用随机压缩加速贝叶斯变系数模型的计算，适合大数据分析。
Bayesian Data Sketching for Varying Coefficient Regression Models
- 通过随机线性变换压缩数据维度，降低计算复杂度。
- 在压缩数据上实现完整贝叶斯推断，保持原模型有效性。
- 无需新算法或硬件，兼容现有经典方法，适合大规模功能数据分析。
变系数模型广泛用于函数型数据中的非线性回归函数估计。其贝叶斯版本在大数据应用中受限，主要因马尔可夫链蒙特卡洛（MCMC）算法导致后验计算过于缓慢。本文提出贝叶斯数据压缩方法，解决大样本带来的计算挑战。通过随机线性变换压缩函数响应向量和预测矩阵，实现降维，并在压缩数据上进行推断。该方法区别于现有大样本函数数据分析方法之处在于：无需开发新模型或算法，也无需专用计算硬件，同时提供完全基于模型的贝叶斯推断。成熟的变系数回归模型方法与算法可直接应用于压缩数据，显著提升计算效率。
原文摘要 · Abstract (English)
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.
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