From 37e3cc52803dbaffd755be751db2fd11e8ccb333 Mon Sep 17 00:00:00 2001 From: Ray Kim Date: Tue, 4 Jun 2024 22:52:08 +0100 Subject: [PATCH] fix docs --- docs/src/elbo/overview.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/docs/src/elbo/overview.md b/docs/src/elbo/overview.md index 05c6d425..4afac4db 100644 --- a/docs/src/elbo/overview.md +++ b/docs/src/elbo/overview.md @@ -10,17 +10,18 @@ More generally, they aim to solve the following problem: ``` where $$\mathcal{Q}$$ is some family of distributions, often called the variational family. Since the target distribution ``\pi`` is intractable in general, the KL divergence is also intractable. -Instead, the ELBO maximization strategy maximizes a surrogate objective, the *ELBO*, which serves as a lower bound to the KL. ELBO is defined as +Instead, the ELBO maximization strategy maximizes a surrogate objective, the *ELBO*: ```math \mathrm{ELBO}\left(q\right) \triangleq \mathbb{E}_{\theta \sim q} \log \pi\left(\theta\right) + \mathbb{H}\left(q\right), ``` -which can be readily estimated through various strategies. -Overall, we solve the problem +which serves as a lower bound to the KL. +The ELBO and its gradient can be readily estimated through various strategies. +Overall, ELBO maximization algorithms aim to solve the problem: ```math \mathrm{maximize}_{q \in \mathcal{Q}}\quad \mathrm{ELBO}\left(q\right). ``` -Multiple ways to solve this problem exist, leading to different variational inference algorithms. +Multiple ways to solve this problem exist, each leading to a different variational inference algorithm. ## Algorithms Currently, `AdvancedVI` only provides the approach known as black-box variational inference (also known as Monte Carlo VI, Stochastic Gradient VI).