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Tag: dimension

  • Structural Dimension Reduction in Bayesian Networks

    Structural Dimension Reduction in Bayesian Networks arXiv:2601.08236v1 Announce Type: new Abstract: This work introduces a novel technique, named structural dimension reduction, to collapse a Bayesian network onto a minimum and localized one while ensuring that probabilistic inferences between the original and reduced networks remain consistent. To this end, we propose a new combinatorial structure in…

  • Dimension-reduced outcome-weighted learning for estimating individualized treatment regimes in observational studies

    Dimension-reduced outcome-weighted learning for estimating individualized treatment regimes in observational studies arXiv:2601.06782v1 Announce Type: new Abstract: Individualized treatment regimes (ITRs) aim to improve clinical outcomes by assigning treatment based on patient-specific characteristics. However, existing methods often struggle with high-dimensional covariates, limiting accuracy, interpretability, and real-world applicability. We propose a novel sufficient dimension reduction approach that…

  • Evidence Slopes and Effective Dimension in Singular Linear Models

    Evidence Slopes and Effective Dimension in Singular Linear Models arXiv:2601.01238v1 Announce Type: new Abstract: Bayesian model selection commonly relies on Laplace approximation or the Bayesian Information Criterion (BIC), which assume that the effective model dimension equals the number of parameters. Singular learning theory replaces this assumption with the real log canonical threshold (RLCT), an effective…

  • Dimension-Free Minimax Rates for Learning Pairwise Interactions in Attention-Style Models

    Dimension-Free Minimax Rates for Learning Pairwise Interactions in Attention-Style Models arXiv:2510.11789v1 Announce Type: new Abstract: We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a non-linear activation function. We prove that the minimax rate is $M^{-frac{2beta}{2beta+1}}$ with $M$ being the sample size, depending…

  • Active Subspaces in Infinite Dimension

    Active Subspaces in Infinite Dimension arXiv:2510.11871v1 Announce Type: new Abstract: Active subspace analysis uses the leading eigenspace of the gradient’s second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a…

  • A Survey of Dimension Estimation Methods

    A Survey of Dimension Estimation Methods arXiv:2507.13887v1 Announce Type: new Abstract: It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence…

  • Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inference

    Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inference arXiv:2505.21721v1 Announce Type: new Abstract: We prove that, given a mean-field location-scale variational family, black-box variational inference (BBVI) with the reparametrization gradient converges at an almost dimension-independent rate. Specifically, for strongly log-concave and log-smooth targets, the number of iterations for BBVI with a sub-Gaussian family to achieve…

  • A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data

    A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data arXiv:2412.09779v1 Announce Type: new Abstract: Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing…

  • Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction

    Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction arXiv:2412.08961v1 Announce Type: new Abstract: We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the targets of estimation. This unified framework…