We study unsupervised learning by developing introspective generative modeling (IGM) that attains a generator using progressively learned deep convolutional neural networks. The generator is itself a discriminator, capable of introspection: being able to self-evaluate the difference between its generated samples and the given training data. When followed by repeated discriminative learning, desirable properties of modern discriminative classifiers are directly inherited by the generator. IGM learns a cascade of CNN classifiers using a synthesis-by-classification algorithm. In the experiments, we observe encouraging results on a number of applications including texture modeling, artistic style transferring, face modeling, and semi-supervised learning.
 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. 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.  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.  The ability of learning networks to generalize can be greatly enhanced by providing constraints from the task domain. This paper demonstrates how such constraints can be integrated into a backpropagation network through the architecture of the network. This approach has been successfully applied to the recognition of handwritten zip code digits provided by the U.S. Postal Service. A single network learns the entire recognition operation, going from the normalized image of the character to the final classification. In fine art, especially painting, humans have mastered the skill to create unique visual experiences through composing a complex interplay between the content and style of an image. Thus far the algorithmic basis of this process is unknown and there exists no artificial system with similar capabilities. However, in other key areas of visual perception such as object and face recognition near-human performance was recently demonstrated by a class of biologically inspired vision models called Deep Neural Networks. Here we introduce an artificial system based on a Deep Neural Network that creates artistic images of high perceptual quality. The system uses neural representations to separate and recombine content and style of arbitrary images, providing a neural algorithm for the creation of artistic images. Moreover, in light of the striking similarities between performance-optimised artificial neural networks and biological vision, our work offers a path forward to an algorithmic understanding of how humans create and perceive artistic imagery.