arXiv Statistics ML
Sep 3

Copula Transformations for Data-Consistent Inversion

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.

By Troy Butler, Tianyi Jiang, Jo\~ao Silva, Harri Hakula, Timothy Wildey
arXiv AI
Jul 7

Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation

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.

By Alberto Foresti, Ivan Butakov, Alexander Tolmachev, Giulio Franzese, Alexey Frolov, Pietro Michiardi
arXiv Machine Learning
Jul 2

TiRex-2: Generalizing TiRex to Multivariate Data and Streaming

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.

By Patrick Podest, Marco Pichler, Elias B\"urger, Levente Z\'olyomi, Bernhard Voggenberger, Wilhelm Berghammer, Daniel Klotz, Sebastian B\"ock, G\"unter Klambauer, Sepp Hochreiter