Related papers: A multi-resolution approximation via linear projec…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
In the new perspective of spatial quantization, this article systematically studies the advantages of reconfigurable reflectarray (RRA) designed with closely spaced elements in terms of sidelobe level (SLL), scanning accuracy and scan loss,…
Challenging indoor and urban environments with severe multipath propagation and obstructed LoS (OLoS) degrade classical radio frequency (RF) positioning. Multipath-based simultaneous localization and mapping (MP-SLAM) is a promising remedy,…
This paper presents two novel algorithms for approximately projecting symmetric matrices onto the Positive Semidefinite (PSD) cone using Randomized Numerical Linear Algebra (RNLA). Classical PSD projection methods rely on full-rank…
Representational similarity analysis (RSA) is a multivariate technique to investigate cortical representations of objects or constructs. While avoiding ill-posed matrix inversions that plague multivariate approaches in the presence of many…
The emergence of Vision-Language Models (VLMs) has introduced new paradigms for global image geo-localization through retrieval-augmented generation (RAG) and reasoning-driven inference. However, RAG methods are constrained by retrieval…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
Spatial statistical modeling and prediction involve generating and manipulating an n*n symmetric positive definite covariance matrix, where n denotes the number of spatial locations. However, when n is large, processing this covariance…
Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks…
Accurate and long-term spatiotemporal prediction for complex physical systems remains a fundamental challenge in scientific computing. While deep learning models, as powerful parametric approximators, have shown remarkable success, they…
In our companion paper "Multidimensional rational covariance extension with applications to spectral estimation and image compression" we discussed the multidimensional rational covariance extension problem (RCEP), which has important…
Despite recent advancements in the Large Reconstruction Model (LRM) demonstrating impressive results, when extending its input from single image to multiple images, it exhibits inefficiencies, subpar geometric and texture quality, as well…
Multilevel regression and poststratification (MRP) is a computationally efficient indirect estimation method that can quickly produce improved population-adjusted estimates with limited data. Recent computational advancements allow…
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by…
This article introduces a novel methodology for the massive parallelization of projection-based depths, addressing the computational challenges of data depth in high-dimensional spaces. We propose an algorithmic framework based on Refined…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…