Variational Auto Encoder (VAE) - Theory

VAE's are a mix between VI and Auto Encoders NN. They are used mainly for generating new data. In this video we will outline the theory behind the original paper, including looking at regular Auto Encoders, Variational Inference, and how they mix together to create VAE.
Original Paper (Kingma & Welling 2014): arxiv.org/pdf/1312.6114
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“VI in R” Course Outline:
Administration
* Administration
Intro
* Intuition - what is VI?
* Notebook - Intuition
* Origin, Outline, Context
KL Divergence
* KL Introduction
* KL - Extra Intuition
* Notebook - KL - Exercises
* Notebook - KL - Additional Topics
* KL vs. Other Metrics
VI vs. ML
* VI (using KL) vs. Maximum Likelihood
ELBO & “Mean Field”
* ELBO
* “Mean Field” Approximation
Coordinate Ascent VI (CAVI)
* Coordinate Ascent VI (CAVI)
* Functional Derivative & Euler-Lagrange Equation
* CAVI - Toy Example
* CAVI - Bayesian GMM Example
* Notebook - Normal-Gamma Conjugate Prior
* Notebook - Bayesian GMM - Unknown Precision
* Notebook - Image Denoising (Ising Model)
Exponential Family
* CAVI for the Exponential Family
* Conjugacy in the Exponential Family
* Notebook - Latent Dirichlet Allocations Example
VI vs. EM
* VI vs. EM
Stochastic VI / Advanced VI
* SVI - Review
* SVI for Exponential Family
* Automatic Differentiation VI (ADVI)
* Notebook - ADVI Example (using STAN)
* Black Box VI (BBVI)
* Notebook - BBVI Example
Expectation Propagation
* Forward vs. Reverse KL
* Expectation Propagation
Variational Auto Encoder
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Intro/Outro Music: Dreamer - by Johny Grimes
• Johny Grimes - Dreamer

[@paedrufernando2351]

@6:10 VI starts.The run down was awesome..puts eveything into perspective

[@user-qt5xd9lk5j]

Fantastic video! This effectively resolved my queries.

[@evgeniyazarov4230]

Great explanation! The two ways of looking on the loss function is insightful

[@123sendodo4]

Very clear and useful information!

[@shounakdesai4283]

awesome video.

[@evaggelosantypas5139]

Hey great video, thank you for your efforts. Is it possible to get your slides ?

[@MeerkatStatistics]

Thanks. The slides are offered on my website meerkatstatistics.com/courses/variational-inference-in-r/lessons/variational-auto-encoder-theory/ for members. Please consider subscribing to also support this channel.

[@evaggelosantypas5139]

@@MeerkatStatistics ok thnx

[@minuklee6735]

Thank you for the awesome video! I have a question @11:35. I don't clearly understand why g_\theta takes x. am I correct that it does not take x if g_\theta is a gaussian distribution? as it will just be g_\theta(\epsilon) = \sigma*\epsilon + \mu (where \sigma and \mu comes from \theta)??
Again, I appreciate your video a lot!

[@MeerkatStatistics]

Although not explicitly denoted, q(z) is also dependent on the data. This is why g(theta) will usually also be depending on x. I didn't want to write q(z|x) as in the paper, because it is not a posterior, but rather a distribution who's parameters you tweak until it reaches the true posterior p(z|x).
I have a simple example (for the CAVI algorithm) on my website (for members) meerkatstatistics.com/courses/variational-inference-in-r/lessons/cavi-toy-example/
and also a bit more elaborate example free on TH-cam th-cam.com/video/8DzIPZnZ12k/w-d-xo.htmlsi=8Un505QqOEtij9XV - in both cases you'll see a q(z) that is a Gaussian, but whose parameters depend on the data x.

[@marcospiotto9755]

What is the difference between denoting p_theta (x|z) vs p(x|z,theta) ?

[@MeerkatStatistics]

I think "subscript" theta is just the standard way of denoting when we are optimizing theta, that is we are changing theta. While "conditioned on" theta is usually when the theta's are given. Also note that the subscript theta refers to the NN parameters, while often the "conditioned on" refers to distributional parameters. I don't think these are rules set in stone, though, and I'm not an expert in notation. As long as you understand what's going on - that's the important part.

[@marcospiotto9755]

@@MeerkatStatistics got it, thanks!

[@stazizov]

Could you please tell me if there is a mistake in the notation? @8:26 z_{i} = z_{l}?

[@MeerkatStatistics]

Hey, yes of course. Sorry for the typo.

[@stazizov]

​@@MeerkatStatistics Thank you so much) Great video!!! 🔥