How to understand the fsrmrmr function in Regression Learner App

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ako
ako 2023-4-11
回答： Drew 2023-4-12

It is not known the end of the running indices: i(n) and j(m)? Different running indices for x and z suggests that the two vectors are of different lengths. Is it true? Are the pairs of x(i=1) and z(j=1), x(i=2) and z(j=2) … x(i=n) and z(j=m) matching?

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ako
ako 2023-4-12
I also found that the algorithms used in fcrmrmr and fsrmrmr are consistent, but according to the literature referenced by this algorithm, MIQ is a better choice for discrete/categorical features, while FCQ (Fisher's criterion quotient) is preferred for continuous features [1]."

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Drew
Drew 2023-4-12
You have not given the context of what formula you are asking about, but I will take a guess. The fsrmrmr and fscmrmr functions are described on their respective doc pages:
https://www.mathworks.com/help/stats/fsrmrmr.html
https://www.mathworks.com/help/stats/fscmrmr.html
At the bottom of each of those doc pages, see the sections labelled "More About" and "Algorithms". In the "More About" section for fsrmrmr, https://www.mathworks.com/help/stats/fsrmrmr.html#mw_8850d730-881b-45de-a1c9-f01861283880, the mutual information of a pair of random variables is defined (see the link, or see the image below). Note the last paragraph: "The fsrmrmr function uses this definition to compute the mutual information values for both categorical (discrete) and continuous variables. For each continuous variable, including the response, fsrmrmr discretizes the variable into 256 bins or the number of unique values in the variable if it is less than 256. The function finds optimal bivariate bins for each pair of variables using the adaptive algorithm [2]." In that equation, the variable i will "run" over all the unique values or "bins" of variable X (depending on whether X is continuous or discrete, and if continuous, how many unique values it had to begin with). Similarly, the variable j will "run" over all the unique values or "bins" of variable Z. The number of unique values or "bins" of variables X and Z are not necessarily the same, but they can be the same sometimes. It will depend on the underlying data.

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