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From Common Information to Canonical Correlation Analysis and Beyond: Bridging Information Theory, Signal Processing, and Machine Learning

Paris A. Karakasis, Walid Saad · 2026 · Entropy

DOI: 10.3390/e28101161 · cited by 0 works (OpenAlex) · open-access PDF

Japanese

信号処理、機械学習、およびニューロイメージングの多くの問題は、それらすべてに共通のコンポーネントを混合するプロセスのいくつかの共通の測定を提供し、それらは、それ自体に共通のコンポーネントをリサイクルする必要があるので、この問題は、主に独立して、いくつかのコミュニティで研究されています。統計学者は、1936年にHotellingによって導入されたカノニカル関連分析(CCA)の主要な結果とツールを提示し、情報理論家は、GácsとKörnerおよびWinerのために共通のコンポーネントをリサイクルするために、共通のコンポーネントの2つの概念を提案しました。エンジニアは、初めから原則から情報理

Machine translation (Meta M2M100); the English original follows.

Abstract

Many problems in signal processing, machine learning, and neuroimaging provide several jointly observed measurements of one process, each mixing a component common to all of them with a component private to itself, and require the common component to be recovered without supervision. This problem has been studied in several communities, largely independently. Statisticians proposed canonical correlation analysis (CCA), introduced by Hotelling in 1936. Information theorists proposed two notions of common information, due to Gács and Körner and to Wyner. Engineers developed subspace methods for sensor arrays and multiuser communications to design multiview receivers. This tutorial presents the main results and tools each community developed for this problem in a single exposition, and explains the connections that emerge where they meet, distinguishing exact equivalences from special cases and analogies. We develop the information-theoretic foundation from first principles. We then introduce CCA and its extension to several views, followed by the engineering thread from blind multiuser detection to CCA as a blind receiver. Next, we turn to nonlinear CCA, covering kernel, deep, and probabilistic formulations, the conditions under which the common factor is identifiable, and connections to self-supervised learning. We conclude with a discussion of further extensions and open directions. The exposition is self-contained, so that readers from each of these communities can follow the parts developed by the others.

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Topics: Canonical correlation, Probabilistic logic, Computer science, Artificial intelligence, Bridging (networking), Subspace topology

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