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/...
The first and only Variational Inference (VI) course on-line!
Become a member and get full access to this online course:
meerkatstatist...
** 🎉 Special KZbin 60% Discount on Yearly Plan - valid for the 1st 100 subscribers; Voucher code: First100 🎉 **
“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
Why become a member?
All video content
Extra material (notebooks)
Access to code and notes
Community Discussion
No Ads
Support the Creator ❤️
VI (restricted) playlist: bit.ly/389QSm1
If you’re looking for statistical consultation, someone to work on interesting projects, or give training workshops, visit my website meerkatstatist... or contact me directly at [e-mail]
~~~~~ SUPPORT ~~~~~
Paypal me: paypal.me/Meer...
~~~~~~~~~~~~~~~~~
Intro/Outro Music: Dreamer - by Johny Grimes
• Johny Grimes - Dreamer

[@paedrufernando2351]

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

[@evgeniyazarov4230]

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

[@YICHAOCAI]

Fantastic video! This effectively resolved my queries.

[@Omsip123]

Thanks for your efforts, very well explained

[@nabinbk1065]

great, thank you so much

[@123sendodo4]

Very clear and useful information!

[@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!!! 🔥

[@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 KZbin kzbin.info/www/bejne/bnXdeoOQo79kaM0si=8Un505QqOEtij9XV - in both cases you'll see a q(z) that is a Gaussian, but whose parameters depend on the data x.

[@tassangherman]

You're awesome !

[@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

[@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!

[@SpringhallBess-g1b]

Lindgren Expressway

[@LauraJohnson-f3v]

Price Tunnel

[@JeffreyParsons-h5u]

Peyton Place

[@BackBaird-y8l]

Mertie Flat