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Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew $t$ copulas, factor copulas, time series copulas and…

This paper explores the dependence modeling of financial assets in a dynamic way and its critical role in measuring risk. Two new methods, called Accelerated Moving Window method and Bottom-up method are proposed to detect the change of…

Accurate and reliable forecasting of renewable energy generation is crucial for the efficient integration of renewable sources into the power grid. In particular, probabilistic forecasts are becoming essential for managing the intrinsic…

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of…

Diffusion models offer a physically grounded framework for probabilistic weather forecasting, but their typical reliance on slow, iterative solvers during inference makes them impractical for subseasonal-to-seasonal (S2S) applications where…

We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend…

Many types of bounded data defined on the unit interval arise naturally as ratios of the form $X/(X + Y)$. In the existing literature, the main statistical models proposed for this type of bounded data typically based on the assumption that…

Autoregressive models have emerged as a powerful approach for visual generation but suffer from slow inference speed due to their sequential token-by-token prediction process. In this paper, we propose a simple yet effective approach for…

Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…

Renewable energy power is influenced by the atmospheric system, which exhibits nonlinear and time-varying features. To address this, a dynamic temporal correlation modeling framework is proposed for renewable energy scenario generation. A…

Large language models (LLMs) have demonstrated remarkable performance in diverse tasks using zero-shot and few-shot prompting. Even though their capabilities of data synthesis have been studied well in recent years, the generated data…

Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully…

In many studies multivariate event time data are generated from clusters having a possibly complex association pattern. Flexible models are needed to capture this dependence. Vine copulas serve this purpose. Inference methods for vine…

In this work, we propose FlowTime, a generative model for probabilistic forecasting of multivariate timeseries data. Given historical measurements and optional future covariates, we formulate forecasting as sampling from a learned…

Time series prediction underpins a broad range of downstream tasks across many scientific domains. Recent advances and increasing adoption of black-box machine learning models for time series prediction highlight the critical need for…

We develop a Bayesian spatio-temporal framework for extreme-value analysis that augments a hierarchical copula model with an autoregressive factor to capture residual temporal dependence in threshold exceedances. The factor can be specified…

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…

We introduce a new model for multivariate probabilistic time series prediction, designed to flexibly address a range of tasks including forecasting, interpolation, and their combinations. Building on copula theory, we propose a simplified…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

Copula-based time series models can model univariate and stationary time series in a flexible way by decomposing the joint distribution of consecutive observations into a copula and the stationary distribution. Implicitly this approach…