We propose introspective convolutional networks (ICN) that emphasize the importance of having convolutional neural networks empowered with generative capabilities. We employ a reclassification-by-synthesis algorithm to perform training using a formulation stemmed from the Bayes theory. Our ICN tries to iteratively: (1) synthesize pseudo-negative samples; and (2) enhance itself by improving the classification. The single CNN classifier learned is at the same time generative --- being able to directly synthesize new samples within its own discriminative model. We conduct experiments on benchmark datasets including MNIST, CIFAR-10, and SVHN using state-of-the-art CNN architectures, and observe improved classification results.
Neural Networks are function approximators that have achieved state-of-the-art accuracy in numerous machine learning tasks. In spite of their great success in terms of accuracy, their large training time makes it difficult to use them for various tasks. In this paper, we explore the idea of learning weight evolution pattern from a simple network for accelerating training of novel neural networks. We use a neural network to learn the training pattern from MNIST classification and utilize it to accelerate training of neural networks used for CIFAR-10 and ImageNet classification. Our method has a low memory footprint and is computationally efficient. This method can also be used with other optimizers to give faster convergence. The results indicate a general trend in the weight evolution during training of neural networks. Autoencoders play a fundamental role in unsupervised learning and in deep architectures for transfer learning and other tasks. In spite of their fundamental role, only linear autoencoders over the real numbers have been solved analytically. Here we present a general mathematical framework for the study of both linear and non-linear autoencoders. The framework allows one to derive an analytical treatment for the most non-linear autoencoder, the Boolean autoencoder. Learning in the Boolean autoencoder is equivalent to a clustering problem that can be solved in polynomial time when the number of clusters is small and becomes NP complete when the number of clusters is large. The framework sheds light on the different kinds of autoencoders, their learning complexity, their horizontal and vertical composability in deep architectures, their critical points, and their fundamental connections to clustering, Hebbian learning, and information theory. This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a given set of observed feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed; in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and an information criterion for feature pursuit is derived. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (filter, random field, and minimax entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. The relationship between our theory and the mechanisms of neural computation is also discussed. Boosting algorithms and successful applications thereof abound for classification and regression learning problems, but not for unsupervised learning. We propose a sequential approach to adding features to a random field model by training them to improve classification performance between the data and an equal-sized sample of "negative examples" generated from the model's current estimate of the data density. Training in each boosting round proceeds in three stages: first we sample negative examples from the model's current Boltzmann distribution. Next, a feature is trained to improve classification performance between data and negative examples. Finally, a coefficient is learned which determines the importance of this feature relative to ones already in the pool. Negative examples only need to be generated once to learn each new feature. The validity of the approach is demonstrated on binary digits and continuous synthetic data. Statistical and computational concerns have motivated parameter estimators based on various forms of likelihood, e.g., joint, conditional, and pseudolikelihood. In this paper, we present a unified framework for studying these estimators, which allows us to compare their relative (statistical) efficiencies. Our asymptotic analysis suggests that modeling more of the data tends to reduce variance, but at the cost of being more sensitive to model misspecification. We present experiments validating our analysis.  Generative model learning is one of the key problems in machine learning and computer vision. Currently the use of generative models is limited due to the difficulty in effectively learning them. A new learning framework is proposed in this paper which progressively learns a target generative distribution through discriminative approaches. This framework provides many interesting aspects to the literature. From the generative model side: (1) A reference distribution is used to assist the learning process, which removes the need for a sampling processes in the early stages. (2) The classification power of discriminative approaches, e.g. boosting, is directly utilized. (3) The ability to select explore features from a large candidate pool allows us to make nearly no assumptions about the training data. From the discriminative model side: (1) This framework improves the modeling capability of discriminative models. (2) It can start with source training data only and gradually "invent" negative samples. (3) We show how sampling schemes can be introduced to discriminative models. (4) The learning procedure helps to tighten the decision boundaries for classification, and therefore, improves robustness. In this paper, we show a variety of applications including texture modeling and classification, non-photorealistic rendering, learning image statistics denoising, and face modeling. The framework handles both homogeneous patterns, e.g. textures, and inhomogeneous patterns, e.g. faces, with nearly an identical parameter setting for all the tasks in the learning stage. In this paper, a hybrid discriminative generative model for brain anatomical structure segmentation is proposed. The learning aspect of the approach is emphasized. In the discriminative appearance models, various cues such as intensity and curvatures are combined to locally capture the complex appearances of different anatomical structures. A probabilistic boosting tree (PBT) framework is adopted to learn multiclass discriminative models that combine hundreds of features across different scales. On the generative model side, both global and local shape models are used to capture the shape information about each anatomical structure. The parameters to combine the discriminative appearance and generative shape models are also automatically learned. Thus, low-level and high-level information is learned and integrated in a hybrid model. Segmentations are obtained by minimizing an energy function associated with the proposed hybrid model. Finally, a grid-face structure is designed to explicitly represent the 3-D region topology. This representation handles an arbitrary number of regions and facilitates fast surface evolution. Our system was trained and tested on a set of 3-D magnetic resonance imaging (MRI) volumes and the results obtained are encouraging. We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this auto-encoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns.   The increasingly photorealistic sample quality of generative image models suggests their feasibility in applications beyond image generation. We present the Neural Photo Editor, an interface that leverages the power of generative neural networks to make large, semantically coherent changes to existing images. To tackle the challenge of achieving accurate reconstructions without loss of feature quality, we introduce the Introspective Adversarial Network, a novel hybridization of the VAE and GAN. Our model efficiently captures long-range dependencies through use of a computational block based on weight-shared dilated convolutions, and improves generalization performance with Orthogonal Regularization, a novel weight regularization method. We validate our contributions on CelebA, SVHN, and CIFAR-100, and produce samples and reconstructions with high visual fidelity. This paper studies the cooperative training of two generative models for image modeling and synthesis. Both models are parametrized by convolutional neural networks (ConvNets). The first model is a deep energy-based model, whose energy function is defined by a bottom-up ConvNet, which maps the observed image to the energy. We call it the descriptor network. The second model is a generator network, which is a non-linear version of factor analysis. It is defined by a top-down ConvNet, which maps the latent factors to the observed image. The maximum likelihood learning algorithms of both models involve MCMC sampling such as Langevin dynamics. We observe that the two learning algorithms can be seamlessly interwoven into a cooperative learning algorithm that can train both models simultaneously. Specifically, within each iteration of the cooperative learning algorithm, the generator model generates initial synthesized examples to initialize a finite-step MCMC that samples and trains the energy-based descriptor model. After that, the generator model learns from how the MCMC changes its synthesized examples. That is, the descriptor model teaches the generator model by MCMC, so that the generator model accumulates the MCMC transitions and reproduces them by direct ancestral sampling. We call this scheme MCMC teaching. We show that the cooperative algorithm can learn highly realistic generative models.  