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Problem

I am analysing a dataset containing variables of different types: continuous, ordinal and categorical. To prioritise in which order to analyse the variables, I would like to evaluate the relatedness of all of these variables to one another.

In other words: is there a measure that takes two variables of any type and results in a number where a higher number indicates the variables are more related.

Relatedness

The analysis is a first step to modelling the data, so the relatedness should measure how well one variable would be as a predictor in regression or classification towards the other variable.

Work so far

I came across covariance analysis, which has different approaches depending on the types of the dependent and independent variable. I was not sure if the resulting $R^2$ can be used to order the variable pairs for my means. Secondly, Mutual Information seems to work for all variable types and could therefore be interesting, however I have not found an implementation of this method that would work for any variable type.

Additional information

We work in Python so measures implemented to work with Numpy are preferred.

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