diff --git a/content/method/method.tex b/content/method/method.tex index 04e35d8..673c343 100644 --- a/content/method/method.tex +++ b/content/method/method.tex @@ -695,7 +695,7 @@ of both classes. \begin{proposition}[Gradient balance] \label{prop:gradient-balance} Let $\mathcal{F}$ be any distribution family whose CDF estimator is translation-invariant, -meaning $\hat{F}_k(t\,;\,\mathbf{s}+\delta\mathbf{1}) = \hat{F}_k(t-\delta\,;\,\mathbf{s})$ +meaning $\hat{F}_k(t\,;\,\mathbf{s}+\delta) = \hat{F}_k(t-\delta\,;\,\mathbf{s})$ for all $\delta \in \mathbb{R}$. Then for any batch $\mathcal{B} = \mathcal{B}_0 \cup \mathcal{B}_1$: \begin{equation} \sum_{\mathbf{x}_i \in \mathcal{B}_1}