We consider the problem of sample degeneracy in Approximate Bayesian Computation. It arises when proposed values of the parameters, once given as input to the generative model, rarely lead to simulations resembling the observed data and are hence discarded. Such “poor” parameter proposals do not contribute at all to the representation of the parameter’s posterior distribution. This leads to a very large number of required simulations and/or a waste of computational resources, as well as to distortions in the computed posterior distribution. To mitigate this problem, we propose an algorithm, referred to as the Large Deviations Weighted Approximate Bayesian Computation algorithm, where, via Sanov’s Theorem, strictly positive weights are computed for all proposed parameters, thus avoiding the rejection step altogether. In order to derive a computable asymptotic approximation from Sanov’s result, we adopt the information theoretic “method of types” formulation of the method of Large Deviations, thus restricting our attention to models for i.i.d. discrete random variables. Finally, we experimentally evaluate our method through a proof-of-concept implementation.

我们在近似贝叶斯计算中考虑样本退化的问题。当建议的参数值一旦作为生成模型的输入给出时，就很少出现类似于观察数据的模拟，因此被抛弃，就会出现这种情况。此类“较差”的参数建议完全不代表参数的后验分布。这导致非常大量的所需仿真和/或计算资源的浪费，以及所计算的后验分布中的失真。为了缓解这个问题，我们提出了一种算法，称为大偏差加权近似贝叶斯计算算法，该算法通过Sanov定理为所有建议参数计算严格的正权重，从而完全避免了拒绝步骤。为了从Sanov的结果中得出可计算的渐近近似，我们采用大偏差方法的信息理论“类型方法”表述，从而将我们的注意力集中在iid离散随机变量的模型上。最后，我们通过概念验证的实现对我们的方法进行实验评估。