Modeling complex phenomena typically involves the use of both discrete and continuous variables. Such a setting applies across a wide range of problems, from identifying trends in time-series data to performing effective compositional scene understanding in images. Here, we propose Hybrid Memoised Wake-Sleep (HMWS), an algorithm for effective inference in such hybrid discrete-continuous models. Prior approaches to learning suffer as they need to perform repeated expensive inner-loop discrete inference. We build on a recent approach, Memoised Wake-Sleep (MWS), which alleviates part of the problem by memoising discrete variables, and extend it to allow for a principled and effective way to handle continuous variables by learning a separate recognition model used for importance-sampling based approximate inference and marginalization. We evaluate HMWS in the GP-kernel learning and 3D scene understanding domains, and show that it outperforms current state-of-the-art inference methods.

翻译：模拟复杂现象通常涉及使用离散和连续的变量。这种设置适用于范围广泛的问题,从确定时间序列数据的趋势到对图像进行有效的构成场面理解。在这里,我们提议混合的混合休眠(HMWS),这是在这种混合的离散连续模型中有效推断的一种算法。在学习方法受到影响之前,它们需要反复进行昂贵的内环离性推断。我们以最近的方法Metmoized Wake-Sleep(MWS)为基础,该方法通过回忆离散变量来缓解部分问题,并扩展它,以便通过学习用于基于重要性的抽样近似推论和边缘化的单独识别模型,从而允许有原则和有效的方式处理连续变量。我们在GP-内核学习和3D场理解域中评估HMWS,并表明它比目前最先进的推论方法要强。