Approximate Bayesian Computation (ABC) is a popular sampling method in applications involving intractable likelihood functions. Without evaluating the likelihood function, ABC approximates the posterior distribution by the set of accepted samples which are simulated with parameters drawn from the prior distribution, where acceptance is determined by the distance between the summary statistics of the sample and the observation. The sufficiency and dimensionality of the summary statistics play a central role in the application of ABC. This paper proposes Local Gradient Kernel Dimension Reduction (LGKDR) to construct low dimensional summary statistics for ABC. The proposed method identifies a sufficient subspace of the original summary statistics by implicitly considers all nonlinear transforms therein, and a weighting kernel is used for the concentration of the projections. No strong assumptions are made on the marginal distributions nor the regression model, permitting usage in a wide range of applications. Experiments are done with both simple rejection ABC and sequential Monte Carlo ABC methods. Results are reported as competitive in the former and substantially better in the latter cases in which Monte Carlo errors are compressed as much as possible.
Variational Inference for Nonlinear Inverse Problems via Neural Net Kernels: Comparison to Bayesian Neural Networks, Application to Topology Optimization
Kernel Approximate Bayesian Computation for Population Genetic Inferences
近似贝叶斯计算（ABC）是一种基于拒绝算法方法的贝叶斯推断的无似然方法，该方法应用了观察数据和模拟数据的汇总统计量之间的差异容限。虽然已经提出了对算法的几种改进，但是这些改进都没有避免以下两个近似源：1）缺乏足够的统计量：采样不是来自给定数据的真实后验密度，而是来自给定汇总统计量的近似后验密度;以及2）非零公差：仅在零公差的极限下实现从给定汇总统计量的后验密度采样。近似值的第一个来源可以通过添加汇总统计量来改进，但是汇总统计量数量的增加可能会引入由低接受率引起的额外方差。因此，许多研究人员试图开发技术来选择信息汇总统计量。本研究评估了基于核的ABC方法（Kazumizu et al. 2010，arXiv：1009.5736 and 2011，NIPS 24：1549-1557）在需要许多汇总统计量的复杂问题中的实用性。将核ABC应用于群体遗传推理。我们证明，在传统的ABC相比，内核ABC可以将大量的汇总统计，同时保持高性能的推理。
Some discussions of D. Fearnhead and D. Prangle's Read Paper "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation"
Approximate Bayesian Computation Based on Maxima Weighted Isolation Kernel Mapping
NEC-AIST AI Cooperative Research Laboratory（NEC-产业技术综合研究所人工智能合作研究实验室）；Artificial Intelligence Research Center（人工智能研究中心）；The National Institute of Advanced Industrial Science and Technology（日本产业技术综合研究所）
SIKA-GP: Accelerating Gaussian Process Inference with Sparse Inducing Kernel Approximations for Bayesian Deep Learning
Department of Electrical；Computer Engineering, Texas A\&M University, College Station, US；Department of Industrial；Systems Engineering, Texas A\&M University, College Station, US
Bayesian bandwidth estimation for a nonparametric functional regression model with mixed types of regressors and unknown error density
在误差密度未知的框架下，研究了具有函数值、连续实值和离散值回归变量的非参数函数回归模型的带宽估计问题.从Shang（2013，Computational Statistics & Data Analysis）的最近工作扩展，我们通过残差的核密度估计来近似未知误差密度，其中回归函数由允许混合类型回归变量的函数Nadaraya-Watson估计器估计。在核形式误差密度下，推导了带宽参数的核似然和后验密度，提出了一种同时估计带宽的贝叶斯带宽估计方法。仿真研究表明，所提出的贝叶斯方法的回归函数和误差密度的估计精度。以食品质量控制中的光谱数据集为例，我们应用贝叶斯方法来选择具有混合类型回归变量的非参数函数回归模型中的最佳带宽。
