text: The paper proposes an inductive semi-supervised learning method, called Smooth Neighbors on Teacher Graphs (SNTG). At each iteration during training, a graph is dynamically constructed based on predictions of the teacher model, i.e., the implicit self-ensemble of models. Then the graph serves as a similarity measure with respect to which the representations of "similar" neighboring points are learned to be smooth on the low dimensional manifold. We achieve state-of-the-art results on semi-supervised learning benchmarks. The error rates are 9.89 , 3.99 for CIFAR-10 with 4000 labels, SVHN with 500 labels, respectively. In particular, the improvements are significant when the labels are scarce. For non-augmented MNIST with only 20 labels, the error rate is reduced from previous 4.81 to 1.36 . Our method is also effective under noisy supervision and shows robustness to incorrect labels.
  @cite_18: The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.
  @cite_36: Generative Adversarial Nets (GANs) have shown promise in image generation and semi-supervised learning (SSL). However, existing GANs in SSL have two problems: (1) the generator and the discriminator (i.e. the classifier) may not be optimal at the same time; and (2) the generator cannot control the semantics of the generated samples. The problems essentially arise from the two-player formulation, where a single discriminator shares incompatible roles of identifying fake samples and predicting labels and it only estimates the data without considering the labels. To address the problems, we present triple generative adversarial net (Triple-GAN), which consists of three players---a generator, a discriminator and a classifier. The generator and the classifier characterize the conditional distributions between images and labels, and the discriminator solely focuses on identifying fake image-label pairs. We design compatible utilities to ensure that the distributions characterized by the classifier and the generator both converge to the data distribution. Our results on various datasets demonstrate that Triple-GAN as a unified model can simultaneously (1) achieve the state-of-the-art classification results among deep generative models, and (2) disentangle the classes and styles of the input and transfer smoothly in the data space via interpolation in the latent space class-conditionally.
  @cite_19: When labelled training data is plentiful, discriminative techniques are widely used since they give excellent generalization performance. However, for large-scale applications such as object recognition, hand labelling of data is expensive, and there is much interest in semi-supervised techniques based on generative models in which the majority of the training data is unlabelled. Although the generalization performance of generative models can often be improved by training them discriminatively, they can then no longer make use of unlabelled data. In an attempt to gain the benefit of both generative and discriminative approaches, heuristic procedure have been proposed [2, 3] which interpolate between these two extremes by taking a convex combination of the generative and discriminative objective functions. In this paper we adopt a new perspective which says that there is only one correct way to train a given model, and that a discriminatively trained generative model is fundamentally a new model [7]. From this viewpoint, generative and discriminative models correspond to specific choices for the prior over parameters. As well as giving a principled interpretation of discriminative training, this approach opens door to very general ways of interpolating between generative and discriminative extremes through alternative choices of prior. We illustrate this framework using both synthetic data and a practical example in the domain of multi-class object recognition. Our results show that, when the supply of labelled training data is limited, the optimum performance corresponds to a balance between the purely generative and the purely discriminative.
  @cite_43: Semi-supervised learning methods based on generative adversarial networks (GANs) obtained strong empirical results, but it is not clear 1) how the discriminator benefits from joint training with a generator, and 2) why good semi-supervised classification performance and a good generator cannot be obtained at the same time. Theoretically, we show that given the discriminator objective, good semisupervised learning indeed requires a bad generator, and propose the definition of a preferred generator. Empirically, we derive a novel formulation based on our analysis that substantially improves over feature matching GANs, obtaining state-of-the-art results on multiple benchmark datasets.
  @cite_45: Door lock apparatus in which a door latch mechanism is operated by inner and outer door handles coupled to a latch shaft extending through the latch mechanism. Handles are coupled to ends of latch shaft by coupling devices enabling door to be locked from the inside to prevent entry from the outside but can still be opened from the inside by normal operation of outside handle. Inside coupling device has limited lost-motion which is used to operate cam device to unlock the door on actuation of inner handles.
  @cite_49: In this paper we present a method for learning a discriminative classifier from unlabeled or partially labeled data. Our approach is based on an objective function that trades-off mutual information between observed examples and their predicted categorical class distribution, against robustness of the classifier to an adversarial generative model. The resulting algorithm can either be interpreted as a natural generalization of the generative adversarial networks (GAN) framework or as an extension of the regularized information maximization (RIM) framework to robust classification against an optimal adversary. We empirically evaluate our method - which we dub categorical generative adversarial networks (or CatGAN) - on synthetic data as well as on challenging image classification tasks, demonstrating the robustness of the learned classifiers. We further qualitatively assess the fidelity of samples generated by the adversarial generator that is learned alongside the discriminative classifier, and identify links between the CatGAN objective and discriminative clustering algorithms (such as RIM).
  @cite_51: We present a variety of new architectural features and training procedures that we apply to the generative adversarial networks (GANs) framework. We focus on two applications of GANs: semi-supervised learning, and the generation of images that humans find visually realistic. Unlike most work on generative models, our primary goal is not to train a model that assigns high likelihood to test data, nor do we require the model to be able to learn well without using any labels. Using our new techniques, we achieve state-of-the-art results in semi-supervised classification on MNIST, CIFAR-10 and SVHN. The generated images are of high quality as confirmed by a visual Turing test: our model generates MNIST samples that humans cannot distinguish from real data, and CIFAR-10 samples that yield a human error rate of 21.3 . We also present ImageNet samples with unprecedented resolution and show that our methods enable the model to learn recognizable features of ImageNet classes.
summary: Besides aforementioned discriminative approaches, another line is generative models, which pay efforts to learn the input distribution @math that is believed to share some information with the conditional distribution @math @cite_19 . Traditional models such as Gaussian mixtures @cite_45 try to maximize the joint log-likelihood of both labeled and unlabeled data using EM. For modern deep generative models, variational auto-encoder (VAE) makes it scalable by employing variational methods combined with deep learning @cite_18 while generative adversarial networks (GAN) generate samples by optimizing an adversarial game between the discriminator and the generator @cite_49 @cite_51 @cite_36 @cite_43 . The samples generated by GAN can be viewed as another kind of data augmentation'' to tell'' the decision boundary where to lie. For example, fake'' samples can be generated in low density regions where the training data is rare @cite_51 @cite_43 based on the assumption. Alternatively, more pseudo'' samples could be generated in high density regions to keep away from the decision boundary thus improve the robustness of the classifier @cite_36 . Our work is complementary to these efforts and can be easily combined with them. We observe improvements over feature matching GAN @cite_51 with SNTG (see ).