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Bayesian Data Sketching for Varying Coefficient Regression Models.

Rajarshi Guhaniyogi1, Laura Baracaldo2, Sudipto Banerjee3

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|December 3, 2025
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Summary
This summary is machine-generated.

Bayesian data sketching speeds up analysis of large functional data. This method compresses data for efficient varying coefficient model inference without new algorithms or hardware.

Keywords:
B-splinesPosterior contractionPredictive ProcessRandom compression matrixVarying coefficient models

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Area of Science:

  • Statistics
  • Machine Learning
  • Functional Data Analysis

Background:

  • Varying coefficient models are essential for nonlinear regression in functional data analysis.
  • Bayesian approaches to these models are computationally intensive for large datasets, hindering their application.
  • Markov chain Monte Carlo (MCMC) algorithms contribute to slow posterior computations.

Purpose of the Study:

  • To introduce Bayesian data sketching as an efficient computational method for varying coefficient models with large sample sizes.
  • To enable faster Bayesian inference on functional data without requiring new models, algorithms, or specialized hardware.
  • To demonstrate the applicability of established varying coefficient regression methods on compressed data.

Main Methods:

  • Data compression using random linear transformation for dimension reduction.
  • Conducting Bayesian inference on the compressed functional response vector and predictor matrix.
  • Applying established varying coefficient regression algorithms to the reduced-dimension data.

Main Results:

  • Established posterior contraction rates for estimating varying coefficients and predicting outcomes with compressed data.
  • Demonstrated inferential and computational efficiency through simulation experiments.
  • Validated the approach on remote sensed vegetation data, showcasing practical utility.

Conclusions:

  • Bayesian data sketching offers a computationally efficient solution for large-scale functional data analysis.
  • The method preserves the integrity of model-based Bayesian inference while significantly reducing computational burden.
  • This technique facilitates the broader adoption of Bayesian varying coefficient models in big data applications.