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This article explores minimum of an extremal in the variational problem with delay under the degeneracy of the Weierstrass condition. Here for study the minimality of extremal, variations of the Weierstrass type are used in two forms: in…

In standard generative adversarial network (SGAN), the discriminator estimates the probability that the input data is real. The generator is trained to increase the probability that fake data is real. We argue that it should also…

GANs have matured in recent years and are able to generate high-resolution, realistic images. However, the computational resources and the data required for the training of high-quality GANs are enormous, and the study of transfer learning…

In this work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a necessary condition for the extremum…

High-resolution (HR) precipitation prediction is essential for reducing damage from stationary and localized heavy rainfall; however, HR precipitation forecasts using process-driven numerical weather prediction models remains challenging.…

We consider a general task called partial Wasserstein covering with the goal of providing information on what patterns are not being taken into account in a dataset (e.g., dataset used during development) compared with another dataset(e.g.,…

We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case of some integro-differential operators acting on spaces with…

Langevin dynamics (LD) is widely used for sampling from distributions and for optimization. In this work, we derive a closed-form expression for the expected loss of preconditioned LD near stationary points of the objective function. We use…

We investigate under and overfitting in Generative Adversarial Networks (GANs), using discriminators unseen by the generator to measure generalization. We find that the model capacity of the discriminator has a significant effect on the…

Paraphrase generation is an important and challenging natural language processing (NLP) task. In this work, we propose a deep generative model to generate paraphrase with diversity. Our model is based on an encoder-decoder architecture. An…

Generative adversarial training can be generally understood as minimizing certain moment matching loss defined by a set of discriminator functions, typically neural networks. The discriminator set should be large enough to be able to…

Generative adversarial networks (GANs)successfully generate high quality data by learning amapping from a latent vector to the data. Various studies assert that the latent space of a GAN is semanticallymeaningful and can be utilized for…

The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on…

Distributional causal inference requires estimating not only average treatment effects but also interventional outcome distributions, including quantiles, tail risks, and policy-dependent uncertainty. As a method for distributional causal…

We examine the use of different randomisation policies for stochastic gradient algorithms used in sampling, based on first-order (or overdamped) Langevin dynamics, the most popular of which is known as Stochastic Gradient Langevin Dynamics.…

It is shown that under suitable regularity conditions, differential entropy is a Lipschitz functional on the space of distributions on $n$-dimensional Euclidean space with respect to the quadratic Wasserstein distance. Under similar…

A recurring task in particle physics and statistics is to compute the complex critical points of a product of powers of affine-linear functions. The logarithmic discriminant characterizes exponents for which such a function has a degenerate…

This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian…