Quantifying Data Dependencies with Rényi Mutual Information and Minimum Spanning Trees.

Area of Science:

• Data Science
• Information Theory
• Computational Statistics

Background:

• Quantifying dependencies in multivariate data is crucial for uncertainty quantification and sensitivity analysis.
• Estimating mutual information is key to understanding these dependencies.
• Existing methods often require distribution knowledge or are computationally intensive.

Purpose of the Study:

• To develop a novel, data-driven method for quantifying dependencies using Rényi mutual information.
• To explore efficient computation of minimum spanning trees (MSTs) for large datasets.
• To apply the method to both artificial and real-world datasets.

Main Methods:

• Estimating Rényi mutual information via minimum spanning trees (MSTs) based on data.
• Utilizing the Hero et al. method for entropy estimation from MST length.
• Investigating approximate MST computation, specifically the multilevel approach by Zhong et al. (2015).

Main Results:

• The proposed method effectively quantifies dependencies without requiring prior distribution knowledge.
• Approximate MST methods, particularly the multilevel approach, reduce computational cost for large datasets.
• The method was successfully applied to the Ishigami function and an El Nino dataset.

Conclusions:

• The novel quantifier of dependency based on MSTs offers an efficient and robust approach.
• Combining approximate MSTs with Rényi mutual information estimation is a valuable contribution.
• The methodology is well-suited for analyzing complex datasets where distributions are unknown.