# Bayesian Data Sketching for Varying Coefficient Regression Models

arXiv: https://arxiv.org/abs/2506.00270 · HTML: https://mlsanity.com/paper/2506.00270/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 89 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 25 of 25)

- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget](https://mlsanity.com/paper/1304.5299/) (2013)
- [A multi-resolution approximation for massive spatial datasets](https://mlsanity.com/paper/1507.04789/) (2015)
- [An Efficient Minibatch Acceptance Test for Metropolis-Hastings](https://mlsanity.com/paper/1610.06848/) (2016)
- [VCBART: Bayesian trees for varying coefficients](https://mlsanity.com/paper/2003.06416/) (2020)
- [Statistical properties of sketching algorithms](https://mlsanity.com/paper/1706.03665/) (2017)
- [Mini-batch Metropolis-Hastings MCMC with Reversible SGLD Proposal](https://mlsanity.com/paper/1908.02910/) (2019)
- [Distributed Bayesian Varying Coefficient Modeling Using a Gaussian Process Prior](https://mlsanity.com/paper/2006.00783/) (2020)
- [Adaptive Bayesian procedures using random series priors](https://mlsanity.com/paper/1403.0625/) (2014)
- [A Divide-and-Conquer Bayesian Approach to Large-Scale Kriging](https://mlsanity.com/paper/1712.09767/) (2017)
- [Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments](https://mlsanity.com/paper/1802.00495/) (2018)
- [Minibatch Gibbs Sampling on Large Graphical Models](https://mlsanity.com/paper/1806.06086/) (2018)
- [Bayesian Compressed Regression](https://mlsanity.com/paper/1303.0642/) (2013)
- [High-Dimensional Bayesian Geostatistics](https://mlsanity.com/paper/1705.07265/) (2017)
- [Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains](https://mlsanity.com/paper/2003.11208/) (2020)
- [Sketching in Bayesian High Dimensional Regression With Big Data Using Gaussian Scale Mixture Priors](https://mlsanity.com/paper/2105.04795/) (2021)
- [Bayesian Geostatistics Using Predictive Stacking](https://mlsanity.com/paper/2304.12414/) (2023)
- [Asymptotics for Sketching in Least Squares Regression](https://mlsanity.com/paper/1810.06089/) (2018)
- [Tree-Structure Bayesian Compressive Sensing for Video](https://mlsanity.com/paper/1410.3080/) (2014)

## Built on by (most cited first, 2 of 2)

- [Mapping Drivers of Greenness: Spatial Variable Selection for MODIS Vegetation Indices](https://mlsanity.com/paper/2602.07681/) (2026)
- [A Bayesian Vertical Federated Learning Framework for Multivariate Reduced-Rank High-Dimensional Regression](https://mlsanity.com/paper/2609.22654/) (2026)

## Abstract (arXiv)

Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow posterior computations using Markov chain Monte Carlo (MCMC) algorithms. We introduce Bayesian data sketching for varying coefficient models to obviate computational challenges presented by large sample sizes. To address the challenges of analyzing large data, we compress the functional response vector and predictor matrix by a random linear transformation to achieve dimension reduction and conduct inference on the compressed data. Our approach distinguishes itself from several existing methods for analyzing large functional data in that it requires neither the development of new models or algorithms, nor any specialized computational hardware while delivering fully model-based Bayesian inference. Well-established methods and algorithms for varying coefficient regression models can be applied to the compressed data.