近似贝叶斯计算中的局部核维降维

Jin Zhou, K. Fukumizu
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引用次数: 4

摘要

近似贝叶斯计算(ABC)是一种广泛应用于难处理似然函数的采样方法。ABC在不评估似然函数的情况下,通过接受样本的集合来近似后验分布,接受样本的集合用从先验分布中提取的参数来模拟,其中接受度由样本的汇总统计量与观测值之间的距离决定。摘要统计量的充分性和维度性在ABC的应用中起着核心作用。本文提出了局部梯度核降维(LGKDR)来构造ABC的低维汇总统计量。该方法通过隐式考虑原始汇总统计量的所有非线性变换来识别一个足够的子空间,并使用加权核对投影进行集中。没有对边际分布和回归模型做出强有力的假设,允许在广泛的应用中使用。用简单拒绝ABC法和顺序蒙特卡罗ABC法分别进行了实验。前者的结果具有竞争性,而后者的结果则好得多,因为后者尽可能地压缩了蒙特卡洛误差。
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Local Kernel Dimension Reduction in Approximate Bayesian Computation
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.
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