mailitics

Tag: dimensional

  • Topological Exploration of High-Dimensional Empirical Risk Landscapes: general approach, and applications to phase retrieval

    Topological Exploration of High-Dimensional Empirical Risk Landscapes: general approach, and applications to phase retrieval arXiv:2602.17779v1 Announce Type: new Abstract: We consider the landscape of empirical risk minimization for high-dimensional Gaussian single-index models (generalized linear models). The objective is to recover an unknown signal $boldsymbol{theta}^star in mathbb{R}^d$ (where $d gg 1$) from a loss function $hat{R}(boldsymbol{theta})$…

  • High-Dimensional Limit of Stochastic Gradient Flow via Dynamical Mean-Field Theory

    High-Dimensional Limit of Stochastic Gradient Flow via Dynamical Mean-Field Theory arXiv:2602.06320v1 Announce Type: new Abstract: Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for describing the high-dimensional asymptotic behavior of multi-pass…

  • An approach to Fisher-Rao metric for infinite dimensional non-parametric information geometry

    An approach to Fisher-Rao metric for infinite dimensional non-parametric information geometry arXiv:2512.21451v1 Announce Type: new Abstract: Being infinite dimensional, non-parametric information geometry has long faced an “intractability barrier” due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces a novel framework to resolve the…

  • High-Dimensional Partial Least Squares: Spectral Analysis and Fundamental Limitations

    High-Dimensional Partial Least Squares: Spectral Analysis and Fundamental Limitations arXiv:2512.15684v1 Announce Type: new Abstract: Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its behavior in high-dimensional regimes remains limited. In this…

  • Generalized infinite dimensional Alpha-Procrustes based geometries

    Generalized infinite dimensional Alpha-Procrustes based geometries arXiv:2511.09801v1 Announce Type: new Abstract: This work extends the recently introduced Alpha-Procrustes family of Riemannian metrics for symmetric positive definite (SPD) matrices by incorporating generalized versions of the Bures-Wasserstein (GBW), Log-Euclidean, and Wasserstein distances. While the Alpha-Procrustes framework has unified many classical metrics in both finite- and infinite- dimensional…

  • Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces

    Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces arXiv:2511.06239v1 Announce Type: new Abstract: Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their strong potential for sampling the paths of conditional diffusion processes, enabling…

  • High-Dimensional BWDM: A Robust Nonparametric Clustering Validation Index for Large-Scale Data

    High-Dimensional BWDM: A Robust Nonparametric Clustering Validation Index for Large-Scale Data arXiv:2510.14145v1 Announce Type: new Abstract: Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based distances and therefore degrade in high-dimensional or contaminated data. This…

  • A hierarchical entropy method for the delocalization of bias in high-dimensional Langevin Monte Carlo

    A hierarchical entropy method for the delocalization of bias in high-dimensional Langevin Monte Carlo arXiv:2509.08619v1 Announce Type: new Abstract: The unadjusted Langevin algorithm is widely used for sampling from complex high-dimensional distributions. It is well known to be biased, with the bias typically scaling linearly with the dimension when measured in squared Wasserstein distance. However,…

  • Assessing One-Dimensional Cluster Stability by Extreme-Point Trimming

    Assessing One-Dimensional Cluster Stability by Extreme-Point Trimming arXiv:2509.00258v1 Announce Type: new Abstract: We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional n i.i.d. samples by tracking how their span contracts when the most extreme points are trimmed. Central to our approach is the diameter-shrinkage ratio, that quantifies the relative…

  • Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights

    Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights arXiv:2507.12686v1 Announce Type: new Abstract: We study the Finite-Dimensional Distributions (FDDs) of deep neural networks with randomly initialized weights that have finite-order moments. Specifically, we establish Gaussian approximation bounds in the Wasserstein-$1$ norm between the FDDs and their Gaussian limit assuming a Lipschitz activation…

  • On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiologic boundary conditions

    On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiologic boundary conditions arXiv:2506.11683v1 Announce Type: new Abstract: Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the…

  • Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems

    Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems arXiv:2505.18276v1 Announce Type: new Abstract: Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite-dimensional function spaces – where such problems are naturally formulated – is crucial to ensure stability and convergence as the discretization of the underlying problem is refined.…

  • High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality

    High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality arXiv:2505.06531v1 Announce Type: new Abstract: Imori and Ing (2025) proposed the importance-weighted orthogonal greedy algorithm (IWOGA) for model selection in high-dimensional misspecified regression models under covariate shift. To determine the number of IWOGA iterations, they introduced the high-dimensional importance-weighted information criterion (HDIWIC). They argued that the combined use…

  • Sparse Additive Contextual Bandits: A Nonparametric Approach for Online Decision-making with High-dimensional Covariates

    Sparse Additive Contextual Bandits: A Nonparametric Approach for Online Decision-making with High-dimensional Covariates arXiv:2503.16941v1 Announce Type: new Abstract: Personalized services are central to today’s digital landscape, where online decision-making is commonly formulated as contextual bandit problems. Two key challenges emerge in modern applications: high-dimensional covariates and the need for nonparametric models to capture complex reward-covariate…

  • A dimensionality reduction technique based on the Gromov-Wasserstein distance

    A dimensionality reduction technique based on the Gromov-Wasserstein distance arXiv:2501.13732v1 Announce Type: new Abstract: Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new method for dimensionality reduction, based on optimal transportation…

  • Robust Multi-Dimensional Scaling via Accelerated Alternating Projections

    Robust Multi-Dimensional Scaling via Accelerated Alternating Projections arXiv:2501.02208v1 Announce Type: new Abstract: We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the robust principal component analysis (RPCA) problem,…

  • BOIDS: High-dimensional Bayesian Optimization via Incumbent-guided Direction Lines and Subspace Embeddings

    BOIDS: High-dimensional Bayesian Optimization via Incumbent-guided Direction Lines and Subspace Embeddings arXiv:2412.12918v1 Announce Type: new Abstract: When it comes to expensive black-box optimization problems, Bayesian Optimization (BO) is a well-known and powerful solution. Many real-world applications involve a large number of dimensions, hence scaling BO to high dimension is of much interest. However, state-of-the-art high-dimensional…

  • Modeling High-Dimensional Dependent Data in the Presence of Many Explanatory Variables and Weak Signals

    Modeling High-Dimensional Dependent Data in the Presence of Many Explanatory Variables and Weak Signals arXiv:2412.04736v1 Announce Type: cross Abstract: This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional response series…

  • How well behaved is finite dimensional Diffusion Maps?

    How well behaved is finite dimensional Diffusion Maps? arXiv:2412.03992v1 Announce Type: new Abstract: Under a set of assumptions on a family of submanifolds $subset {mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform density, finite polynomial approximation and local reach. Leveraging…