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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.

And many other methods of determination, though the problem is none of them can helo ones to determine if a certain hypothetical method is parametric or not. (For instance, why k-means' number of parameters are constant but KNN is variable or basically what do we call a parameter and what we do not?)

Richard Hardy
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  • As far as I am aware these are NOT definitions that align with the traditional, widely recognized definitions of nonparametric and parametric which come from statistics. – LSC Mar 14 '19 at 18:11
  • Thank you @LSC for taking time, answering my question. Basically, I am looking for a method to determine if a learning method is parametric or not. – M.Hossein Rahimi Mar 14 '19 at 18:16
  • Is there a particular method you're wondering about? – LSC Mar 14 '19 at 20:58

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