Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2604.23826

Building a GPU-Accelerated Multivariate Statistics Platform

Mike Crowhurst
View original source ↗Read source document ↗Export metadata ↓

Abstract

Classical multivariate statistical methods such as covariance estimation and principal component analysis are well understood mathematically, yet their application at extreme data scales remains challenging. When the number of observations reaches billions, performance is limited by data movement, input-output bottlenecks, and numerical stability rather than arithmetic complexity. This work presents a case study of scaling classical multivariate statistics on a single multi-GPU node. Using C++ and CUDA, a GPU-accelerated workflow was developed to compute sufficient statistics in a single pass over a 10-billion-row dataset. Column sums and cross-product matrices are used to enable downstream computation of means, covariance, correlation, and principal component analysis without revisiting the raw data. The results highlight the importance of data representation, validation using known invariants, and careful numerical treatment when applying established statistical methods at large scale.

Explore related subjects

stat.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mike Crowhurst. 2026-05-19. Building a GPU-Accelerated Multivariate Statistics Platform. https://arxiv.org/abs/2604.23826

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Delayed Acceptance Slice Sampling

Slice sampling is a well-established Markov chain Monte Carlo method for approximate sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a superlevel set of the given unnormalized target density (with respect to a reference measure). However, slice sampling algorithms usually require per step multiple evaluations of the target density, and thus can become computationally expensive. This is particularly the case for Bayesian inference with costly likelihoods. In this paper, we exploit deterministic approximations of the target density, which are relatively cheap to evaluate, and propose delayed acceptance versions of several common (hybrid) slice samplers. We show ergodicity of the resulting slice sampling methods, discuss the superiority of delayed acceptance (ideal) slice sampling over delayed acceptance Metropolis-Hastings algorithms, and illustrate the benefits of our novel approach in terms of improved computational efficiency in numerical experiments.

stat.CO↗
arXiv2026

Repulsive normalizing flow mixtures for adaptive importance sampling: reliability analysis of complex systems

Accurate rare-event estimation can be computationally expensive. Classical adaptive importance sampling (IS) schemes often rely on restrictive proposal families and can struggle under multiple failure modes. We propose FAMIS, a flow-based multiple importance sampling (MIS) framework that learns a nonuniform mixture of normalizing flow proposals for rare event estimation. The method does not require presampled failure data or prior knowledge of the number, location, or geometry of the failure modes. Instead, it adaptively learns the mixture through sequential evaluations of the limit state function. To guide training toward the failure domain, FAMIS uses a smooth rare-event surrogate and a tempered target sequence. A defensive exploration mixture improves early-stage coverage, a Rao Blackwellized update adapts the mixture weights, and a Jensen-Shannon repulsion term promotes separation and diversity among the base components. The final failure probability is computed with a deterministic-mixture MIS estimator. Numerical experiments demonstrate that FAMIS accurately approximates quasi-optimal IS densities with fewer training samples and model evaluations, providing stable variance reduction across complex reliability problems.

stat.CO↗
arXiv2026

Scentree: a framework for generating scenario trees for multistage stochastic programming

We present scentree, an open-source Python package for constructing a scenario fan and a scenario tree for multistage stochastic programming from historical data. It combines machine learning and multivariate time series models to obtain a scenario fan that captures inter-stage dependencies in the stochastic processes. This scenario fan is subsequently transformed into a scenario tree suitable for multistage stochastic optimization, providing a flexible and extensible framework for uncertainty modeling. A key contribution is the automation of the complete workflow, including model selection, parameter estimation, scenario fan generation, and scenario tree construction. Scentree does not rely on assumptions about the underlying data distribution, reducing the statistical expertise required to produce a scenario tree. Furthermore, it is agnostic to the specific multistage stochastic problem to be solved.

stat.CO↗