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.
In @cite_19 , image completion was performed on the Olivetti @cite_4 and Caltech @cite_6 datasets showing superior results compared to other generative models.
@cite_19 @cite_4 @cite_6
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The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are the most general conditions under which the partition function is tractable? The answer leads to a new kind of deep architecture, which we call sum-product networks (SPNs) and will present in this abstract. Recent work on face identification using continuous density Hidden Markov Models (HMMs) has shown that stochastic modelling can be used successfully to encode feature information. When frontal images of faces are sampled using top-bottom scanning, there is a natural order in which the features appear and this can be conveniently modelled using a top-bottom HMM. However, a top-bottom HMM is characterised by different parameters, the choice of which has so far been based on subjective intuition. This paper presents a set of experimental results in which various HMM parameterisations are analysed. > Current computational approaches to learning visual object categories require thousands of training images, are slow, cannot learn in an incremental manner and cannot incorporate prior information into the learning process. In addition, no algorithm presented in the literature has been tested on more than a handful of object categories. We present an method for learning object categories from just a few training images. It is quick and it uses prior information in a principled way. We test it on a dataset composed of images of objects belonging to 101 widely varied categories. Our proposed method is based on making use of prior information, assembled from (unrelated) object categories which were previously learnt. A generative probabilistic model is used, which represents the shape and appearance of a constellation of features belonging to the object. The parameters of the model are learnt incrementally in a Bayesian manner. Our incremental algorithm is compared experimentally to an earlier batch Bayesian algorithm, as well as to one based on maximum-likelihood. The incremental and batch versions have comparable classification performance on small training sets, but incremental learning is significantly faster, making real-time learning feasible. Both Bayesian methods outperform maximum likelihood on small training sets.