Bayesian Data Sketching for Varying Coefficient Regression Models

TL;DR

This paper introduces a Bayesian data sketching method that enables efficient large-scale inference in varying coefficient regression models by compressing data through random linear transformations, avoiding the need for specialized hardware or new algorithms.

Contribution

It proposes a novel data compression technique for Bayesian inference in large functional data sets, simplifying computation without altering existing models.

Findings

Achieves dimension reduction while preserving inference accuracy

Enables Bayesian analysis on large datasets without specialized hardware

Maintains compatibility with existing varying coefficient model algorithms

Abstract

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.