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It's done first draft wahoo

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Aner Zakobar
2026-08-31 23:58:01 +03:00
parent 275e29bde0
commit d217b2356a
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content/appendixs/appendix_kde_grad.tex
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@@ -117,7 +117,7 @@ then multiplying numerator and denominator by $\sigma_0'(\tau - f_\theta(\mathbf
\paragraph{Efficient computation via the sigmoid identity.}
Direct evaluation of \eqref{eq:kde-grad-tau} requires computing $\sigma_0'$ for every
point — potentially unstable when a point is far from $\tau$. For the sigmoid kernel,
point, potentially unstable when a point is far from $\tau$. For the sigmoid kernel,
the identity
\begin{equation}
content/appendixs/appendix_kde_sigmoid.tex
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@@ -27,8 +27,7 @@ Substituting \eqref{eq:sigmoid-kernel} into the KDE CDF:
\label{eq:kde-sigmoid-cdf}
\end{equation}
%
The derivative of $\hat{F}_k$ with respect to $\tau$ — used in Newton--Raphson inversion
and in the gradient — is:
The derivative of $\hat{F}_k$ with respect to $\tau$ is:
%
\begin{equation}
\frac{\partial \hat{F}_{k}(\tau)}{\partial \tau}
content/appendixs/appendix_keel_noise.tex
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@@ -1,14 +1,14 @@
The tables below report mean test AUC at $\varepsilon = 5\%$ and $\varepsilon = 10\%$ asymmetric label noise on the KEEL benchmark.
The tables below report mean test AUC at $\varepsilon = 5\%$ and $\varepsilon = 10\%$ symmetric label noise on the KEEL benchmark.
Results at $\varepsilon = 20\%$ noise, where differentiation between methods is strongest, are discussed and tabled in the main text (\Cref{sec:results:keel}).
\begin{table}[htbp]
\centering
\caption{Mean test AUC ($\pm$\,std, $n=10$ episodes) on KEEL datasets at $\epsilon=5\%$ asymmetric label noise. Best per row in \textbf{bold}.}
\caption{Mean test AUC ($\pm$\,std, $n=10$ episodes) on KEEL datasets at $\epsilon=5\%$ symmetric label noise. Best per row in \textbf{bold}.}
\label{tab:results:keel-noise-05}
\resizebox{\textwidth}{!}{%
\begin{tabular}{lccccccc}
\toprule
Dataset & \textsc{Roll}-AOC & BCE-W & Focal & Asym. & GCE & LibAUC & MAE \\
Dataset & \textsc{ROLL}-AOC & BCE-W & Focal & Asym. & GCE & LibAUC & MAE \\
\midrule
Glass0 & 0.797{\tiny{$\pm$0.046}} & 0.786{\tiny{$\pm$0.019}} & \textbf{0.806{\tiny{$\pm$0.030}}} & 0.792{\tiny{$\pm$0.041}} & 0.794{\tiny{$\pm$0.029}} & 0.791{\tiny{$\pm$0.056}} & 0.792{\tiny{$\pm$0.058}} \\
Glass1 & 0.728{\tiny{$\pm$0.037}} & 0.736{\tiny{$\pm$0.032}} & 0.730{\tiny{$\pm$0.074}} & 0.704{\tiny{$\pm$0.028}} & 0.717{\tiny{$\pm$0.059}} & 0.694{\tiny{$\pm$0.060}} & \textbf{0.738{\tiny{$\pm$0.047}}} \\
@@ -29,12 +29,12 @@ Yeast3 & 0.900{\tiny{$\pm$0.020}} & 0.914{\tiny{$\pm$0.028}} & 0.915{\tiny
\begin{table}[htbp]
\centering
\caption{Mean test AUC ($\pm$\,std, $n=10$ episodes) on KEEL datasets at $\epsilon=10\%$ asymmetric label noise. Best per row in \textbf{bold}.}
\caption{Mean test AUC ($\pm$\,std, $n=10$ episodes) on KEEL datasets at $\epsilon=10\%$ symmetric label noise. Best per row in \textbf{bold}.}
\label{tab:results:keel-noise-10}
\resizebox{\textwidth}{!}{%
\begin{tabular}{lccccccc}
\toprule
Dataset & \textsc{Roll}-AOC & BCE-W & Focal & Asym. & GCE & LibAUC & MAE \\
Dataset & \textsc{ROLL}-AOC & BCE-W & Focal & Asym. & GCE & LibAUC & MAE \\
\midrule
Glass0 & 0.773{\tiny{$\pm$0.070}} & 0.789{\tiny{$\pm$0.037}} & 0.771{\tiny{$\pm$0.037}} & \textbf{0.821{\tiny{$\pm$0.026}}} & 0.786{\tiny{$\pm$0.057}} & 0.800{\tiny{$\pm$0.032}} & 0.807{\tiny{$\pm$0.050}} \\
Glass1 & 0.719{\tiny{$\pm$0.040}} & 0.716{\tiny{$\pm$0.079}} & 0.718{\tiny{$\pm$0.056}} & 0.710{\tiny{$\pm$0.049}} & 0.729{\tiny{$\pm$0.048}} & 0.675{\tiny{$\pm$0.070}} & \textbf{0.738{\tiny{$\pm$0.060}}} \\