<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>

CC BY-SA 4.0
2020-03-24T11:10:22.577Z
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.
Oliver Mason
CC BY-SA 4.0
2020-03-24T11:41:18.103Z
@OliverMason You may explain in which case which is better.
Abhas Kumar Sinha
<neural-networks><comparison><regression>
Which one is better: multivariate regression with basis expansion or neural networks?
Abhas Kumar Sinha
# 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**: @OliverMason You may explain in which case which is better.  

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## 0 answers

