From 5857cc2cbc27a145e5760092832e7bf584de1e5f Mon Sep 17 00:00:00 2001
From: Michael Mathioudakis <mmathioudakis@gmail.com>
Date: Wed, 29 May 2019 10:11:21 +0300
Subject: [PATCH] alternative empirical formula
---
paper/sl.tex | 9 +++++++++
1 file changed, 9 insertions(+)
diff --git a/paper/sl.tex b/paper/sl.tex
index 51511af..d77c6c1 100755
--- a/paper/sl.tex
+++ b/paper/sl.tex
@@ -38,6 +38,7 @@
\newcommand{\ourtitle}{A Causal Approach for Selective Labels}
\input{macros}
+\usepackage{chato-notes}
\title{\ourtitle}
@@ -173,6 +174,14 @@ Alternatively, we can have an empirical measure \empiricalPerformance of perform
\label{eqn:gp}
\end{equation}
+\note[MM]{
+ Use the following for empirical performance?
+ \begin{equation}
+\empiricalPerformance = \frac{1}{\datasize} \sum_{(\featuresValue, \outcomeValue)\in\dataset} \score{\featuresValue} \indicator{F(\featuresValue) < r}
+\label{eqn:gp}
+\end{equation}
+}
+
\subsection{Comments}
Roughly speaking, the above formulas should work well if `bail' cases (\decision = 1) cover well the area spanned by the observed features of defendants -- i.e., we do not have large areas of \features with no or too few bail cases.
--
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