Answers.Body: <p>When reading books and articles about machine learning or artificial intelligence in general, one can safely assume that the word &quot;model&quot; is used as an abbreviation for &quot;<a href="https://en.wikipedia.org/wiki/Statistical_model" rel="nofollow noreferrer">Statistical model</a>&quot;. Surprisingly many books skip
  the job of providing a definition for it, allegedly cause the authors consider it a sort of primitive concept, i.e. they leave the hot potato there hoping that the readers are already familiar with statistics and data science (special mention in this regard to <a href="http://users.isr.ist.utl.pt/%7Ewurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf" rel="nofollow noreferrer">Pattern Recognition and Machine Learning </a>, big classic in which Bishop just use the word from the very beginning without any concern). But in general the closest entity associated with statistical model is just a mathematical function.</p>
  <p>Here some references to point that out:</p>
  <ul>
  <li><a href="https://link.springer.com/book/10.1007/978-1-4614-6849-3" rel="nofollow noreferrer">Applied predictive Modeling (Max Kuhn, Kjell Johnson, 2013)</a>:</li>
  </ul>
  <p>&quot;Predictive modeling: the process of developing a <strong>mathematical tool or model</strong>
  that generates an accurate prediction&quot; [page 2, Introduction]</p>
  <ul>
  <li><a href="https://www.ime.unicamp.br/%7Edias/Intoduction%20to%20Statistical%20Learning.pdf" rel="nofollow noreferrer">An Introduction to Statistical Learning (G. James, D. Witten, T. Hastie, R. Tibshirani, 2021)</a></li>
  </ul>
  <p>&quot;Broadly speaking, supervised statistical learning involves building a <strong>statistical model</strong> for predicting, or estimating, an output based on one or more inputs.&quot; [page 1 Introduction]</p>
  <ul>
  <li><a href="https://www.deeplearningbook.org/" rel="nofollow noreferrer">Deep Learning (I. Goodfellow, Y. Bengio, A. Courville, 2016)</a></li>
  </ul>
  <p>&quot;The quintessential example of a <strong>deep learning model</strong> is the feedforward deep
  network, or multilayer perceptron (MLP). A multilayer perceptron is just a
  <strong>mathematical function</strong> mapping some set of input values to output values.&quot; [page 7 Introduction]</p>
  <p>If you're not satisfied and you're looking for a dense, algebraic definition of statistical model, you can check <a href="http://www.stat.uchicago.edu/%7Epmcc/pubs/AOS023.pdf" rel="nofollow noreferrer">What is a statistical model?</a> by Peter McCullagh. I won't try to explain the definition in the answer cause honestly it's really though and it goes beyond my math skills.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-02-07T18:56:27.560Z
Answers.LastActivityDate: 2022-02-07T18:56:27.560Z
Answers.UserDisplayName: Edoardo Guerriero
Body: <p>What is the definition of a &quot;model&quot; in the discussion of a neural network?</p>
  <p>I need a canonical definition.</p>
  <p>Can you please supply me with a definition along with a reference from any book or research article?</p>
  
Tags: <neural-networks><machine-learning><models>
Title: What is the definition of a "model"?
UserDisplayName: user366312
ThreadText: # What is the definition of a "model"?
  
  (Asked by: username_0 on 2022-02-07)
  
  What is the definition of a "model" in the discussion of a neural network?
  
  I need a canonical definition.
  
  Can you please supply me with a definition along with a reference from any book or research article?
  
  **Tags:** neural-networks, machine-learning, models
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2022-02-07. Score: 3 | Accepted answer
  
  When reading books and articles about machine learning or artificial intelligence in general, one can safely assume that the word "model" is used as an abbreviation for "[Statistical model](https://en.wikipedia.org/wiki/Statistical_model)". Surprisingly many books skip
  the job of providing a definition for it, allegedly cause the authors consider it a sort of primitive concept, i.e. they leave the hot potato there hoping that the readers are already familiar with statistics and data science (special mention in this regard to [Pattern Recognition and Machine Learning](http://users.isr.ist.utl.pt/%7Ewurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf) , big classic in which Bishop just use the word from the very beginning without any concern). But in general the closest entity associated with statistical model is just a mathematical function.
  
  Here some references to point that out:
  
  * [Applied predictive Modeling (Max Kuhn, Kjell Johnson, 2013)](https://link.springer.com/book/10.1007/978-1-4614-6849-3):
  
  "Predictive modeling: the process of developing a **mathematical tool or model**
  that generates an accurate prediction" [page 2, Introduction]
  
  * [An Introduction to Statistical Learning (G. James, D. Witten, T. Hastie, R. Tibshirani, 2021)](https://www.ime.unicamp.br/%7Edias/Intoduction%20to%20Statistical%20Learning.pdf)
  
  "Broadly speaking, supervised statistical learning involves building a **statistical model** for predicting, or estimating, an output based on one or more inputs." [page 1 Introduction]
  
  * [Deep Learning (I. Goodfellow, Y. Bengio, A. Courville, 2016)](https://www.deeplearningbook.org/)
  
  "The quintessential example of a **deep learning model** is the feedforward deep
  network, or multilayer perceptron (MLP). A multilayer perceptron is just a
  **mathematical function** mapping some set of input values to output values." [page 7 Introduction]
  
  If you're not satisfied and you're looking for a dense, algebraic definition of statistical model, you can check [What is a statistical model?](http://www.stat.uchicago.edu/%7Epmcc/pubs/AOS023.pdf) by Peter McCullagh. I won't try to explain the definition in the answer cause honestly it's really though and it goes beyond my math skills.
  
  
  ---
  
  