond arXiv:2502.04575v1 Announce Type: new Abstract: Given an unnormalized probability density $piproptomathrm{e}^{-V}$, estimating its normalizing constant $Z=int_{mathbb{R}^d}mathrm{e}^{-V(x)}mathrm{d}x$ or free energy $F=-log Z$ is a crucial problem in Bayesian statistics, statistical mechanics, and machine learning. It is challenging especially in high dimensions…

  • Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs

    Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs arXiv:2412.03271v1 Announce Type: new Abstract: Neural Jump ODEs model the conditional expectation between observations by neural ODEs and jump at arrival of new observations. They have demonstrated effectiveness for fully data-driven online forecasting in settings with irregular and partial observations, operating under weak regularity assumptions. This…