论文标题
使用歧义集的最佳贝叶斯实验设计的强大预期信息增益
Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets
论文作者
论文摘要
贝叶斯实验设计中预期信息增益（EIG）对实验的排名对模型的先前分布的变化敏感，而通过采样产生的EIG的近似值将具有类似于使用扰动先验的错误。我们定义和分析\ emph {强大的预期信息增益}（REIG），这是通过将EIG的仿射放松对eig最大化的修改，而在歧义性分布集上，EIG的仿射松弛与KL-Divergence中原始先验的歧义性分布集。我们表明，当与基于采样的估计EIG的方法结合使用时，REIG对应于用于估计EIG的样品的“ log-sum-exp”稳定化，这意味着它可以在实践中有效地实现。将REIG与变异嵌套蒙特卡洛（VNMC），自适应对比度估计（ACE）和相互信息神经估计（MINE）相结合的数值测试表明，REIG还可以补偿不足下采样的估计器的可变性。
The ranking of experiments by expected information gain (EIG) in Bayesian experimental design is sensitive to changes in the model's prior distribution, and the approximation of EIG yielded by sampling will have errors similar to the use of a perturbed prior. We define and analyze \emph{robust expected information gain} (REIG), a modification of the objective in EIG maximization by minimizing an affine relaxation of EIG over an ambiguity set of distributions that are close to the original prior in KL-divergence. We show that, when combined with a sampling-based approach to estimating EIG, REIG corresponds to a `log-sum-exp' stabilization of the samples used to estimate EIG, meaning that it can be efficiently implemented in practice. Numerical tests combining REIG with variational nested Monte Carlo (VNMC), adaptive contrastive estimation (ACE) and mutual information neural estimation (MINE) suggest that in practice REIG also compensates for the variability of under-sampled estimators.
