Sum-Product Networks (SPNs) are hierarchical, probabilistic graphical models capable of fast and exact inference that can be trained directly from high-dimensional, noisy data. Traditionally, SPNs struggle with capturing relationships in complex spatial data such as images. To this end, we introduce Deep Generalized Convolutional Sum-Product Networks (DGC-SPNs), which encode spatial features through products and sums with scopes corresponding to local receptive fields. As opposed to existing convolutional SPNs, DGC-SPNs allow for overlapping convolution patches through a novel parameterization of dilation and strides, resulting in significantly improved feature coverage and feature resolution. DGC-SPNs substantially outperform other convolutional and non-convolutional SPN approaches across several visual datasets and for both generative and discriminative tasks, including image completion and image classification. In addition, we demonstrate a modificiation to hard EM learning that further improves the generative performance of DGC-SPNs. While fully probabilistic and versatile, our model is scalable and straightforward to apply in practical applications in place of traditional deep models. Our implementation is tensorized, employs efficient GPU-accelerated optimization techniques, and is available as part of an open-source library based on TensorFlow.
翻译:平价生产网络(SPNS)是分级、概率和精确的图形模型,能够直接从高维、吵闹的数据中进行快速和精确的推断。传统上,SPNS与在图像等复杂的空间数据中捕捉关系挣扎。为此,我们引入深通用共价生产网络(DGC-SPNS),通过产品和数字将空间特征编码,其范围与当地可接收域相对应。与现有的革命性 SPN相比,DGC-SPN允许通过新颖的变相和进步参数化来重叠变异补丁,从而大大改进地貌覆盖和特征分辨率。DGC-SPNS大大优于其他革命性和非革命性 SPN方法,横跨多个视觉数据集,并用于变异和有区别性的任务,包括图像完成和图像分类。此外,我们展示了硬式EM学习的变形结构,以进一步提高DGC-SPSPN的变异性性性表现。我们模型在传统的稳定和多功能化和多功能化的深度模型应用上,在可扩展的、直截然的GF-S-F-F-Sirpral-lial-Siral-todal-comlistal-todal-pal-todal-topplipal-shipal-pal-topal-pal-topplipal-spal-shipalpalpalpalpal 上,这是一个可以应用一个可以应用的开放的开放的开放和直接地点。