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This table is mentioned in What algorithms need feature scaling, beside from SVM?

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It says that linear regression, logistic regression, and naive bayes are parametric, while KNN, decision trees, random forests, adaboost, and neural networks are not. What does parametric mean here? Don't all these models use parameters that influence the predictions?

tomjavg
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  • So I am not aware of an exact definition, but I would classify it as a fixed set of parameters vs arbitrary number. ( nb Murphy's book referred to in https://stats.stackexchange.com/questions/268638/what-exactly-is-the-difference-between-a-parametric-and-non-parametric-model - defines neural nets are parametric!! - I would define linear regression as parametric, but polynomial regression as nonparametric – seanv507 Apr 01 '22 at 17:25
  • @seanv507 Polynomial regression is a linear regression. Could you please explain your comment more? – Dave Apr 01 '22 at 17:39
  • linear regression operates over a fixed set of inputs. eg (1,x). a polynomial regre – seanv507 Apr 01 '22 at 20:21
  • What I meant was that a fixed order polynomial regression is parametric, but when you consider the infinite family of polynomials - quadratic, cubics... it is nonparametric ( you need increasing numbers of parameters as you increase the order you consider).[ and similarly I would define any fixed neural network architecture as parametric, but as soon as we entertain arbitrary numbers of neurons, layers etc it is nonparametric] – seanv507 Apr 01 '22 at 20:27

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