From 3ae280523338c3c54566bb47e48987ed3e7207b5 Mon Sep 17 00:00:00 2001 From: Felix Divo <4403130+felixdivo@users.noreply.github.com> Date: Tue, 6 Dec 2022 17:32:48 +0100 Subject: [PATCH] Tiny language fix --- flow/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/flow/index.md b/flow/index.md index c61b1ef..cf4c684 100644 --- a/flow/index.md +++ b/flow/index.md @@ -17,7 +17,7 @@ In this section, we introduce normalizing flows: a type of method that combines In normalizing flows, we wish to map simple distributions (easy to sample and evaluate densities) to complex ones (learned via data). The change of variables formula describe how to evaluate densities of a random variable that is a deterministic transformation from another variable. -**Change of Variables**: $$Z$$ and $$X$$ be random variables which are related by a mapping $$f: \mathbb{R}^n \to \mathbb{R}^n$$ such that $$X = f(Z)$$ and $$Z = f^{-1}(X)$$. Then +**Change of Variables**: Let $$Z$$ and $$X$$ be random variables which are related by a mapping $$f: \mathbb{R}^n \to \mathbb{R}^n$$ such that $$X = f(Z)$$ and $$Z = f^{-1}(X)$$. Then {% math %}p_X(\mathbb{x}) = p_Z(f^{-1}(\mathbb{x})) \left\vert \text{det}\left(\frac{\partial f^{-1}(\mathbb{x})}{\partial \mathbb{x}}\right) \right\vert