相关论文: Universal randomised signatures for generative tim…

The stochastic sewing lemma recently introduced by Le~(2020) allows to construct a unique limit process from a doubly indexed stochastic process that satisfies some regularity. This lemma is stated in a given probability space on which…

Generative-adversarial networks (GANs) have been used to produce data closely resembling example data in a compressed, latent space that is close to sufficient for reconstruction in the original vector space. The Wasserstein metric has been…

In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior…

A novel generative machine learning approach for the simulation of sequences of financial price data with drawdowns quantifiably close to empirical data is introduced. Applications such as pricing drawdown insurance options or developing…

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis…

We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

We derive a Benamou-Brenier type dynamical formulation for the Wasserstein metric $\mathsf W_p$ between stationary random measures recently introduced in [EHJM23]. A key step is a reformulation of the metric $\mathsf W_p$ using Palm…

Adversarial examples are crafted by adding indistinguishable perturbations to normal examples in order to fool a well-trained deep learning model to misclassify. In the context of computer vision, this notion of indistinguishability is…

We propose the Wasserstein-Fourier (WF) distance to measure the (dis)similarity between time series by quantifying the displacement of their energy across frequencies. The WF distance operates by calculating the Wasserstein distance between…

A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…

Synthetic time series are often used in practical applications to augment the historical time series dataset for better performance of machine learning algorithms, amplify the occurrence of rare events, and also create counterfactual…

Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data. Towards…

While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…

We present a deep generative model for unsupervised text style transfer that unifies previously proposed non-generative techniques. Our probabilistic approach models non-parallel data from two domains as a partially observed parallel…

Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high…

The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…

We study the approximation of a (finite) continuous-time Markov chain by a Markov chain on a reduced state space, and we provide formal error bounds for the approximated transient distributions in the Wasserstein distance. These bounds…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…