Image generation remains a fundamental problem in artificial intelligence in general and deep learning in specific. The generative adversarial network (GAN) was successful in generating high quality samples of natural images. We propose a model called composite generative adversarial network, that reveals the complex structure of images with multiple generators in which each generator generates some part of the image. Those parts are combined by alpha blending process to create a new single image. It can generate, for example, background and face sequentially with two generators, after training on face dataset. Training was done in an unsupervised way without any labels about what each generator should generate. We found possibilities of learning the structure by using this generative model empirically.
Variants of probabilistic graphical models have been introduced to capture the underlying data distribution. Undirected graphical models with latent variables, such as restricted Boltzmann machines (RBMs) and deep Boltzmann machines (DBMs) @cite_3 provided the underlying discipline for pre-training deep neural networks. Deep belief networks (DBNs) @cite_13 and its variants are hybrid models in which pre-trained DBMs and sigmoid belief networks are layer-wise mixed. DBNs can reproduce the input from multiple hidden layers, but they are restricted to a simple dataset due to the computationally costly step of Markov chain Monte Carlo (MCMC) methods.
@cite_13 @cite_3
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Restricted Boltzmann machines (RBMs) are probabilistic graphical models that can be interpreted as stochastic neural networks. They have attracted much attention as building blocks for the multi-layer learning systems called deep belief networks, and variants and extensions of RBMs have found application in a wide range of pattern recognition tasks. This tutorial introduces RBMs from the viewpoint of Markov random fields, starting with the required concepts of undirected graphical models. Different learning algorithms for RBMs, including contrastive divergence learning and parallel tempering, are discussed. As sampling from RBMs, and therefore also most of their learning algorithms, are based on Markov chain Monte Carlo (MCMC) methods, an introduction to Markov chains and MCMC techniques is provided. Experiments demonstrate relevant aspects of RBM training. HighlightsWe review the state-of-the-art in training restricted Boltzmann machines (RBMs) from the perspective of graphical models.Variants and extensions of RBMs are used in a wide range of pattern recognition tasks.The required background on graphical models and Markov chain Monte Carlo methods is provided.Theoretical and experimental results are presented. Deep belief networks (DBN) are generative neural network models with many layers of hidden explanatory factors, recently introduced by Hinton, Osindero, and Teh (2006) along with a greedy layer-wise unsupervised learning algorithm. The building block of a DBN is a probabilistic model called a restricted Boltzmann machine (RBM), used to represent one layer of the model. Restricted Boltzmann machines are interesting because inference is easy in them and because they have been successfully used as building blocks for training deeper models. We first prove that adding hidden units yields strictly improved modeling power, while a second theorem shows that RBMs are universal approximators of discrete distributions. We then study the question of whether DBNs with more layers are strictly more powerful in terms of representational power. This suggests a new and less greedy criterion for training RBMs within DBNs. Deep Belief Networks (DBN's) are generative models that contain many layers of hidden variables. Efficient greedy algorithms for learning and approximate inference have allowed these models to be applied successfully in many application domains. The main building block of a DBN is a bipartite undirected graphical model called a restricted Boltzmann machine (RBM). Due to the presence of the partition function, model selection, complexity control, and exact maximum likelihood learning in RBM's are intractable. We show that Annealed Importance Sampling (AIS) can be used to efficiently estimate the partition function of an RBM, and we present a novel AIS scheme for comparing RBM's with different architectures. We further show how an AIS estimator, along with approximate inference, can be used to estimate a lower bound on the log-probability that a DBN model with multiple hidden layers assigns to the test data. This is, to our knowledge, the first step towards obtaining quantitative results that would allow us to directly assess the performance of Deep Belief Networks as generative models of data. Deep multi-layer neural networks have many levels of non-linearities allowing them to compactly represent highly non-linear and highly-varying functions. However, until recently it was not clear how to train such deep networks, since gradient-based optimization starting from random initialization often appears to get stuck in poor solutions. recently proposed a greedy layer-wise unsupervised learning procedure relying on the training algorithm of restricted Boltzmann machines (RBM) to initialize the parameters of a deep belief network (DBN), a generative model with many layers of hidden causal variables. This was followed by the proposal of another greedy layer-wise procedure, relying on the usage of autoassociator networks. In the context of the above optimization problem, we study these algorithms empirically to better understand their success. Our experiments confirm the hypothesis that the greedy layer-wise unsupervised training strategy helps the optimization by initializing weights in a region near a good local minimum, but also implicitly acts as a sort of regularization that brings better generalization and encourages internal distributed representations that are high-level abstractions of the input. We also present a series of experiments aimed at evaluating the link between the performance of deep neural networks and practical aspects of their topology, for example, demonstrating cases where the addition of more depth helps. Finally, we empirically explore simple variants of these training algorithms, such as the use of different RBM input unit distributions, a simple way of combining gradient estimators to improve performance, as well as on-line versions of those algorithms. We present a new approximate inference algorithm for Deep Boltzmann Machines (DBM’s), a generative model with many layers of hidden variables. The algorithm learns a separate “recognition” model that is used to quickly initialize, in a single bottom-up pass, the values of the latent variables in all hidden layers. We show that using such a recognition model, followed by a combined top-down and bottom-up pass, it is possible to efficiently learn a good generative model of high-dimensional highly-structured sensory input. We show that the additional computations required by incorporating a top-down feedback plays a critical role in the performance of a DBM, both as a generative and discriminative model. Moreover, inference is only at most three times slower compared to the approximate inference in a Deep Belief Network (DBN), making large-scale learning of DBM’s practical. Finally, we demonstrate that the DBM’s trained using the proposed approximate inference algorithm perform well compared to DBN’s and SVM’s on the MNIST handwritten digit, OCR English letters, and NORB visual object recognition tasks. Abstract Deep neural networks with several layers have recently become a highly successful and popular research topic in machine learning due to their excellent performance in many benchmark problems and applications. A key idea in deep learning is to learn not only the nonlinear mapping between the inputs and outputs but also the underlying structure of the data (input) vectors. In this chapter, we first consider problems with training deep networks using backpropagation-type algorithms. After this, we consider various structures used in deep learning, including restricted Boltzmann machines, deep belief networks, deep Boltzmann machines, and nonlinear autoencoders. In the latter part of this chapter, we discuss in more detail the recently developed neural autoregressive distribution estimator and its variants. In this paper, we propose a generic technique to model temporal dependencies and sequences using a combination of a recurrent neural network and a Deep Belief Network. Our technique, RNN-DBN, is an amalgamation of the memory state of the RNN that allows it to provide temporal information and a multi-layer DBN that helps in high level representation of the data. This makes RNN-DBNs ideal for sequence generation. Further, the use of a DBN in conjunction with the RNN makes this model capable of significantly more complex data representation than a Restricted Boltzmann Machine (RBM). We apply this technique to the task of polyphonic music generation. An efficient way to learn deep density models that have many layers of latent variables is to learn one layer at a time using a model that has only one layer of latent variables. After learning each layer, samples from the posterior distributions for that layer are used as training data for learning the next layer. This approach is commonly used with Restricted Boltzmann Machines, which are undirected graphical models with a single hidden layer, but it can also be used with Mixtures of Factor Analysers (MFAs) which are directed graphical models. In this paper, we present a greedy layer-wise learning algorithm for Deep Mixtures of Factor Analysers (DMFAs). Even though a DMFA can be converted to an equivalent shallow MFA by multiplying together the factor loading matrices at different levels, learning and inference are much more efficient in a DMFA and the sharing of each lower-level factor loading matrix by many different higher level MFAs prevents overfitting. We demonstrate empirically that DMFAs learn better density models than both MFAs and two types of Restricted Boltzmann Machine on a wide variety of datasets. We develop a novel modeling framework for Boltzmann machines, augmenting each hidden unit with a latent transformation assignment variable which describes the selection of the transformed view of the canonical connection weights associated with the unit. This enables the inferences of the model to transform in response to transformed input data in a stable and predictable way, and avoids learning multiple features differing only with respect to the set of transformations. Extending prior work on translation equivariant (convolutional) models, we develop translation and rotation equivariant restricted Boltzmann machines (RBMs) and deep belief nets (DBNs), and demonstrate their effectiveness in learning frequently occurring statistical structure from artificial and natural images. This paper presents a new spectral modeling method for statistical parametric speech synthesis. In the conventional methods, high-level spectral parameters, such as mel-cepstra or line spectral pairs, are adopted as the features for hidden Markov model (HMM)-based parametric speech synthesis. Our proposed method described in this paper improves the conventional method in two ways. First, distributions of low-level, un-transformed spectral envelopes (extracted by the STRAIGHT vocoder) are used as the parameters for synthesis. Second, instead of using single Gaussian distribution, we adopt the graphical models with multiple hidden variables, including restricted Boltzmann machines (RBM) and deep belief networks (DBN), to represent the distribution of the low-level spectral envelopes at each HMM state. At the synthesis time, the spectral envelopes are predicted from the RBM-HMMs or the DBN-HMMs of the input sentence following the maximum output probability parameter generation criterion with the constraints of the dynamic features. A Gaussian approximation is applied to the marginal distribution of the visible stochastic variables in the RBM or DBN at each HMM state in order to achieve a closed-form solution to the parameter generation problem. Our experimental results show that both RBM-HMM and DBN-HMM are able to generate spectral envelope parameter sequences better than the conventional Gaussian-HMM with superior generalization capabilities and that DBN-HMM and RBM-HMM perform similarly due possibly to the use of Gaussian approximation. As a result, our proposed method can significantly alleviate the over-smoothing effect and improve the naturalness of the conventional HMM-based speech synthesis system using mel-cepstra. Deep Belief Networks (DBNs) are a very competitive alternative to Gaussian mixture models for relating states of a hidden Markov model to frames of coefficients derived from the acoustic input. They are competitive for three reasons: DBNs can be fine-tuned as neural networks; DBNs have many non-linear hidden layers; and DBNs are generatively pre-trained. This paper illustrates how each of these three aspects contributes to the DBN's good recognition performance using both phone recognition performance on the TIMIT corpus and a dimensionally reduced visualization of the relationships between the feature vectors learned by the DBNs that preserves the similarity structure of the feature vectors at multiple scales. The same two methods are also used to investigate the most suitable type of input representation for a DBN. Motivated by recent progress in using restricted Boltzmann machines as preprocess-ing algorithms for deep neural network, we revisit the mean-field equations (belief-propagation and TAP equations) in the best understood such machine, namely the Hopfield model of neural networks, and we explicit how they can be used as iterative message-passing algorithms, providing a fast method to compute the local polariza-tions of neurons. In the "retrieval phase" where neurons polarize in the direction of one memorized pattern, we point out a major difference between the belief propagation and TAP equations : the set of belief propagation equations depends on the pattern which is retrieved, while one can use a unique set of TAP equations. This makes the latter method much better suited for applications in the learning process of restricted Boltzmann machines. In the case where the patterns memorized in the Hopfield model are not independent, but are correlated through a combinatorial structure, we show that the TAP equations have to be modified. This modification can be seen either as an alteration of the reaction term in TAP equations, or, more interestingly, as the consequence of message passing on a graphical model with several hidden layers, where the number of hidden layers depends on the depth of the correlations in the memorized patterns. This layered structure is actually necessary when one deals with more general restricted Boltzmann machines. Fusing the advantages of multiple acoustic features is important for the robustness of voice activity detection (VAD). Recently, the machine-learning-based VADs have shown a superiority to traditional VADs on multiple feature fusion tasks. However, existing machine-learning-based VADs only utilize shallow models, which cannot explore the underlying manifold of the features. In this paper, we propose to fuse multiple features via a deep model, called deep belief network (DBN). DBN is a powerful hierarchical generative model for feature extraction. It can describe highly variant functions and discover the manifold of the features. We take the multiple serially-concatenated features as the input layer of DBN, and then extract a new feature by transferring these features through multiple nonlinear hidden layers. Finally, we predict the class of the new feature by a linear classifier. We further analyze that even a single-hidden-layer-based belief network is as powerful as the state-of-the-art models in the machine-learning-based VADs. In our empirical comparison, ten common features are used for performance analysis. Extensive experimental results on the AURORA2 corpus show that the DBN-based VAD not only outperforms eleven referenced VADs, but also can meet the real-time detection demand of VAD. The results also show that the DBN-based VAD can fuse the advantages of multiple features effectively. We introduce Deep Hybrid Networks that are robust to the recognition of out-of-sample objects, i.e., ones that are drawn from a different probability distribution from the training data distribution. The networks are based on a particular combination of an auto-encoder and stacked Restricted Boltzmann Machines (RBMs). The autoencoder is used to extract sparse features, which are expected to be noise invariant in the observations. The stacked RBMs then observe the sparse features as inputs to learn the top hierarchical features. The use of RBMs is motivated by the fact that the stacked RBMs typically provide good performance when dealing with in-sample observations, as proven in the previous works. To improve the robustness against local noise, we propose a variant of our hybrid network by the usage of a mixture of sparse features and sparse connections in the auto-encoder layer. The experiments show that our proposed deep networks provide good performance in both the in-sample and out-of-sample situations, particularly when the number of training examples is small. Deep belief nets have been successful in modeling handwritten characters, but it has proved more difficult to apply them to real images. The problem lies in the restricted Boltzmann machine (RBM) which is used as a module for learning deep belief nets one layer at a time. The Gaussian-Binary RBMs that have been used to model real-valued data are not a good way to model the covariance structure of natural images. We propose a factored 3-way RBM that uses the states of its hidden units to represent abnormalities in the local covariance structure of an image. This provides a probabilistic framework for the widely used simple complex cell architecture. Our model learns binary features that work very well for object recognition on the “tiny images” data set. Even better features are obtained by then using standard binary RBM’s to learn a deeper model. A hybrid architecture is presented capable of online learning from both labeled and unlabeled samples. It combines both generative and discriminative objectives to derive a new variant of the Deep Belief Network, i.e., the Stacked Boltzmann Experts Network model. The model's training algorithm is built on principles developed from hybrid discriminative Boltzmann machines and composes deep architectures in a greedy fashion. It makes use of its inherent "layer-wise ensemble" nature to perform useful classification work. We (1) compare this architecture against a hybrid denoising autoencoder version of itself as well as several other models and (2) investigate training in the context of an incremental learning procedure. The best-performing hybrid model, the Stacked Boltzmann Experts Network, consistently outperforms all others. Complexity theory of circuits strongly suggests that deep architectures can be much more efficient (sometimes exponentially) than shallow architectures, in terms of computational elements required to represent some functions. Deep multi-layer neural networks have many levels of non-linearities allowing them to compactly represent highly non-linear and highly-varying functions. However, until recently it was not clear how to train such deep networks, since gradient-based optimization starting from random initialization appears to often get stuck in poor solutions. recently introduced a greedy layer-wise unsupervised learning algorithm for Deep Belief Networks (DBN), a generative model with many layers of hidden causal variables. In the context of the above optimization problem, we study this algorithm empirically and explore variants to better understand its success and extend it to cases where the inputs are continuous or where the structure of the input distribution is not revealing enough about the variable to be predicted in a supervised task. Our experiments also confirm the hypothesis that the greedy layer-wise unsupervised training strategy mostly helps the optimization, by initializing weights in a region near a good local minimum, giving rise to internal distributed representations that are high-level abstractions of the input, bringing better generalization. We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent expectations are estimated using a variational approximation that tends to focus on a single mode, and dataindependent expectations are approximated using persistent Markov chains. The use of two quite different techniques for estimating the two types of expectation that enter into the gradient of the log-likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer “pre-training” phase that allows variational inference to be initialized with a single bottomup pass. We present results on the MNIST and NORB datasets showing that deep Boltzmann machines learn good generative models and perform well on handwritten digit and visual object recognition tasks. Hyperspectral data classification is a hot topic in remote sensing community. In recent years, significant effort has been focused on this issue. However, most of the methods extract the features of original data in a shallow manner. In this paper, we introduce a deep learning approach into hyperspectral image classification. A new feature extraction (FE) and image classification framework are proposed for hyperspectral data analysis based on deep belief network (DBN). First, we verify the eligibility of restricted Boltzmann machine (RBM) and DBN by the following spectral information-based classification. Then, we propose a novel deep architecture, which combines the spectral–spatial FE and classification together to get high classification accuracy. The framework is a hybrid of principal component analysis (PCA), hierarchical learning-based FE, and logistic regression (LR). Experimental results with hyperspectral data indicate that the classifier provide competitive solution with the state-of-the-art methods. In addition, this paper reveals that deep learning system has huge potential for hyperspectral data classification. Building intelligent systems that are capable of extracting high-level representations from high-dimensional sensory data lies at the core of solving many AI related tasks, including object recognition, speech perception, and language understanding. Theoretical and biological arguments strongly suggest that building such systems requires models with deep architectures that involve many layers of nonlinear processing. The aim of the thesis is to demonstrate that deep generative models that contain many layers of latent variables and millions of parameters can be learned efficiently, and that the learned high-level feature representations can be successfully applied in a wide spectrum of application domains, including visual object recognition, information retrieval, and classification and regression tasks. In addition, similar methods can be used for nonlinear dimensionality reduction. The first part of the thesis focuses on analysis and applications of probabilistic generative models called Deep Belief Networks. We show that these deep hierarchical models can learn useful feature representations from a large supply of unlabeled sensory inputs. The learned high-level representations capture a lot of structure in the input data, which is useful for subsequent problem-specific tasks, such as classification, regression or information retrieval, even though these tasks are unknown when the generative model is being trained. In the second part of the thesis, we introduce a new learning algorithm for a different type of hierarchical probabilistic model, which we call a Deep Boltzmann Machine. Like Deep Belief Networks, Deep Boltzmann Machines have the potential of learning internal representations that become increasingly complex at higher layers, which is a promising way of solving object and speech recognition problems. Unlike Deep Belief Networks and many existing models with deep architectures, the approximate inference procedure, in addition to a fast bottom-up pass, can incorporate top-down feedback. This allows Deep Boltzmann Machines to better propagate uncertainty about ambiguous inputs.