From 048c4a82b556496594175a3bd42242e0832820fc Mon Sep 17 00:00:00 2001
From: Riku-Laine <28960190+Riku-Laine@users.noreply.github.com>
Date: Wed, 12 Jun 2019 15:22:54 +0300
Subject: [PATCH] Comments about beta_z=0 and epsilon
---
analysis_and_scripts/notes.tex | 12 ++++++++----
1 file changed, 8 insertions(+), 4 deletions(-)
diff --git a/analysis_and_scripts/notes.tex b/analysis_and_scripts/notes.tex
index cb4dbcd..f869912 100644
--- a/analysis_and_scripts/notes.tex
+++ b/analysis_and_scripts/notes.tex
@@ -67,6 +67,8 @@
\maketitle
+\section*{Contents}
+
\tableofcontents
\begin{abstract}
@@ -317,27 +319,29 @@ Causal model, ep & 0.001074039 & 0.0414928\\
\subsection{$\beta_Z=0$ and data generated with unobservables.}
-If we assign $\beta_Z=0$, almost all failure rates drop to zero in the interval 0.1, ..., 0.3 but the human evaluation failure rate. Figures are drawn in Figures \ref{fig:betaZ_1_5} and \ref{fig:betaZ_0}.
+If we assign $\beta_Z=0$, almost all failure rates drop to zero in the interval 0.1, ..., 0.3 but the human evaluation failure rate. Results are presented in Figures \ref{fig:betaZ_1_5} and \ref{fig:betaZ_0}.
+
+The differences between figures \ref{fig:results_without_Z} and \ref{fig:betaZ_0} could be explained in the slight difference in the data generating process, namely the effect of $W$ or $\epsilon$. The effect of adding $\epsilon$ (noise to the decisions) is further explored in section \ref{sec:epsilon}.
\begin{figure}[H]
\centering
\begin{subfigure}[b]{0.5\textwidth}
\includegraphics[width=\textwidth]{sl_with_Z_4iter_betaZ_1_5}
- \caption{$\beta_Z=1.5$}
+ \caption{With unobservables, $\beta_Z$ set to 1.5 in algorithm \ref{alg:data_with_Z}.}
\label{fig:betaZ_1_5}
\end{subfigure}
~ %add desired spacing between images, e. g. ~, \quad, \qquad, \hfill etc.
%(or a blank line to force the subfigure onto a new line)
\begin{subfigure}[b]{0.5\textwidth}
\includegraphics[width=\textwidth]{sl_with_Z_4iter_beta0}
- \caption{$\beta_Z=0$}
+ \caption{With unobservables, $\beta_Z$ set to 0 in algorithm \ref{alg:data_with_Z}.}
\label{fig:betaZ_0}
\end{subfigure}
\caption{Effect of $\beta_z$. Failure rate vs. acceptance rate with unobservables in the data (see algorithm \ref{alg:data_with_Z}). Logistic regression was trained on labeled training data. Results from algorithm \ref{alg:perf_comp} with $N_{iter}=4$.}
\label{fig:betaZ_comp}
\end{figure}
-\subsection{Noise added to the decision and data generated without unobservables}
+\subsection{Noise added to the decision and data generated without unobservables} \label{sec:epsilon}
In this part, Gaussian noise with zero mean and 0.1 variance was added to the probabilities $P(Y=0|X=x)$ after sampling Y but before ordering the observations in line 5 of algorithm \ref{alg:data_without_Z}. Results are presented in Figure \ref{fig:sigma_figure}.
--
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