Paper: arXiv 2402.00543

Authors: Reza Salimi, Kamran Pakizeh

Abstract

Not a matter of serious contention, Pearson’s correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn’t live up to users’ needs and expectations. Specifically, a multivariable version of the correlation coefficient can greatly contribute to better assessment of the risk in a multi-asset investment portfolio. Needless to say, the correlation coefficient is derived from another concept: covariance. Even though covariance can be extended naturally by its mathematical formula, such an extension is to no use. Making matters worse, the correlation coefficient can never be extended based on its mathematical definition. In this article, we briefly explore random matrix theory to extend the notion of Pearson’s correlation coefficient to an arbitrary number of variables. Then, we show that how useful this measure is at gauging noise, thereby selecting features particularly in classification.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically interesting extension of Pearson’s correlation to multiple variables leveraging Random Matrix Theory. However, the practical financial application and backtesting readiness remain limited in the excerpt provided, leaning more theoretical than empirical.

Research Flowchart

  flowchart TD
    A[Goal: Extend Pearson Correlation to Multivariable Settings] --> B[Inputs: Multi-Asset Portfolios & Classification Datasets]
    B --> C[Method: Apply Random Matrix Theory to Covariance & Correlation]
    C --> D[Compute: Multivariable Correlation Coefficient & Noise Levels]
    D --> E[Applications: Portfolio Risk Assessment & Feature Selection]
    E --> F[Outcomes: Improved Multi-Asset Risk Assessment & Noise-Filtered Feature Selection]

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0 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.