Answers.Body: <p>I provided some <a href="https://programming-review.com/machine-learning/parametric-vs-nonparametric/" rel="nofollow noreferrer">details</a> but the most important excerpt is from Stuart Russell and Peter Norvig's <a href="https://aima.cs.berkeley.edu/" rel="nofollow noreferrer">AIMA</a> book:</p>
  <p><em>A learning model that summarizes data with a set of parameters of fixed size (independent of the number of training examples) is called a parametric model. No matter how much data you throw at a parametric model, it won’t change its mind about how many parameters it needs.</em></p>
  <p>For nonparametric models ask yourself a question: What is the number of parameters of the decision tree?</p>
  <p>As the decision tree is an example of nonparametric model the number of parameters in a decision tree depends on the quantity of the data. The more data we have means more parameters.</p>
  
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Answers.Text: What are the parameters of a decision tree?
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Answers.Text: Criterion such as Gini, and max deep are consider as hyper parameters, DT do not have weights and biases in the same way as neural networks or other linear models and DT are considered as non parametric models.
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Answers.Text: I didn't ask about hyperparameters, I asked about "parameters". The distinction between parametric and non-parametric models boils down to whether the number of parameters varies with data. So, in a decision tree what qualifies as a parameter? If we don't have a definition of what is a "parameter" in a decision tree, then statements like "the number of parameters in a decision tree vary/grow with data" are meaningless. The parameters of a decision tree could be the regions of the tree and these indeed can vary with different amount of data.
Answers.UserDisplayName: Antonios Sarikas
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Answers.Text: So you would like to say that  DT is a parametric model.  LOL.
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Answers.Text: Apologize, I realized that my second comment does not make sense and I will remove it. Nevertheless, is there any definition of what a parameter, **not hyperparameter** is in a decision tree?
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Answers.Body: <h3>Parametric Methods</h3>
  <p>A parametric approach (Regression, Linear Support Vector Machines) has a fixed number of parameters and it makes a lot of assumptions about the data. This is because they are used for known data distributions, i.e., it makes a lot of presumptions about the data.</p>
  <h3>Non-Parametric Methods</h3>
  <p>A non-parametric approach (k-Nearest Neighbours, Decision Trees) has a flexible number of parameters, there are no presumptions about the data distribution. The model tries to &quot;explore&quot; the distribution and thus has a flexible number of parameters.</p>
  <h3>Comparision</h3>
  <p>Comparatively speaking, parametric approaches are computationally faster and have more statistical power when compared to non-parametric methods.</p>
  
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Body: <p>A model can be classified as parametric or non-parametric. How are models classified as parametric and non-parametric models? What is the difference between the two approaches?</p>
  
Tags: <machine-learning><comparison><definitions><models>
Title: What is the difference between parametric and non-parametric models?
UserDisplayName: Legend
ThreadText: # What is the difference between parametric and non-parametric models?
  
  (Asked by: username_0 on 2020-09-26)
  
  A model can be classified as parametric or non-parametric. How are models classified as parametric and non-parametric models? What is the difference between the two approaches?
  
  **Tags:** machine-learning, comparison, definitions, models
  
  ---
  
  ## 2 answers
  
  ### Answer by username_3 on 2020-09-27. Score: 8 | Accepted answer
  
  ### Parametric Methods
  
  A parametric approach (Regression, Linear Support Vector Machines) has a fixed number of parameters and it makes a lot of assumptions about the data. This is because they are used for known data distributions, i.e., it makes a lot of presumptions about the data.
  
  ### Non-Parametric Methods
  
  A non-parametric approach (k-Nearest Neighbours, Decision Trees) has a flexible number of parameters, there are no presumptions about the data distribution. The model tries to "explore" the distribution and thus has a flexible number of parameters.
  
  ### Comparision
  
  Comparatively speaking, parametric approaches are computationally faster and have more statistical power when compared to non-parametric methods.
  
  
  ---
  
  ### Answer by username_1 on 2023-03-27. Score: 0
  
  I provided some [details](https://programming-review.com/machine-learning/parametric-vs-nonparametric/) but the most important excerpt is from Stuart Russell and Peter Norvig's [AIMA](https://aima.cs.berkeley.edu/) book:
  
  *A learning model that summarizes data with a set of parameters of fixed size (independent of the number of training examples) is called a parametric model. No matter how much data you throw at a parametric model, it won’t change its mind about how many parameters it needs.*
  
  For nonparametric models ask yourself a question: What is the number of parameters of the decision tree?
  
  As the decision tree is an example of nonparametric model the number of parameters in a decision tree depends on the quantity of the data. The more data we have means more parameters.
  
  > **Comments:**
  > **username_2**: What are the parameters of a decision tree?  
  > **username_1**: Criterion such as Gini, and max deep are consider as hyper parameters, DT do not have weights and biases in the same way as neural networks or other linear models and DT are considered as non parametric models.  
  > **username_2**: I didn't ask about hyperparameters, I asked about "parameters". The distinction between parametric and non-parametric models boils down to whether the number of parameters varies with data. So, in a decision tree what qualifies as a parameter? If we don't have a definition of what is a "parameter" in a decision tree, then statements like "the number of parameters in a decision tree vary/grow with data" are meaningless. The parameters of a decision tree could be the regions of the tree and these indeed can vary with different amount of data.  
  > **username_1**: So you would like to say that  DT is a parametric model.  LOL.  
  > **username_2**: Apologize, I realized that my second comment does not make sense and I will remove it. Nevertheless, is there any definition of what a parameter, **not hyperparameter** is in a decision tree?  
  
  ---
  
  