Score Matched Neural Exponential Families for Likelihood-Free Inference
Score Matched Neural Exponential Families for Likelihood-Free Inference
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发表时间：
2020-12
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通讯作者：
Lorenzo Pacchiardi;Ritabrata Dutta
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作者：
Lorenzo Pacchiardi;Ritabrata Dutta
贝叶斯无似然推理 (LFI) 方法允许通过依赖模型模拟来获得具有棘手似然性的随机模型的后验分布。在近似贝叶斯计算（ABC）（一种流行的 LFI 方法）中，使用汇总统计来降低数据维度。 ABC 算法自适应地根据观察结果定制模拟，以便从近似后验样本中进行采样，其形式取决于所选的统计数据。在这项工作中，我们引入了一种学习 ABC 统计的新方法：我们首先独立于观察从模型生成参数模拟对；然后，我们使用分数匹配来训练神经条件指数族来近似可能性。指数族是最大的一类分布，具有固定大小的足够统计量；因此，我们在 ABC 中使用它们，它直观上有吸引力并且具有最先进的性能。同时，我们将似然近似插入到 MCMC 中，以处理双重棘手的分布来绘制后验样本。我们可以对任意数量的观察重复这一点，无需额外的模型模拟，其性能与相关方法相当。我们在具有已知可能性的玩具模型和大维时间序列模型上验证了我们的方法。
Bayesian Likelihood-Free Inference (LFI) approaches allow to obtain posterior distributions for stochastic models with intractable likelihood, by relying on model simulations. In Approximate Bayesian Computation (ABC), a popular LFI method, summary statistics are used to reduce data dimensionality. ABC algorithms adaptively tailor simulations to the observation in order to sample from an approximate posterior, whose form depends on the chosen statistics. In this work, we introduce a new way to learn ABC statistics: we first generate parameter-simulation pairs from the model independently on the observation; then, we use Score Matching to train a neural conditional exponential family to approximate the likelihood. The exponential family is the largest class of distributions with fixed-size sufficient statistics; thus, we use them in ABC, which is intuitively appealing and has state-of-the-art performance. In parallel, we insert our likelihood approximation in an MCMC for doubly intractable distributions to draw posterior samples. We can repeat that for any number of observations with no additional model simulations, with performance comparable to related approaches. We validate our methods on toy models with known likelihood and a largedimensional time-series model.