In the absence of explicit or tractable likelihoods, Bayesians often resort to approximate Bayesian computation (ABC) for inference. Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs. Once the mapping has been trained, iid posterior samples are obtained by filtering noise at a negligible additional cost. We propose two post-processing local refinements using (1) data-driven proposals with importance reweighting, and (2) variational Bayes. We support our findings with frequentist-Bayesian results, showing that the typical total variation distance between the true and approximate posteriors converges to zero for certain neural network generators and discriminators. Our findings on simulated data show highly competitive performance relative to some of the most recent likelihood-free posterior simulators.

翻译：在缺乏显式或可处理的似然函数时，贝叶斯统计通常采用近似贝叶斯计算（ABC）进行推断。本研究将ABC与基于生成对抗网络（GANs）和对抗变分贝叶斯的深度神经隐式采样器相融合。ABC与GANs均通过比较观测数据与生成数据的特征来分别从后验分布和似然函数中进行模拟。我们提出了一种直接面向后验分布的贝叶斯GAN（B-GAN）采样器，通过求解对抗优化问题实现目标。B-GAN由条件GAN在ABC参考集上学习的确定性映射驱动。该映射训练完成后，通过滤波噪声以极低的额外成本即可获得独立同分布的后验样本。我们提出了两种后处理局部精化方法：（1）结合重要性重加权的数据驱动提议分布，（2）变分贝叶斯。我们通过频率-贝叶斯双重检验证实：对于特定神经网络生成器和判别器，真实后验与近似后验之间的典型总变差距离渐近收敛至零。在模拟数据上的实验表明，与当前最先进的无似然后验采样器相比，本方法展现出高度竞争力。