Tractable Generative Convolutional Arithmetic Circuits
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Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Existing methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. To truly leverage the power of generative models, tractable marginalization is needed, a feature outside the realm of current methods. We present a generative model based on convolutional arithmetic circuits, a variant of convolutional networks that computes high-dimensional functions through tensor decompositions. Our method admits tractable marginalization, combining the expressive power of convolutional networks with all the abilities that may be offered by a generative framework. We focus on the application of classification under missing data, where unknown portions of classified instances are absent at test time. Our model, which theoretically achieves optimal classification, provides state of the art performance when classifying images with missing pixels, as well as promising results when treating speech with occluded samples.
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