Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture models is computationally challenging due to issues such as high-dimensional posterior inference and label switching. Furthermore, traditional methods such as MCMC are applicable only if the likelihoods for each mixture component are analytically tractable. Amortized Bayesian Inference (ABI) is a simulation-based framework for estimating Bayesian models using generative neural networks. This allows the fitting of models without explicit likelihoods, and provides fast inference. ABI is therefore an attractive framework for estimating mixture models. This paper introduces a novel extension of ABI tailored to mixture models. We factorize the posterior into a distribution of the parameters and a distribution of (categorical) mixture indicators, which allows us to use a combination of generative neural networks for parameter inference, and classification networks for mixture membership identification. The proposed framework accommodates both independent and dependent mixture models, enabling filtering and smoothing. We validate and demonstrate our approach through synthetic and real-world datasets.

翻译：有限混合模型是一类广泛的模型，适用于观测数据由多个不同过程生成但缺乏每个数据点所属过程显式信息的场景。由于高维后验推断和标签切换等问题，贝叶斯混合模型的估计在计算上具有挑战性。此外，传统方法如MCMC仅在各混合分量的似然函数解析可处理时才适用。摊销贝叶斯推断是一种基于模拟的框架，利用生成式神经网络估计贝叶斯模型。这使得无需显式似然函数即可拟合模型，并提供快速推断能力。因此，ABI成为估计混合模型的有力框架。本文提出一种针对混合模型定制的新型ABI扩展方法。我们将后验分解为参数分布与（分类）混合指示符分布，从而能够结合使用生成式神经网络进行参数推断，以及分类网络进行混合成员识别。所提框架同时适用于独立与依赖混合模型，支持滤波与平滑操作。我们通过合成数据集和真实数据集验证并展示了该方法。