Distilling Importance Sampling for Likelihood Free Inference
Distilling Importance Sampling for Likelihood Free Inference
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DOI：
10.1080/10618600.2023.2175688
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发表时间：
2019-10
影响因子：
2.4
通讯作者：
D. Prangle;Cecilia Viscardi
中科院分区：
文献类型：
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作者：
D. Prangle;Cecilia Viscardi
摘要无似然推理涉及给定观测数据和模拟器模型来推断参数值。模拟器是计算机代码，它接受参数，执行随机计算，并输出模拟数据。在这项工作中，我们将模拟器视为一个函数，其输入是（1）参数和（2）伪随机抽取向量。我们试图根据观察结果推断所有这些输入。这具有挑战性，因为由此产生的后验可能是高维的并且涉及强依赖性。我们近似后使用规范化流，一个灵活的参数族的密度。训练数据由具有大带宽值的无似然重要性采样产生，这使得目标与先验相似。训练数据通过使用它来训练更新的归一化流而被“提炼”。该过程是迭代的，使用更新的流作为重要性采样建议，并慢慢减少冗余，使目标变得更接近后验。与大多数其他无似然方法不同，我们避免了将数据简化为低维汇总统计量的需要，因此可以获得更准确的结果。我们说明了我们的方法在两个具有挑战性的例子，排队和流行病学。本文的补充材料可在网上查阅。
Abstract Likelihood-free inference involves inferring parameter values given observed data and a simulator model. The simulator is computer code which takes parameters, performs stochastic calculations, and outputs simulated data. In this work, we view the simulator as a function whose inputs are (1) the parameters and (2) a vector of pseudo-random draws. We attempt to infer all these inputs conditional on the observations. This is challenging as the resulting posterior can be high dimensional and involves strong dependence. We approximate the posterior using normalizing flows, a flexible parametric family of densities. Training data is generated by likelihood-free importance sampling with a large bandwidth value ϵ , which makes the target similar to the prior. The training data is “distilled” by using it to train an updated normalizing flow. The process is iterated, using the updated flow as the importance sampling proposal, and slowly reducing ϵ so the target becomes closer to the posterior. Unlike most other likelihood-free methods, we avoid the need to reduce data to low-dimensional summary statistics, and hence can achieve more accurate results. We illustrate our method in two challenging examples, on queuing and epidemiology. Supplementary materials for this article are available online.