Title: Bayesian Data Sketching for Varying Coefficient Regression Models Show Chinese title

Title: 贝叶斯数据速写在变系数回归模型中的应用

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. Show Chinese abstract

Abstract: 变系数模型在函数数据分析中广泛用于估计非线性回归函数。然而，它们的贝叶斯变体在大规模数据应用中受到的关注有限，主要原因是使用马尔可夫链蒙特卡洛（MCMC）算法进行后验计算的速度极其缓慢。我们引入了变系数模型的贝叶斯数据压缩方法，以克服大样本量带来的计算挑战。为了解决分析大规模数据的难题，我们通过随机线性变换压缩函数响应向量和预测变量矩阵，实现降维，并在压缩后的数据上进行推断。与现有几种分析大规模函数数据的方法不同，我们的方法无需开发新的模型或算法，也无需特殊的计算硬件，同时能够提供基于模型的完全贝叶斯推断。现有的变系数回归模型的方法和算法可以直接应用于压缩后的数据。