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.

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

Example Input: Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by transforming Gaussian noise through a deep neural network whose output are the parameters of a spline. Unlike Gaussian processes, Deep Random Splines allow us to readily enforce shape constraints while inheriting the richness and tractability of deep generative models. We also present an observational model for point process data which uses Deep Random Splines to model the intensity function of each point process and apply it to neuroscience data to obtain a low-dimensional representation of spiking activity. Inference is performed via a variational autoencoder that uses a novel recurrent encoder architecture that can handle multiple point processes as input.
Example Output: We combine splines with neural networks to obtain a novel distribution over functions and use it to model intensity functions of point processes.

Example Input: We augment adversarial training (AT) with worst case adversarial training
 (WCAT) which improves adversarial robustness by 11% over the current state-
 of-the-art result in the `2-norm on CIFAR-10. We interpret adversarial training as
 Total Variation Regularization, which is a fundamental tool in mathematical im-
 age processing, and WCAT as Lipschitz regularization, which appears in Image
 Inpainting. We obtain verifiable worst and average case robustness guarantees,
 based on the expected and maximum values of the norm of the gradient of the
 loss.
Example Output:
Improvements to adversarial robustness, as well as provable robustness guarantees, are obtained by augmenting adversarial training with a tractable Lipschitz regularization