<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>

CC BY-SA 4.0
2020-02-04T09:56:06.393Z
2020-02-04T09:56:06.393Z
jkm
<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>

CC BY-SA 4.0
2020-02-04T09:19:29.103Z
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.
razvanc92
<neural-networks><machine-learning><math><autoencoders><variational-autoencoder>
What is the mean in the variational auto-encoder?
Dan D.
# 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.  

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## 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'.


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