Variational AutoEncoder VAE

Tags: #machine learning #VAE

Equation

logpθ(x)=Eqϕ(z|x)[logpθ(x)]=Eqϕ(z|x)[logpθ(x,z)pθ(z|x)]=Eqϕ(z|x)[log[pθ(x,z)qϕ(z|x)×qϕ(z|x)pθ(z|x)]]=Eqϕ(z|x)[log[pθ(x,z)qϕ(z|x)]]+DKL(qϕ(z|x)||pθ(z|x))

Latex Code

1
2
3
4
                         \log p_{\theta}(x)=\mathbb{E}_{q_{\phi}(z|x)}[\log p_{\theta}(x)] \\
=\mathbb{E}_{q_{\phi}(z|x)}[\log \frac{p_{\theta}(x,z)}{p_{\theta}(z|x)}] \\
=\mathbb{E}_{q_{\phi}(z|x)}[\log [\frac{p_{\theta}(x,z)}{q_{\phi}(z|x)} \times \frac{q_{\phi}(z|x)}{p_{\theta}(z|x)}]] \\
=\mathbb{E}_{q_{\phi}(z|x)}[\log [\frac{p_{\theta}(x,z)}{q_{\phi}(z|x)} ]] +D_{KL}(q_{\phi}(z|x) || p_{\theta}(z|x))\\

Have Fun

Let's Vote for the Most Difficult Equation!

Introduction

Estimating the Log-likelihood and Posterior

Equation



Latex Code

1
2
3
4
\log p_{\theta}(x)=\mathbb{E}_{q_{\phi}(z|x)}[\log p_{\theta}(x)] \\
=\mathbb{E}_{q_{\phi}(z|x)}[\log \frac{p_{\theta}(x,z)}{p_{\theta}(z|x)}] \\
=\mathbb{E}_{q_{\phi}(z|x)}[\log [\frac{p_{\theta}(x,z)}{q_{\phi}(z|x)} \times \frac{q_{\phi}(z|x)}{p_{\theta}(z|x)}]] \\
=\mathbb{E}_{q_{\phi}(z|x)}[\log [\frac{p_{\theta}(x,z)}{q_{\phi}(z|x)} ]] +D_{KL}(q_{\phi}(z|x) || p_{\theta}(z|x))\\

Explanation

Evidence Lower Bound

Equation



Latex Code

1
\mathbb{L}_{\theta,\phi}(\mathbf{x})=\mathbb{E}_{q_{\phi}(\mathbf{z}|\mathbf{x})}[\log p_{\theta}(\mathbf{x},\mathbf{z})-\log q_{\phi}(\mathbf{z}|\mathbf{x}) ]

Explanation

Reparameterization trick

Equation


Latex Code
1
z = \mu + \epsilon \cdot \sigma

Explanation

VAE latex code is illustrated above. See paper for more details Auto-Encoding Variational Bayes

Related Documents

Related Videos

Comments

Write Your Comment

Upload Pictures and Videos