The paper presents a closed‑form solution for the BROJA partial information decomposition (PID) when all variables are jointly Gaussian. This analytic expression eliminates the need for numerical optimization, allowing direct computation of unique, redundant, and synergistic information components in multivariate Gaussian settings. The resulting formula yields speedups of more than two orders of magnitude for high‑dimensional Gaussian PID calculations.
By Ohad Sheelo, Tal Golan, Ari Pakman
arXiv:2511. 02584v2 Announce Type: replace-cross Abstract: Associative memory, traditionally modeled by Hopfield networks, enables the retrieval of previously stored patterns from partial or noisy cues.
By Mark Bl\"umel, Andreas C. Schneider, Valentin Neuhaus, David A. Ehrlich, Marcel Graetz, Michael Wibral, Abdullah Makkeh, Viola Priesemann
The article surveys how the problem of extracting a common component from multiple jointly observed signals has been approached independently by statisticians, information theorists, and engineers. It reviews canonical correlation analysis, common information concepts, and subspace methods, then unifies these perspectives, extending to nonlinear CCA and discussing identifiability and links to self‑supervised learning. The tutorial aims to provide a self‑contained exposition that bridges signal processing, machine learning, and information theory.
By Paris A. Karakasis, Walid Saad
arXiv:2606. 18997v1 Announce Type: new Abstract: Uncovering the true informational architecture of real-world complex systems requires disentangling how their components uniquely store, redundantly share, and synergistically integrate information over time.
By Simon Pedro Galeano Munoz, Mustapha Bounoua, Giulio Franzese, Pietro Michiardi, Maurizio Filippone
arXiv:2410. 02628v5 Announce Type: replace Abstract: Learning conditional distributions $\pi^*(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^*$.
By Mikhail Persiianov, Arip Asadulaev, Nikita Andreev, Nikita Starodubcev, Dmitry Baranchuk, Anastasis Kratsios, Evgeny Burnaev, Alexander Korotin
arXiv:2607. 18559v1 Announce Type: cross Abstract: Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process.
By Vignesh Tirukkonda, Gautam Dasarathy
The paper proposes using the $q$Gaussian distribution, derived from Tsallis entropy maximization, to address the shortcomings of Gaussian assumptions in sparse learning with correlated and heterogeneous data. It introduces a new framework that adapts numerical equilibrium methods to composite optimization problems, applying it to the Hager‑Zhang conjugate gradient algorithm to create a stable, efficient sparse learning algorithm. The work offers both theoretical insights into alternative statistical distributions and practical tools for data analysis in fields like biostatistics.
By Kai Yang, Masoud Asgharian, Celia M. T. Greenwood
The paper introduces SCORE, a scalable framework that learns an expressive covariance approximation for high‑dimensional Gaussian targets by combining scoring rule training with spectral‑space modeling. It decomposes the learning task into marginal distribution estimation and structured correlation matrix learning, achieving dense dependencies with linear storage and ≠(d log d) computational cost. The method employs a closed‑form Gaussian kernel score that remains valid for degenerate covariances, provides bounded gradients, and is invariant under unitary transforms, with theoretical guarantees on marginal recovery and correlation projection, and demonstrates improved performance on time‑series forecasting, monocular depth estimation, and spatial weather prediction.
By Christopher B\"ulte, Emil Partow, Astha Gupta, Pascal Esser, Gitta Kutyniok
The paper studies the numerical solution of the Beurling‑LASSO (BLASSO) for estimating Gaussian mixture models (GMMs) with unknown numbers of components and unknown diagonal covariance matrices. It introduces a Conic Particle Gradient Descent (CPGD) algorithm that incorporates Riemannian gradient descent to respect the Fisher‑Rao geometry of Gaussian distributions. The authors provide theoretical convergence guarantees, including exponential local convergence under a non‑degeneracy condition related to component separation, and demonstrate through numerical experiments that CPGD is more robust to overspecification of components than the EM algorithm.
By Romane Giard, Yohann De Castro, Roland Denis, Cl\'ement Marteau
arXiv:2609.17802v1 Announce Type: cross
Abstract: Measures on function spaces arise throughout Bayesian inverse problems and generative modeling, often with low-dimensional structure relative to a tr...
By Ricardo Baptista, Bamdad Hosseini, Alexander W. Hsu
arXiv:2608. 00503v1 Announce Type: cross Abstract: Predictive coding offers a powerful framework for cortical computation, yet scalable implementations that respect both Bayesian exactness and neurobiological constraints remain scarce.
By Moumita Das, Dipanjan Ray, Sourabh Bhattacharya
The paper introduces a weak Gromov-Wasserstein (wGW) framework that compares source relations with relations between target conditional laws, focusing on inner-product relations and preserving conditional means. It defines the barycentric weak inner-product GW (wIGW) distance, proves existence of minimizers under finite second moments, and presents a ridge-regularized dual formulation leading to an iterative algorithm for finitely supported measures. Experiments on point clouds, graphs, and a PBMC multiome study demonstrate that mean-preserving target refinements can incur zero cost and improve atlas-based cell type transfer.
By Youssef Mroueh