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Definition of "Consistent nearest neighbour", runs our usual KNN classifier but instead of viewing k as a hyper-parameter it always sets k = ceil[log(n)].

So far, I looked-up many references and websites and researched on how to determine if a method is between parametric or non-parametric. I came up with below definitions,

A parametric algorithm has a fixed number of parameters. In contrast, a non-parametric algorithm uses a flexible number of parameters, and the number of parameters often grows as it learns from more data.

From https://chemicalstatistician.wordpress.com/2014/01/14/machine-learning-lesson-of-the-day-parametric-vs-non-parametric-models/.

Moreover, I found,

A parametric model, we have a finite number of parameters, and in nonparametric models, the number of parameters is (potentially) infinite.

From https://sebastianraschka.com/faq/docs/parametric_vs_nonparametric.html.

My question is, why do we count it as a Non-parametric model, while the number of parameters can increase to infinity in the mentioned method and it will gets more complicated by increasing test data?

M.Hossein Rahimi
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  • Related question: Why is “condensed nearest neighbour” Non-parametric?. – Richard Hardy Apr 05 '19 at 07:24
  • Please notice that condensed nearest neighbour and consistent nearest neighbour are two different methods such one is Parametric and the other one is Non-parametric. – M.Hossein Rahimi Apr 05 '19 at 16:24
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    Whatever the distinction might be, @Richard is providing a useful comment because your other question is identical to this one apart from the substitution of "condensed" for "consistent." We can therefore expect that answers to one will be highly relevant to the other--probably to the point of being exact duplicates. – whuber Apr 05 '19 at 16:30
  • @whuber, thank you for the feedback. With all due respect, I do not think so. Yet, if I found out that the answers are somehow similar, I would delete one of the questions. – M.Hossein Rahimi Apr 05 '19 at 16:49
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    @HosseinRahimi, I think the point is that once you understand the meanings of parametric vs non-p, you'll be able to see why any given algorithm would be classified as 1 or the other. So really, you just need your 1st question to clarify the distinction. If you're wondering something about how these knn variants work, you should edit your Q to clarify that. Even then, 1 question would probably be adequate to cover both condensed & consistent. – gung - Reinstate Monica Apr 05 '19 at 17:33

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