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I recently saw someone using 'Categorial variables' while talking about Loss functions.

However, I think in English that word is rarely used. The frequency is 10 times less than the proper word "categorical" recently, and more than 200 times less than "categorical" before 1910 AD.

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Is it just originated from a typo?

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I have never seen the word "catergorial" before. I just did a Google search for it and got just 2 hits, both to the same book. (https://ebooksilo.com/pdf/catergorial-grammar-and-the-logical-form-of-quantification) And I looked it up in thefreedictionary.com and it wasn't found.

It's possible that it's a technical term from some field. Or it could be a mis-spelling, probably of "categorical" as you suggest, both in your example and in the title of that book.

If someone else on here knows a definition for this word, please shout it out.

There are so many specialized words in English used only by a small community that I'm reluctant to say that it is a mis-spelling. It may just be a word I've never heard before. There are surely many such words. But my first guess would be mis-spelling.

  • Update

I see the post has been updated to change "catergorial" to "categorial". If this is the word encountered, that completely changes the answer.

"Categorial" is found in many dictionaries and means "of or relating to a category". This is also a definition of "categorical", so the two words can be synonyms. ("Categorical" also has other meanings.)

So the original writer might well have intended to write "categorial".

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  • categorial or catergorial? The OP is asking about the first, but you've mentioned the second in your answer.
    – stangdon
    Jun 30, 2022 at 21:09
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    @stangdon The question was "catergorial" and now it was edited by moderator to "categorial"
    – High GPA
    Jun 30, 2022 at 21:15
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    @stangdon The post was edited. It originally said "catergorial" (with an "r"). I'll update my reply.
    – Jay
    Jun 30, 2022 at 21:15
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It's almost certainly a typo. Categorical variables are those which can take on discrete values from an unordered set of values; hair color, breed of dog, etc. Categorial is closely related in meaning to categorical, but I've only ever heard the former in this maths context.

By contrast, catergorial and catagorial, whether or not describing variables, are probably signs of finger cramp. One might even describe them as phantasmagorical.

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  • So you are suggesting that categorial is also a legit word, but with different meaning?
    – High GPA
    Jun 30, 2022 at 22:59
  • Yes. See towards the end of @Jay's answer.
    – tkp
    Jul 1, 2022 at 2:40

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