In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Input: Consider Input: We present Cross-View Training (CVT), a simple but effective method for deep semi-supervised learning. On labeled examples, the model is trained with standard cross-entropy loss. On an unlabeled example, the model first performs inference (acting as a "teacher") to produce soft targets. The model then learns from these soft targets (acting as a ``"student"). We deviate from prior work by adding multiple auxiliary student prediction layers to the model. The input to each student layer is a sub-network of the full model that has a restricted view of the input  (e.g., only seeing one region of an image). The students can learn from the teacher (the full model) because the teacher sees more of each example. Concurrently, the students improve the quality of the representations used by the teacher as they learn to make predictions with limited data. When combined with Virtual Adversarial Training, CVT improves upon the current state-of-the-art on semi-supervised CIFAR-10 and semi-supervised SVHN. We also apply CVT to train models on five natural language processing tasks using hundreds of millions of sentences of unlabeled data. On all tasks CVT substantially outperforms supervised learning alone, resulting in models that improve upon or are competitive with the current state-of-the-art.


Output: Self-training with different views of the input gives excellent results for semi-supervised image recognition, sequence tagging, and dependency parsing.


Input: Consider Input: Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Rate-optimal procedures such as Tukey's median and other estimators based on statistical depth functions are impractical because of their computational intractability. In this paper, we establish an intriguing connection between f-GANs and various depth functions through the lens of f-Learning. Similar to the derivation of f-GAN, we show that these depth functions that lead to rate-optimal robust estimators can all be viewed as variational lower bounds of the total variation distance in the framework of f-Learning. This connection opens the door of computing robust estimators using tools developed for training GANs. In particular, we show that a JS-GAN that uses a neural network discriminator with at least one hidden layer is able to achieve the minimax rate of robust mean estimation under Huber's $\epsilon$-contamination model. Interestingly, the hidden layers of the neural net structure in the discriminator class are shown to be necessary for robust estimation.

Output: GANs are shown to provide us a new effective robust mean estimate against agnostic contaminations with both statistical optimality and practical tractability.


Input: Consider Input: We investigate the properties of multidimensional probability distributions in the context of latent space prior distributions of implicit generative models. Our work revolves around the phenomena arising while decoding linear interpolations between two random latent vectors -- regions of latent space in close proximity to the origin of the space are oversampled, which restricts the usability of linear interpolations as a tool to analyse the latent space. We show that the distribution mismatch can be eliminated completely by a proper choice of the latent probability distribution or using non-linear interpolations. We prove that there is a trade off between the interpolation being linear, and the latent distribution having even the most basic properties required for stable training, such as finite mean. We use the multidimensional Cauchy distribution as an example of the prior distribution, and also provide a general method of creating non-linear interpolations, that is easily applicable to a large family of commonly used latent distributions.


Output: We theoretically prove that linear interpolations are unsuitable for analysis of trained implicit generative models.