arXiv:2607. 10410v1 Announce Type: cross Abstract: Reliable forecasting of several interrelated environmental variables - such as regional precipitation and temperature, or other correlated geophysical fields - across many locations calls for accurate predictions accompanied by trustworthy statements of their uncertainty.
The paper introduces a copula-based framework to relate Data‑Consistent Inversion (DCI) and its iterative variant (iDCI). By applying Sklar’s theorem, the authors factor the DCI update into marginal and dependence components, showing that any remaining discrepancy after iDCI convergence is fully captured by the copulas of the observed and predicted joint distributions. They prove that an exact copula transformation recovers the original DCI solution and provide convergence results for approximate transformations, supported by numerical examples illustrating adaptive refinement and progressive problem refinement.
arXiv:2607. 03487v1 Announce Type: cross Abstract: Mutual information (MI) estimation is a central problem in machine learning and statistics; however, existing benchmarks typically evaluate estimators on simplified, low-dimensional distributions, leaving their performance on complex, realistic data largely unexplored.
arXiv:2609.25980v1 Announce Type: new Abstract: Probabilistic time series foundation models (TSFMs) provide coordinate-wise predictive distributions, but these marginals do not determine a joint dist...
arXiv:2607. 01204v1 Announce Type: new Abstract: We introduce TiRex-2, a recurrent xLSTM-based time series foundation model that generalizes the univariate TiRex to multivariate forecasting with both past and future covariates.
arXiv:2508. 13831v4 Announce Type: replace-cross Abstract: Functional data, i.
arXiv:2607. 25020v1 Announce Type: new Abstract: Vine copulas provide a flexible framework for modeling complex multivariate distributions through a hierarchical decomposition into bivariate pair-copulas.
Vine copulas provide a flexible framework for modeling complex multivariate distributions through a hierarchical decomposition into bivariate pair-copulas. Fitting a D-vine requires selecting a copula family and parameter configuration for each pair-copula from a set of candidates encoding different dependence patterns.
arXiv:2608. 20025v1 Announce Type: new Abstract: Probabilistic forecasting models are widely used for time series forecasting in domains such as energy systems, finance, medicine, and transportation.
arXiv:2609.13345v1 Announce Type: cross Abstract: Probabilistic forecasting is central to decision-making under uncertainty, yet its methodological landscape has become increasingly fragmented across...
arXiv:2608. 11114v1 Announce Type: cross Abstract: Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings.
The paper introduces Personalized Federated Hierarchical Gaussian Processes (pFedHGP), a method for probabilistic regression and classification on data distributed across heterogeneous clients. Each client’s latent function is split into a shared global component, a client‑specific deviation that shares the global kernel, and a flexible local residual. Using sparse inducing‑variable approximations and federated variational inference, raw data remain local while the server exchanges only low‑dimensional statistics, enabling full predictive distributions for uncertainty‑aware decisions. In experiments, pFedHGP achieves perfect fault classification in press tonnage monitoring with only 13.77% of labeled cycles and accurately recovers geographic zones in federated air‑quality modeling without centralizing station‑level time series.