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Measuring Interactions in Categorical Datasets Using Multivariate Symmetrical Uncertainty.

Santiago Gómez-Guerrero1, Inocencio Ortiz1, Gustavo Sosa-Cabrera1

  • 1Polytechnic School, National University of Asuncion, San Lorenzo 2111, Paraguay.

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Summary
This summary is machine-generated.

This study introduces a new method to define and detect variable interactions in statistical models, especially for categorical data. The Multivariate Symmetrical Uncertainty (MSU) measure successfully identifies interactions in both continuous and discretized datasets.

Keywords:
categorical datagain in multiple correlationinteractionintrinsic interactionmultivariable correlationmultivariate symmetrical uncertaintypatterned data

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Area of Science:

  • Statistics
  • Data Mining
  • Machine Learning

Background:

  • Variable interactions are crucial in statistical models but challenging to define and detect for categorical or mixed data types.
  • Existing methods often struggle with the complexities of non-numeric variable interactions.

Purpose of the Study:

  • To propose a formal and broader definition for variable interactions applicable to categorical and mixed data.
  • To introduce the Multivariate Symmetrical Uncertainty (MSU) as an entropy-based measure for detecting these interactions.

Main Methods:

  • Developed a novel definition of variable interaction based on the Multivariate Symmetrical Uncertainty (MSU) measure.
  • Conducted two experimental series: one analyzing record patterns in datasets and another comparing continuous and discretized regression models.

Main Results:

  • Observed that absent record types or category combinations (patterns) often indicate attribute interactions.
  • Demonstrated successful replication of interaction/non-interaction behavior from continuous to discretized datasets, showing interaction-wise correspondence.
  • Validated the proposed MSU-based definition as effective for detecting and measuring interactions in linear and non-linear models.

Conclusions:

  • The proposed MSU-based definition provides a valuable tool for understanding and quantifying variable interactions, particularly in datasets with categorical variables.
  • This approach bridges the gap in interaction analysis between continuous and discrete data, enhancing statistical modeling capabilities.