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.
arXiv:2602. 23785v2 Announce Type: replace Abstract: We investigate the identifiability of nonlinear canonical correlation analysis (CCA) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise.
Unpaired Canonical Correlation Analysis (UCCA) introduces a method for learning linear projections that maximize correlation between views without requiring paired data. By linking the Quadratic Assignment Problem to CCA, the authors derive a practical algorithm that operates solely on unpaired samples. Experiments on real-world multimodal datasets show that UCCA outperforms existing unpaired alignment baselines in recovering true correlations.
arXiv:2510. 04758v3 Announce Type: replace Abstract: In this work, we establish the sufficient conditions under which nonlinear Canonical Correlation Analysis (CCA) recovers ground-truth latent factors up to an affine transformation.
The paper investigates which data sources should be jointly learned when training shared feature extractors. Focusing on a linear setting where sources share a low‑dimensional subspace, it shows that carefully selecting a subset of sources—an informative subpopulation—can achieve minimax optimal subspace estimation, even when much data is discarded. The authors formalize this notion, propose algorithms and heuristics for identifying such subsets, and validate their effectiveness through theory and experiments on synthetic and real datasets.
arXiv:2504. 18455v2 Announce Type: replace-cross Abstract: We study distributed multiview representation learning, a problem in which $K$ clients each observe a distinct but possibly statistically correlated view.
arXiv:2608. 13229v1 Announce Type: cross Abstract: We present the mathematical foundations of linear independent component analysis (ICA) models based on standard literature in a self-contained note.
The article introduces a partial information decomposition (PID) for multivariate Gaussian systems using the Blackwell order, which determines when one channel is more informative than another. It shows that Gaussian channels optimally extract redundant and union information, providing a geometric interpretation and an efficient numerical algorithm. The authors derive closed‑form expressions for two‑source cases, compare their Blackwell redundancy to the BROJA measures, and demonstrate scalability to systems with up to a thousand dimensions or sources, including an application to an optimal control problem.
arXiv:2510.01345v2 Announce Type: replace Abstract: Self-supervised representation learning (SSRL) has demonstrated remarkable empirical success, yet its underlying principles remain insufficiently u...
arXiv:2609.14421v1 Announce Type: cross Abstract: Recent advances in multimodal foundation models have intensified the need to understand how different modalities share, preserve, and complement info...
The paper introduces a method for learning disentangled signals via non‑linear Independent Component Analysis (ICA) by defining self‑sufficient signals, where the conditional distribution of a missing value given the rest remains unchanged when other signals are observed. It formulates this as a conditional KL divergence minimization and proposes a sequential, prior‑free, likelihood‑free algorithm that learns a demixing flow model at each iteration. The authors provide theoretical guarantees of local descent for an idealized Wasserstein‑gradient‑flow variant and demonstrate the method’s effectiveness on toy and real‑world datasets.
arXiv:2608. 12982v1 Announce Type: new Abstract: In this research work, we are constructing the sensing matrix, which is essential for the success of the compressive sensing technique.
arXiv:2312. 06173v2 Announce Type: replace Abstract: Merging models fine-tuned from a common, extensively pre-trained large model but specialized for different tasks has been demonstrated as a cheap and scalable strategy to construct a multi-task model that performs well across diverse tasks.