A generative model based on training deep architectures is proposed. The model consists of K networks that are trained together to learn the underlying distribution of a given data set. The process starts with dividing the input data into K clusters and feeding each of them into a separate network. After few iterations of training networks separately, we use an EM-like algorithm to train the networks together and update the clusters of the data. We call this model Mixture of Networks. The provided model is a platform that can be used for any deep structure and be trained by any conventional objective function for distribution modeling. As the components of the model are neural networks, it has high capability in characterizing complicated data distributions as well as clustering data. We apply the algorithm on MNIST hand-written digits and Yale face datasets. We also demonstrate the clustering ability of the model using some real-world and toy examples.
A fundamental work on deep generative models has been done by hinton2006 , where they introduced a fast algorithm for unsupervised training of deep belief networks (DBNs), which are deep graphical models. In a recent work by Salakhutdinov salakhutdinov2015learning , a comprehensive review over this model is presented. Built upon this model, lee2009 presented a similar network with convolutional layers. They introduced probabilistic max-pooling technique and constructed a translation-invariant model. In @cite_21 , another generative model based on DBNs was presented, which was used for image feature extraction. Unsupervised deep representation learning techniques have been used in @cite_5 to build a generative model that can exploit high-level features to generate high-quality samples.
@cite_5 @cite_21
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It has previously been hypothesized, and supported with some experimental evidence, that deeper representations, when well trained, tend to do a better job at disentangling the underlying factors of variation. We study the following related conjecture: better representations, in the sense of better disentangling, can be exploited to produce faster-mixing Markov chains. Consequently, mixing would be more efficient at higher levels of representation. To better understand why and how this is happening, we propose a secondary conjecture: the higher-level samples fill more uniformly the space they occupy and the high-density manifolds tend to unfold when represented at higher levels. The paper discusses these hypotheses and tests them experimentally through visualization and measurements of mixing and interpolating between samples. The most popular way to use probabilistic models in vision is first to extract some descriptors of small image patches or object parts using well-engineered features, and then to use statistical learning tools to model the dependencies among these features and eventual labels. Learning probabilistic models directly on the raw pixel values has proved to be much more difficult and is typically only used for regularizing discriminative methods. In this work, we use one of the best, pixel-level, generative models of natural images–a gated MRF–as the lowest level of a deep belief network (DBN) that has several hidden layers. We show that the resulting DBN is very good at coping with occlusion when predicting expression categories from face images, and it can produce features that perform comparably to SIFT descriptors for discriminating different types of scene. The generative ability of the model also makes it easy to see what information is captured and what is lost at each level of representation.