Body: <p>Assume we are given a training dataset <span class="math-container">$D = \{ (x_i, y_i)\}_{i=1}^{N}$</span>.</p>
  
  <p>My question is: which is better?</p>
  
  <ol>
  <li>A multivariate regression with basis expansion with <em>independent matrix</em> <span class="math-container">$X$</span> and <em>dependent matrix</em> <span class="math-container">$Y$</span>, such that <span class="math-container">$X \in K; K \subset \mathbb R^n$</span> and <span class="math-container">$Y \in \mathbb R^m$</span> with training data <span class="math-container">$D$</span>.</li>
  </ol>
  
  <p><em>Or</em></p>
  
  <ol start="2">
  <li>A neural network which takes <span class="math-container">$n$</span> <em>input variables</em> and returns <span class="math-container">$m$</span> <em>output</em> with training data <span class="math-container">$D$</span></li>
  </ol>
  
  <blockquote>
    <p>Without a doubt, the multivariate regression option is better with its basis polynomials because it can adapt any curve required in any dimension and doesn't need a large number of datasets than neural networks. Then, why neural networks are used more than multivariate regression?</p>
  </blockquote>
  
  <p><strong>Note: Prefer explaining the mechanism of neural network used as regression in your answers. To help us know the degree of flexibility of both.</strong></p>
  
  <p><strong>Edit: You may prefer choosing your own loss function in case you need.</strong></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-24T11:10:22.577Z
Comments.Text: This question is impossible to answer. There is no objective 'better' solution unless you know more about the shape of the data. It's like asking "what's better, a fork or a spoon?" -- depends on whether you want to eat soup or steak.
Comments.UserDisplayName: Oliver Mason
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-03-24T11:41:18.103Z
Comments.Text: @OliverMason You may explain in which case which is better.
Comments.UserDisplayName: Abhas Kumar Sinha
Tags: <neural-networks><comparison><regression>
Title: Which one is better: multivariate regression with basis expansion or neural networks?
UserDisplayName: Abhas Kumar Sinha
ThreadText: # Which one is better: multivariate regression with basis expansion or neural networks?
  
  (Asked by: username_0 on 2020-03-23)
  
  Assume we are given a training dataset $D = \{ (x\_i, y\_i)\}\_{i=1}^{N}$.
  
  My question is: which is better?
  
  1. A multivariate regression with basis expansion with *independent matrix* $X$ and *dependent matrix* $Y$, such that $X \in K; K \subset \mathbb R^n$ and $Y \in \mathbb R^m$ with training data $D$.
  
  *Or*
  
  2. A neural network which takes $n$ *input variables* and returns $m$ *output* with training data $D$
  
  > Without a doubt, the multivariate regression option is better with its basis polynomials because it can adapt any curve required in any dimension and doesn't need a large number of datasets than neural networks. Then, why neural networks are used more than multivariate regression?
  
  **Note: Prefer explaining the mechanism of neural network used as regression in your answers. To help us know the degree of flexibility of both.**
  
  **Edit: You may prefer choosing your own loss function in case you need.**
  
  **Tags:** neural-networks, comparison, regression
  
  > **Comments:**
  > **username_1**: This question is impossible to answer. There is no objective 'better' solution unless you know more about the shape of the data. It's like asking "what's better, a fork or a spoon?" -- depends on whether you want to eat soup or steak.  
  > **username_0**: @username_1 You may explain in which case which is better.  
  
  ---
  
  ## 0 answers
  
  