Tootfinder

Dimension Reduction for Clustering: The Curious Case of Discrete Centers
Shaofeng H. -C. Jiang, Robert Krauthgamer, Shay Sapir, Sandeep Silwal, Di Yue
https://arxiv.org/abs/2509.07444

Dimension Reduction for Clustering: The Curious Case of Discrete Centers
The Johnson-Lindenstrauss transform is a fundamental method for dimension reduction in Euclidean spaces, that can map any dataset of $n$ points into dimension $O(\log n)$ with low distortion of their distances. This dimension bound is tight in general, but one can bypass it for specific problems. Indeed, tremendous progress has been made for clustering problems, especially in the \emph{continuous} setting where centers can be picked from the ambient space $\mathbb{R}^d$. Most notably, for $k$-m…

Interpretable dimension reduction for compositional data
Junyoung Park, Cheolwoo Park, Jeongyoun Ahn
https://arxiv.org/abs/2509.05563 https://arxiv.org/pdf…

Interpretable dimension reduction for compositional data
High-dimensional compositional data, such as those from human microbiome studies, pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data, conventional approaches often rely on log-ratio transformations that compromise interpretability and distort the data through ad hoc zero replacements. We introduce a novel framework for interpretable dimension reduction of compositional data that avoids extra trans…

Towards an Efficient Shifted Cholesky QR for Applications in Model Order Reduction using pyMOR
Maximilian Bindhak, Art J. R. Pelling, Jens Saak
https://arxiv.org/abs/2507.07788

Towards an Efficient Shifted Cholesky QR for Applications in Model Order Reduction using pyMOR
Many model order reduction (MOR) methods rely on the computation of an orthonormal basis of a subspace onto which the large full order model is projected. Numerically, this entails the orthogonalization of a set of vectors. The nature of the MOR process imposes several requirements for the orthogonalization process. Firstly, MOR is oftentimes performed in an adaptive or iterative manner, where the quality of the reduced order model, i.e., the dimension of the reduced subspace, is decided on the…

Quantum Algorithm for Estimating Intrinsic Geometry
Nhat A. Nghiem, Tuan K. Do, Tzu-Chieh Wei, Trung V. Phan
https://arxiv.org/abs/2508.06355 https://arxiv…

Quantum Algorithm for Estimating Intrinsic Geometry
High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for estimating the intrinsic geometry of a point cloud -- specifically its local intrinsic dimension and local scalar curvature. These quantities are crucial for dimensionality reduction, feature extraction, and anomaly detection -- tasks that are central to a wide range …

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…

Supervised Dynamic Dimension Reduction with Deep Neural Network
Zhanye Luo, Yuefeng Han, Xiufan Yu
https://arxiv.org/abs/2508.03546 https://arxiv.org/pdf/2…

Supervised Dynamic Dimension Reduction with Deep Neural Network
This paper studies the problem of dimension reduction, tailored to improving time series forecasting with high-dimensional predictors. We propose a novel Supervised Deep Dynamic Principal component analysis (SDDP) framework that incorporates the target variable and lagged observations into the factor extraction process. Assisted by a temporal neural network, we construct target-aware predictors by scaling the original predictors in a supervised manner, with larger weights assigned to predictors…

FDR controlling procedures with dimension reduction and their application to GWAS with linkage disequilibrium score
Dayeon Jung, Yewon Kim, Junyong Park
https://arxiv.org/abs/2507.06049

FDR controlling procedures with dimension reduction and their application to GWAS with linkage disequilibrium score
Genome-wide association studies (GWAS) have led to the discovery of numerous single nucleotide polymorphisms (SNPs) associated with various phenotypes and complex diseases. However, the identified genetic variants do not fully explain the heritability of complex traits, known as the missing heritability problem. To address this challenge and accurately control false positives while maximizing true associations, we propose two approaches involving linkage disequilibrium (LD) scores as covariates…

Multiple Timescale Dynamics of Network Adaptation with Constraints
Erik Andreas Martens, Christian Bick
https://arxiv.org/abs/2507.06359 https://

Multiple Timescale Dynamics of Network Adaptation with Constraints
Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resulting dynamics are typically high-dimensional. Here we consider adaptive dynamical systems subject to constraints on network adaptation: Asymptotically, the adaptive dynamics of network connections evolve on a low-dimensional subset of possible connectivity. Such dimension reduction may be intrinsic…

Explainability-Driven Dimensionality Reduction for Hyperspectral Imaging
Salma Haidar, Jos\'e Oramas
https://arxiv.org/abs/2509.02340 https://arxiv.org…

Explainability-Driven Dimensionality Reduction for Hyperspectral Imaging
Hyperspectral imaging (HSI) provides rich spectral information for precise material classification and analysis; however, its high dimensionality introduces a computational burden and redundancy, making dimensionality reduction essential. We present an exploratory study into the application of post-hoc explainability methods in a model--driven framework for band selection, which reduces the spectral dimension while preserving predictive performance. A trained classifier is probed with explanati…

Crosslisted article(s) found for math.ST. https://arxiv.org/list/math.ST/new
[1/1]:
- Interpretable dimension reduction for compositional data
Junyoung Park, Cheolwoo Park, Jeongyoun Ahn

Metric dimension reduction modulus for logarithmic distortion
Dylan J. Altschuler, Konstantin Tikhomirov
https://arxiv.org/abs/2507.02785 https://

Metric dimension reduction modulus for logarithmic distortion
Given parameters $n$ and $α$, the metric dimension reduction modulus $k^α_n(\ell_\infty)$ is defined as the smallest $k$ such that every $n$--point metric space can be embedded into some $k$-dimensional normed space $X$ with bi--Lipschitz distortion at most $α$. A fundamental task in the theory of metric embeddings is to obtain sharp asymptotics for $k^α_n(\ell_\infty)$ for all choices of $α$ and $n$, with the range $α=Θ(\log n)$ bearing special importance. While advances in the theory l…

Dynamics of Liquidity Surfaces in Uniswap v3
Jimmy Risk, Shen-Ning Tung, Tai-Ho Wang
https://arxiv.org/abs/2509.05013 https://arxiv.org/pdf/2509.05013

Dynamics of Liquidity Surfaces in Uniswap v3
This paper presents a comprehensive study on the empirical dynamics of Uniswap v3 liquidity, which we model as a time-tick surface, $L_t(x)$. Using a combination of functional principal component analysis (FPCA) and dynamic factor methods, we analyze three distinct pools over multiple sample periods. Our findings offer three main contributions: a statistical characterization of automated market maker liquidity, an interpretable and portable basis for dimension reduction, and a robust analysis o…

Tensor-based reduction of linear parameter-varying state-space models
Bogoljub Terzin, E. Javier Olucha, Amritam Das, Siep Weiland, Roland T\'oth
https://arxiv.org/abs/2507.23591

Tensor-based reduction of linear parameter-varying state-space models
The Linear Parameter-Varying (LPV) framework is a powerful tool for controlling nonlinear and complex systems, but the conversion of nonlinear models into LPV forms often results in high-dimensional and overly conservative LPV models. To be able to apply control strategies, there is often a need for model reduction in order to reduce computational needs. This paper presents the first systematic approach for the joint reduction of state order and scheduling signal dimension of LPV state space mo…

Dimension Reduction for Conditional Density Estimation with Applications to High-Dimensional Causal Inference
Jianhua Mei, Fu Ouyang, Thomas T. Yang
https://arxiv.org/abs/2507.22312

Dimension Reduction for Conditional Density Estimation with Applications to High-Dimensional Causal Inference
We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form assumptions. To uncover the underlying sparsity structure of the data, we develop an innovative conditional dependence measure and a modified cross-validation procedure that enables data-driven variable selection, thereby circumventing the need for subjective thresh…

Normalizing Flow to Augmented Posterior: Conditional Density Estimation with Interpretable Dimension Reduction for High Dimensional Data
Cheng Zeng, George Michailidis, Hitoshi Iyatomi, Leo L Duan
https://arxiv.org/abs/2507.04216

Normalizing Flow to Augmented Posterior: Conditional Density Estimation with Interpretable Dimension Reduction for High Dimensional Data
The conditional density characterizes the distribution of a response variable $y$ given other predictor $x$, and plays a key role in many statistical tasks, including classification and outlier detection. Although there has been abundant work on the problem of Conditional Density Estimation (CDE) for a low-dimensional response in the presence of a high-dimensional predictor, little work has been done for a high-dimensional response such as images. The promising performance of normalizing flow (…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[6/6]:
- Supervised Dynamic Dimension Reduction with Deep Neural Network
Zhanye Luo, Yuefeng Han, Xiufan Yu

Monomial arrow removal and the finitistic dimension conjecture
Karin Erdmann, Odysseas Giatagantzidis, Chrysostomos Psaroudakis, {\O}yvind Solberg
https://arxiv.org/abs/2506.23747

Monomial arrow removal and the finitistic dimension conjecture
In this paper, we introduce the monomial arrow removal operation for bound quiver algebras, and show that it is a novel reduction technique for determining the finiteness of the finitistic dimension. Our approach first develops a general method within the theory of abelian category cleft extensions. We then demonstrate that the specific conditions of this method are satisfied by the cleft extensions arising from strict monomial arrow removals. This crucial connection is established through the …

A reduced-IRKA method for large-scale $\mathcal{H}_2$-optimal model order reduction
Yiding Lin, Valeria Simoncini
https://arxiv.org/abs/2508.00242 https://…

A reduced-IRKA method for large-scale $\mathcal{H}_2$-optimal model order reduction
The $\mathcal{H}_2$-optimal Model Order Reduction (MOR) is one of the most significant frameworks for reduction methodologies for linear dynamical systems. In this context, the Iterative Rational Krylov Algorithm (\IRKA) is a well established method for computing an optimal projection space of fixed dimension $r$, when the system has small or medium dimensions. However, for large problems the performance of \IRKA\ is not satisfactory. In this paper, we introduce a new rational Krylov subspace p…

Scaling Wideband Massive MIMO Radar via Beamspace Dimension Reduction
Oveys Delafrooz Noroozi, Jiyoon Han, Wei Tang, Zhengya Zhang, Upamanyu Madhow
https://arxiv.org/abs/2508.11790

Scaling Wideband Massive MIMO Radar via Beamspace Dimension Reduction
We present an architecture for scaling digital beamforming for wideband massive MIMO radar. Conventional spatial processing becomes computationally prohibitive as array size grows; for example, the computational complexity of MVDR beamforming scales as O(N^3) for an N-element array. In this paper, we show that energy concentration in beamspace provides the basis for drastic complexity reduction, with array scaling governed by the O(NlogN) complexity of the spatial FFT used for beamspace transfo…

DIT: Dimension Reduction View on Optimal NFT Rarity Meters
Dmitry Belousov, Yury Yanovich
https://arxiv.org/abs/2508.12671 https://arxiv.org/pdf/2508.12671…

DIT: Dimension Reduction View on Optimal NFT Rarity Meters
Non-fungible tokens (NFTs) have become a significant digital asset class, each uniquely representing virtual entities such as artworks. These tokens are stored in collections within smart contracts and are actively traded across platforms on Ethereum, Bitcoin, and Solana blockchains. The value of NFTs is closely tied to their distinctive characteristics that define rarity, leading to a growing interest in quantifying rarity within both industry and academia. While there are existing rarity mete…

Diffusion Generative Models Meet Compressed Sensing, with Applications to Image Data and Financial Time Series
Zhengyi Guo, Jiatu Li, Wenpin Tang, David D. Yao
https://arxiv.org/abs/2509.03898

Diffusion Generative Models Meet Compressed Sensing, with Applications to Image Data and Financial Time Series
This paper develops dimension reduction techniques for accelerating diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models: (i) compress the data into a latent space, (ii) train a diffusion model in the latent space, and (iii) apply a compressed sensing algorithm to the samples generated in the latent space, facilitating the efficiency of both model training and inference. Under suitable sparsity assumptions on da…

Faster Linear Algebra Algorithms with Structured Random Matrices
Chris Cama\~no, Ethan N. Epperly, Raphael A. Meyer, Joel A. Tropp
https://arxiv.org/abs/2508.21189 https://

Faster Linear Algebra Algorithms with Structured Random Matrices
To achieve the greatest possible speed, practitioners regularly implement randomized algorithms for low-rank approximation and least-squares regression with structured dimension reduction maps. Despite significant research effort, basic questions remain about the design and analysis of randomized linear algebra algorithms that employ structured random matrices. This paper develops a new perspective on structured dimension reduction, based on the oblivious subspace injection (OSI) property. Th…

Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space
Luca Lussardi, Andrea Torricelli, Elvira Zappale
https://arxiv.org/abs/2507.18390 https:…

Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space
We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $Γ$-convergence, providing an integral representation result in the space of manifold constrained functions with bounded variation

Replaced article(s) found for stat.ME. https://arxiv.org/list/stat.ME/new
[2/2]:
- Stop Lying to Me: New Visual Tools to Choose the Most Honest Nonlinear Dimension Reduction
Jayani P. Gamage, Dianne Cook, Paul Harrison, Michael Lydeamore, Thiyanga S. Talagala

Dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances
Josie K\"onig, Elizabeth Qian, Melina A. Freitag
https://arxiv.org/abs/2506.23892

Dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter is high-dimensional, making computation of the posterior expensive due to the need to sample in a high-dimensional space and the need to evaluate an expensive high-dimensional forward model relating the unknown parameter to the data. However, inverse problem…

A Block Reduction Method for Random Band Matrices with General Variance Profiles
Jiaqi Fan, Fan Yang, Jun Yin
https://arxiv.org/abs/2507.11945 https://

A Block Reduction Method for Random Band Matrices with General Variance Profiles
We present a novel block reduction method for the study of a general class of random band matrices (RBM) defined on the $d$-dimensional lattice $\mathbb{Z}_{L}^d:=\{1,2,\ldots,L\}^{d}$ for $d\in \{1,2\}$, with band width $W$ and an almost arbitrary variance profile subject to a core condition. We prove the delocalization of bulk eigenvectors for such RBMs under the assumptions $W\ge L^{1/2+\varepsilon}$ in one dimension and $W\geq L^{\varepsilon}$ in two dimensions, where $\varepsilon$ is an ar…

Hot news on the phase-structure of the SMEFT
Mikael Chala, Maria Cristina Fiore, Luis Gil
https://arxiv.org/abs/2507.16905 https://ar…

Hot news on the phase-structure of the SMEFT
We perform dimensional reduction of the electroweak sector of the dimension-six SMEFT to order $g^4$ in coupling constants $g$. This analysis includes one-loop contributions to kinetic terms and quartic couplings; as well as two-loop contributions, where operators such as four-fermion interactions first appear, to squared mass terms. Using lattice data, we also provide evidence that, in contrast with previous statements in the literature, the SMEFT may undergo a first-order phase transition eve…

Stop Lying to Me: New Visual Tools to Choose the Most Honest Nonlinear Dimension Reduction
Jayani P. Gamage, Dianne Cook, Paul Harrison, Michael Lydeamore
https://arxiv.org/abs/2506.22051

Stop Lying to Me: New Visual Tools to Choose the Most Honest Nonlinear Dimension Reduction
Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data (\pD{}) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR views have an important role in data analysis because, if done well, they provide a concise visual (and conceptual) summary of \pD{} distributions. The NLDR methods and hyper-parameter choices can create wildly different representations, making it difficult to deci…

Hierarchy of entanglement detection criteria for random high-dimensional states
Akhil Kumar Awasthi, Sudipta Mondal, Rivu Gupta, Aditi Sen De
https://arxiv.org/abs/2507.21787 ht…

Hierarchy of entanglement detection criteria for random high-dimensional states
Entanglement is a cornerstone in quantum information science, yet detecting it efficiently remains a challenging task. Focusing on non-positive partially transposed (NPT) states, we establish a hierarchy among entropy-based, majorization, realignment, and reduction criteria for Haar uniformly generated random states in finite dimensions, analyzing their performance based on rank and subsystem dimension. We prove lower bounds on the rank of mixed quantum states beyond which the realignment and e…

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
Adrian Padilla-Segarra, Pascal Noble, Olivier Roustant, \'Eric Savin
https://arxiv.org/abs/2507.17582

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions, or kernels, to obtain such estimates. In this paper, we derive physics-informed kernels for simulating two-dimensional velocity fields of an incompressible (divergence-free) flow around aerodynamic profiles. These kernels allow to define Gaussian process pri…

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…

Skyrmions based on optical anisotropy for topological encoding
Yunqi Zhang, An Aloysius Wang, Zimo Zhao, Yifei Ma, Ruofu Liu, Runchen Zhang, Zhi-Kai Pong, Yuxi Cai, Chao He
https://arxiv.org/abs/2508.16483

Skyrmions based on optical anisotropy for topological encoding
The observation of skyrmions across diverse physical domains suggests that they are universal features of S$^{2}$-valued fields, reflecting the ubiquity of topology in the study of the natural world. In this paper, we develop an abstract technique of parameter space dimensionality reduction that extends the skyrmion framework to fields taking values in manifolds of dimension greater than 2, thereby broadening the range of systems that can support skyrmions. To prove that this is more than just …

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 $p$.

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…

Homogenization and 3D-2D dimension reduction of a functional on manifold valued Sobolev spaces
Michela Eleuteri, Luca Lussardi, Andrea Torricelli, Elvira Zappale
https://arxiv.org/abs/2507.16386

Homogenization and 3D-2D dimension reduction of a functional on manifold valued Sobolev spaces
We study simultaneous homogenization and dimensional reduction of integral functionals for maps in manifold-valued Sobolev spaces. Due to the superlinear growth regime, we prove that the density of the $Γ$-limit is a tangential quasiconvex integrand represented by a cell formula.

Generative Flexible Latent Structure Regression (GFLSR) model
Clara Grazian, Qian Jin, Pierre Lafaye De Micheaux
https://arxiv.org/abs/2508.04393 https://a…

Generative Flexible Latent Structure Regression (GFLSR) model
Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of chemometrics, economics, social science and etc. However, due to the lack of model inference, generative form, and unidentifiable parameters, most of these methods are always used as an algorithm, instead of a model. This paper proposed a Generative Flexible Latent Str…

Replaced article(s) found for cond-mat.stat-mech. https://arxiv.org/list/cond-mat.stat-mech/new
[1/1]:
- Effective one-dimension reduction of multi-compartment complex systems dynamics
Giorgio Vittorio Visco, Johannes Nauta, Tomas Scagliarini, Oriol Artime, M…

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, …

The Approach of Sliced Inference in Systems of Stochastic Differential Equations with Comments on the Heston Model
Ahmet Umur \"Ozsoy
https://arxiv.org/abs/2508.15725 https…

The Approach of Sliced Inference in Systems of Stochastic Differential Equations with Comments on the Heston Model
Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality, however, comes with a larger parameter space to estimate. Therefore, via a dimension reduction method, Sliced Inverse Regression, we aim to reduce high-dimensional parameter space to a reduced feature space and aim to estimate the parameters on this new featured…

Multinomial thresholded LASSO for interpretable dimension reduction of human activity sequences
Zuofu Huang, Yingling Fan, James Hodges, Julian Wolfson
https://arxiv.org/abs/2507.17900

Multinomial thresholded LASSO for interpretable dimension reduction of human activity sequences
The widespread collection of data from mobile and wearable devices has created unprecedented opportunities to study human behavior in fine temporal resolution. One common structure for such data is categorical sequences: ordered, multinomial observations across many time points. These sequences present unique statistical challenges due to their high dimensionality and complex temporal dependence, including both short- and long-term correlations. Yet, there has been relatively little methodologi…

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…

A High Performance GPU CountSketch Implementation and Its Application to Multisketching and Least Squares Problems
Andrew J. Higgins, Erik G. Boman, Ichitaro Yamazaki
https://arxiv.org/abs/2508.14209

A High Performance GPU CountSketch Implementation and Its Application to Multisketching and Least Squares Problems
Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and the subsampled randomized Hadamard transform, while the CountSketch has lower complexity. Combining two sketches, known as multisketching, offers an inexpensive means of quickly reducing the dimension of a matrix by combining a CountSketch and Gaussian sketch.…

Existence and uniqueness of radial solutions of semi-linear equations on manifolds
Nicolas Martinez-Alba, Oscar Ria\~no
https://arxiv.org/abs/2507.11431 ht…

Existence and uniqueness of radial solutions of semi-linear equations on manifolds
We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold $M$. By combining differential geometry and analysis techniques, we establish the existence and uniqueness of constant solutions through the orbits of a group action. Our approach transforms such problems into equivalent ones over a submanifold $Σ$ of dimension one, which is transversal to the group action. This reduction leads us to a one-dimens…

Replaced article(s) found for stat.ME. https://arxiv.org/list/stat.ME/new
[1/1]:
- Dimension Reduction for Large-Scale Federated Data: Statistical Rate and Asymptotic Inference
Shuting Shen, Junwei Lu, Xihong Lin

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…

Contrastive CUR: Interpretable Joint Feature and Sample Selection for Case-Control Studies
Eric Zhang, Michael Love, Didong Li
https://arxiv.org/abs/2508.11557 https://

Contrastive CUR: Interpretable Joint Feature and Sample Selection for Case-Control Studies
Dimension reduction is an essential tool for analyzing high dimensional data. Most existing methods, including principal component analysis (PCA), as well as their extensions, provide principal components that are often linear combinations of features, which are often challenging to interpret. CUR decomposition, another matrix decomposition technique, is a more interpretable and efficient alternative, offers simultaneous feature and sample selection. Despite this, many biomedical studies involv…

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…