Answers.Body: <p>Kind of neither, although leaning towards the first definition of the Mean as a simple average of values.</p>
  
  <p>It's a <strong>distribution parameter</strong> of the Gaussian, so it's the <em>expected</em> average of samples as the number of samples approaches infinity.</p>
  
  <p>The distrinction is that you could draw three samples, -2, 0 and -1, from a Standard Normal - the mean of samples would be -1, but the <em>distribution</em> mean is still 0.</p>
  
  <p>From a network architecture PoV, it's a learnable transformation applied on top of samples from a Standard Normal, so you only need to learn the transformation and get sampling for 'free'.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-02-04T09:56:06.393Z
Answers.LastActivityDate: 2020-02-04T09:56:06.393Z
Answers.UserDisplayName: jkm
Body: <p>Here's a diagram of a variational auto-encoder.</p>
  
  <p><a href="https://i.sstatic.net/NVEHA.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NVEHA.png" alt="enter image description here"></a></p>
  
  <p>There are 2 nodes before the sample (encoding vector). One is the <em>mean</em>, one is the <em>standard deviation</em>. The <em>mean</em> one is confusing. </p>
  
  <p>Is it the mean of values or is it the mean deviation?</p>
  
  <p><span class="math-container">$$\text{mean} = \dfrac{X_i+..+X_n}{N}$$</span></p>
  
  <p><span class="math-container">$$\text{mean deviation} = \dfrac{[X_i|+..+|X_n|}{N}$$</span></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-02-04T09:19:29.103Z
Comments.Text: Hello, I'm no expert but I assume is the Mean of the values. Usually you need the mean and the standard deviation to describe a distribution.
Comments.UserDisplayName: razvanc92
Tags: <neural-networks><machine-learning><math><autoencoders><variational-autoencoder>
Title: What is the mean in the variational auto-encoder?
UserDisplayName: Dan D.
ThreadText: # What is the mean in the variational auto-encoder?
  
  (Asked by: username_0 on 2020-02-04)
  
  Here's a diagram of a variational auto-encoder.
  
  [![enter image description here](https://i.sstatic.net/NVEHA.png)](https://i.sstatic.net/NVEHA.png)
  
  There are 2 nodes before the sample (encoding vector). One is the *mean*, one is the *standard deviation*. The *mean* one is confusing.
  
  Is it the mean of values or is it the mean deviation?
  
  $$\text{mean} = \dfrac{X\_i+..+X\_n}{N}$$
  
  $$\text{mean deviation} = \dfrac{[X\_i|+..+|X\_n|}{N}$$
  
  **Tags:** neural-networks, machine-learning, math, autoencoders, variational-autoencoder
  
  > **Comments:**
  > **username_1**: Hello, I'm no expert but I assume is the Mean of the values. Usually you need the mean and the standard deviation to describe a distribution.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2020-02-04. Score: 1 | Accepted answer
  
  Kind of neither, although leaning towards the first definition of the Mean as a simple average of values.
  
  It's a **distribution parameter** of the Gaussian, so it's the *expected* average of samples as the number of samples approaches infinity.
  
  The distrinction is that you could draw three samples, -2, 0 and -1, from a Standard Normal - the mean of samples would be -1, but the *distribution* mean is still 0.
  
  From a network architecture PoV, it's a learnable transformation applied on top of samples from a Standard Normal, so you only need to learn the transformation and get sampling for 'free'.
  
  
  ---
  
  