Neural random fields (NRFs), which are defined by using neural networks to implement potential functions in undirected models (sometimes known as energy-based models), provide an interesting family of model spaces for machine learning, besides various directed models such as generative adversarial networks (GANs). In this paper we propose a new approach, the inclusive-NRF approach, to learning NRFs for continuous data (e.g. images), by developing inclusive-divergence minimized auxiliary generators and stochastic gradient sampling. As demonstrations of how the new approach can be flexibly and effectively used, specific inclusive-NRF models are developed and thoroughly evaluated for a number of tasks - unsupervised supervised image generation, semi-supervised classification and anomaly detection. The proposed models consistently achieve strong experimental results in all these tasks compared to state-of-the-art methods. Remarkably, in addition to superior sample generation, one fundamental additional benefit of our inclusive-NRF approach is that, unlike GANs, it directly provides (unnormalized) density estimate for sample evaluation. With these contributions and results, this paper significantly advances the learning and applications of undirected models to a new level, both theoretically and empirically, which have never been obtained before.
On the one hand, there are some efforts that aim to address the inability of GANs to provide sensible energy estimates for samples. The energy-based GANs (EBGAN) @cite_40 proposes to view the discriminator as an energy function by designing an auto-encoder discriminator. The recent work in @cite_21 connects @cite_40 and @cite_13 , and show another two approximations for the entropy term. However, it is known that as the generator converges to the true data distribution, the GAN discriminator converges to a degenerate uniform solution. This basically afflicts the GAN discriminator to provide density information, though there are some modifications. In contrast, our inclusive-NRFs, unlike GANs, naturally provide (unnormalized) density estimate, which is examined with GMM synthetic experiments and anomaly detection benchmarking experiments. Moreover, none of the above energy-related GAN studies examine their methods or models for SSL, except in EBGAN which performs moderately.
@cite_40 @cite_21 @cite_13
2521028896 2962775818 2787223504 2962900302
We introduce the "Energy-based Generative Adversarial Network" model (EBGAN) which views the discriminator as an energy function that attributes low energies to the regions near the data manifold and higher energies to other regions. Similar to the probabilistic GANs, a generator is seen as being trained to produce contrastive samples with minimal energies, while the discriminator is trained to assign high energies to these generated samples. Viewing the discriminator as an energy function allows to use a wide variety of architectures and loss functionals in addition to the usual binary classifier with logistic output. Among them, we show one instantiation of EBGAN framework as using an auto-encoder architecture, with the energy being the reconstruction error, in place of the discriminator. We show that this form of EBGAN exhibits more stable behavior than regular GANs during training. We also show that a single-scale architecture can be trained to generate high-resolution images. We introduce the "Energy-based Generative Adversarial Network" model (EBGAN) which views the discriminator as an energy function that attributes low energies to the regions near the data manifold and higher energies to other regions. Similar to the probabilistic GANs, a generator is seen as being trained to produce contrastive samples with minimal energies, while the discriminator is trained to assign high energies to these generated samples. Viewing the discriminator as an energy function allows to use a wide variety of architectures and loss functionals in addition to the usual binary classifier with logistic output. Among them, we show one instantiation of EBGAN framework as using an auto-encoder architecture, with the energy being the reconstruction error, in place of the discriminator. We show that this form of EBGAN exhibits more stable behavior than regular GANs during training. We also show that a single-scale architecture can be trained to generate high-resolution images. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. We propose in this paper a novel approach to tackle the problem of mode collapse encountered in generative adversarial network (GAN). Our idea is intuitive but proven to be very effective, especially in addressing some key limitations of GAN. In essence, it combines the Kullback-Leibler (KL) and reverse KL divergences into a unified objective function, thus it exploits the complementary statistical properties from these divergences to effectively diversify the estimated density in capturing multi-modes. We term our method dual discriminator generative adversarial nets (D2GAN) which, unlike GAN, has two discriminators; and together with a generator, it also has the analogy of a minimax game, wherein a discriminator rewards high scores for samples from data distribution whilst another discriminator, conversely, favoring data from the generator, and the generator produces data to fool both two discriminators. We develop theoretical analysis to show that, given the maximal discriminators, optimizing the generator of D2GAN reduces to minimizing both KL and reverse KL divergences between data distribution and the distribution induced from the data generated by the generator, hence effectively avoiding the mode collapsing problem. We conduct extensive experiments on synthetic and real-world large-scale datasets (MNIST, CIFAR-10, STL-10, ImageNet), where we have made our best effort to compare our D2GAN with the latest state-of-the-art GAN's variants in comprehensive qualitative and quantitative evaluations. The experimental results demonstrate the competitive and superior performance of our approach in generating good quality and diverse samples over baselines, and the capability of our method to scale up to ImageNet database.