Tootfinder

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Derik T. Boonstra, Rakheon Kim, Dean M. Young
https://arxiv.org/abs/2506.19192

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original feature-space dimension, precision matrix estimation becomes unstable and, as a result, increases the variability of the linear dimension reduction (LDR) matrix. Ultimately, this fact causes suboptimal supervised classification. To address this problem, we develo…

Discrete Poincar\'e inequalities and universal approximators for random graphs
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov, Konstantinos Tyros
https://arxiv.org/abs/2506.17433

Discrete Poincaré inequalities and universal approximators for random graphs
Nonlinear Poincaré inequalities are indispensable tools in the study of dimension reduction and low-distortion embeddings of graphs into metric spaces, and have found remarkable algorithmic applications. A basic open problem, posed by Jon Kleinberg (2013), asks whether the optimal nonlinear Poincaré constant for maps between two independent $3$-regular random graphs is dimension-free, i.e., independent of vertex-set sizes. We give a complete and affirmative resolution to Kleinberg's problem, …

Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures
Jie Gao, Rajesh Jayaram, Benedikt Kolbe, Shay Sapir, Chris Schwiegelshohn, Sandeep Silwal, Erik Waingarten
https://arxiv.org/abs/2506.00165

Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including max-matching, max-spanning tree, max TSP, as well as various measures for dataset diversity. For these problems, we show that the effect of dimension reduction is intimately tied to the \emph{doubling dimension} $λ_X$ of the underlying dataset $X$ -- a quantity measur…

Gravitomagnetism from Temporal Dimensional Reduction
Mehran Z-Abyaneh, Mehrdad Farhoudi
https://arxiv.org/abs/2506.00525 https://arxi…

Gravitomagnetism from Temporal Dimensional Reduction
We propose that the Taub-NUT metric can be envisaged as a (3+1) dimensional analog of the Kaluza-Klein (4+1) dimensional metric. After dimensional reduction of the Taub-NUT metric to (3) spatial dimensions, by treating time as the extra curled dimension (since the closed time-like curves can exist in the Taub-NUT framework, such a dimensional reduction is justified), we end up with three dimensional Einstein field equations plus the Maxwell equations for the gravitomagnetic field, which also ac…

On volumes and the generic invariance of Fano type varieties
Donghyeon Kim
https://arxiv.org/abs/2506.13603 https://arxiv.org/pdf/250…

On volumes and the generic invariance of Fano type varieties
We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod $p$.

Bayesian Semiparametric Orthogonal Tucker Factorized Mixed Models for Multi-dimensional Longitudinal Functional Data
Arkaprava Roy, Abhra Sarkar
https://arxiv.org/abs/2506.16668

Bayesian Semiparametric Orthogonal Tucker Factorized Mixed Models for Multi-dimensional Longitudinal Functional Data
We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension reduction techniques, including basis function representation and Tucker tensor decomposition, to model complex functional (e.g., spatial and temporal) variations, group differences, and individual heterogeneity while drastically reducing model dimensions. The mod…

Data-Driven Prediction of Dynamic Interactions Between Robot Appendage and Granular Material
Guanjin Wang, Xiangxue Zhao, Shapour Azarm, Balakumar Balachandran
https://arxiv.org/abs/2506.10875

Data-Driven Prediction of Dynamic Interactions Between Robot Appendage and Granular Material
An alternative data-driven modeling approach has been proposed and employed to gain fundamental insights into robot motion interaction with granular terrain at certain length scales. The approach is based on an integration of dimension reduction (Sequentially Truncated Higher-Order Singular Value Decomposition), surrogate modeling (Gaussian Process), and data assimilation techniques (Reduced Order Particle Filter). This approach can be used online and is based on offline data, obtained from the…

A dimension reduction for extreme types of directed dependence
Sebastian Fuchs, Carsten Limbach
https://arxiv.org/abs/2506.04825 https://

A dimension reduction for extreme types of directed dependence
In recent years, a variety of novel measures of dependence have been introduced being capable of characterizing diverse types of directed dependence, hence diverse types of how a number of predictor variables $\mathbf{X} = (X_1, \dots, X_p)$, $p \in \mathbb{N}$, may affect a response variable $Y$. This includes perfect dependence of $Y$ on $\mathbf{X}$ and independence between $\mathbf{X}$ and $Y$, but also less well-known concepts such as zero-explainability, stochastic comparability and compl…

Let the Tree Decide: FABART A Non-Parametric Factor Model
Sofia Velasco
https://arxiv.org/abs/2506.11551 https://arxiv.org/pdf/2506.1…

Let the Tree Decide: FABART A Non-Parametric Factor Model
This article proposes a novel framework that integrates Bayesian Additive Regression Trees (BART) into a Factor-Augmented Vector Autoregressive (FAVAR) model to forecast macro-financial variables and examine asymmetries in the transmission of oil price shocks. By employing nonparametric techniques for dimension reduction, the model captures complex, nonlinear relationships between observables and latent factors that are often missed by linear approaches. A simulation experiment comparing FABART…

Norming Sets for Tensor and Polynomial Sketching
Yifan Zhang, Joe Kileel
https://arxiv.org/abs/2506.05174 https://arxiv.org/pdf/2506.…

Norming Sets for Tensor and Polynomial Sketching
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets, we provide a framework for controlling the sketching dimension for \textit{any} sketch operator used to embed said sets, including sub-Gaussian, fast Johnson-Lindenstrauss, and tensor structured sketch operators. Leveraging norming set theory, we propose a ne…

Homogenization of elasto-plastic plate equations with vanishing hardening
Marin Bu\v{z}an\v{c}i\'c, Igor Vel\v{c}i\'c, Josip \v{Z}ubrini\'c
https://arxiv.org/abs/2506.08215

Homogenization of elasto-plastic plate equations with vanishing hardening
Building on recent work analyzing the interaction between homogenization and dimension reduction in perfectly plastic materials, we focus on the extreme regime where the plate thickness vanishes much faster than the period of oscillation of the heterogeneous material. Our investigation is devoted to the derivation of the existence of a quasistatic evolution for a multiphase elasto-plastic composite without imposing any kind of ordering constraints on admissible yield surfaces of the various pha…

This https://arxiv.org/abs/2506.00525 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Gravitomagnetism from Temporal Dimensional Reduction
We propose that the Taub-NUT metric can be envisaged as a (3+1) dimensional analog of the Kaluza-Klein (4+1) dimensional metric. After dimensional reduction of the Taub-NUT metric to (3) spatial dimensions, by treating time as the extra curled dimension (since the closed time-like curves can exist in the Taub-NUT framework, such a dimensional reduction is justified), we end up with three dimensional Einstein field equations plus the Maxwell equations for the gravitomagnetic field, which also ac…

Assessing parameter identifiability of a hemodynamics PDE model using spectral surrogates and dimension reduction
Mitchel J. Colebank
https://arxiv.org/abs/2506.04538

Assessing parameter identifiability of a hemodynamics PDE model using spectral surrogates and dimension reduction
Computational inverse problems for biomedical simulators suffer from limited data and relatively high parameter dimensionality. This often requires sensitivity analysis, where parameters of the model are ranked based on their influence on the specific quantities of interest. This is especially important for simulators used to build medical digital twins, as the amount of data is typically limited. For expensive models, such as blood flow models, emulation is employed to expedite the simulation …

Functional Change Point Detection via Adjacent Deviation Subspace
Luoyao Yu, Long Feng, Xuehu Zhu
https://arxiv.org/abs/2506.15143 https://

Functional Change Point Detection via Adjacent Deviation Subspace
This paper develops the concept of the Adjacent Deviation Subspace (ADS), a novel framework for reducing infinite-dimensional functional data into finite-dimensional vector or scalar representations while preserving critical information of functional change points. To identify this functional subspace, we propose an efficient dimension reduction operator that overcomes the critical limitation of information loss inherent in traditional functional principal component analysis (FPCA). Building up…

An Efficient and Interpretable Autoregressive Model for High-Dimensional Tensor-Valued Time Series
Yuxi Cai, Lan Li, Yize Wang, Guodong Li
https://arxiv.org/abs/2506.01658

An Efficient and Interpretable Autoregressive Model for High-Dimensional Tensor-Valued Time Series
In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor order. Conversely, canonical polyadic (CP) decomposition maintains efficiency but lacks a precise statistical interpretation. To attain both interpretability and powerful dimension reduction, this paper proposes a novel approach under the supervised factor mode…