From ae56a721eb63e6e2032e10436a4944d9203aa560 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 12 Feb 2025 16:23:43 -0300
Subject: More writing

---
 ictp-saifr_colloquium.tex | 350 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 350 insertions(+)

(limited to 'ictp-saifr_colloquium.tex')

diff --git a/ictp-saifr_colloquium.tex b/ictp-saifr_colloquium.tex
index 1fa3a0b..92b4904 100644
--- a/ictp-saifr_colloquium.tex
+++ b/ictp-saifr_colloquium.tex
@@ -426,11 +426,361 @@
       \]
     \end{column}
     \begin{column}{0.5\textwidth}
+      \begin{overprint}
+        \onslide<1>\includegraphics[width=\columnwidth]{figs/fit_gradient_1.pdf}
+        \onslide<2>\includegraphics[width=\columnwidth]{figs/fit_gradient_2.pdf}
+        \onslide<3>\includegraphics[width=\columnwidth]{figs/fit_gradient_3.pdf}
+        \onslide<4>\includegraphics[width=\columnwidth]{figs/fit_gradient_4.pdf}
+        \onslide<5>\includegraphics[width=\columnwidth]{figs/fit_gradient_5.pdf}
+        \onslide<6>\includegraphics[width=\columnwidth]{figs/fit_gradient_6.pdf}
+      \end{overprint}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Curve fitting: choice of basis}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \centering
+      \textbf{Polynomial basis}
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_basis_poly.pdf}
+    \end{column}
+    \begin{column}{0.5\textwidth}
+      \centering
+      \textbf{Absolute value basis}
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_basis_abs.pdf}
     \end{column}
   \end{columns}
 \end{frame}
 
 \begin{frame}
+  \frametitle{Curve fitting: choice of basis}
+  \centering
+  \Large\textbf{Polynomial basis}\normalsize
+
+  \bigskip
+
+  \begin{columns}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=2$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_underfit_poly.pdf}
+
+      \bigskip
+
+      Underfit
+
+      \smallskip
+
+      $\chi^2$ is large
+
+      \smallskip
+
+      Best fit has \emph{high bias} \phantom{variance}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=7$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_goodfit_poly.pdf}
+
+      \bigskip
+
+      Good fit!
+
+      \smallskip
+
+      $\chi^2$ is moderate
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=40$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_overfit_poly.pdf}
+
+      \bigskip
+
+      Overfit
+
+      \smallskip
+
+      $\chi^2$ is zero
+
+      \smallskip
+
+      Best fit has \emph{high variance}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=80$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_overparamfit_poly.pdf}
+
+      \bigskip
+
+      Good fit?
+
+      \smallskip
+
+      $\chi^2$ is zero
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Curve fitting: choice of basis}
+  \centering
+  \Large\textbf{Absolute value basis\vphantom{y}}\normalsize
+
+  \bigskip
+
+  \begin{columns}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=2$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_underfit_abs.pdf}
+
+      \bigskip
+
+      Underfit
+
+      \smallskip
+
+      $\chi^2$ is large
+
+      \smallskip
+
+      Best fit has \emph{high bias} \phantom{variance}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=7$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_goodfit_abs.pdf}
+
+      \bigskip
+
+      Good fit!
+
+      \smallskip
+
+      $\chi^2$ is moderate
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=40$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_overfit_abs.pdf}
+
+      \bigskip
+
+      Good fit?
+
+      \smallskip
+
+      $\chi^2$ is zero
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=40$, $N=80$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_overparamfit_abs.pdf}
+
+      \bigskip
+
+      Good fit?
+
+      \smallskip
+
+      $\chi^2$ is zero
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Curve fitting: choice of basis}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \centering
+      \textbf{Polynomial basis}
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_bias-variance2_poly.pdf}
+    \end{column}
+    \begin{column}{0.5\textwidth}
+      \centering
+      \textbf{Absolute value basis}
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_bias-variance_abs.pdf}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Curve fitting: sparseness and level of noise}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \includegraphics[width=\columnwidth]{figs/fit_data.pdf}
+    \end{column}
+    \begin{column}{0.5\textwidth}
+      \includegraphics[width=\columnwidth]{figs/fit_data_abs2.pdf}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Curve fitting: sparseness and level of noise}
+  \begin{columns}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=10$, $N=4$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_underfit_abs2.pdf}
+
+      \bigskip
+
+      Underfit
+
+      \smallskip
+
+      $\chi^2$ is large
+
+      \smallskip
+
+      Best fit has \emph{high bias} \phantom{variance}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=10$, $N=6$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_goodfit_abs2.pdf}
+
+      \bigskip
+
+      Good fit!
+
+      \smallskip
+
+      $\chi^2$ is moderate
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=10$, $N=10$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_overfit_abs2.pdf}
+
+      \bigskip
+
+      Good fit?
+
+      \smallskip
+
+      $\chi^2$ is zero
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+    \begin{column}{0.25\textwidth}
+      \centering
+      $M=10$, $N=15$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_overparamfit_abs2.pdf}
+
+      \bigskip
+
+      Better fit?!
+
+      \smallskip
+
+      $\chi^2$ is zero
+
+      \smallskip
+
+      Best fit has \emph{low variance} and \emph{low bias}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Curve fitting: sparseness and level of noise}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \centering
+      $M=10$, $N=15$
+
+      \bigskip
+
+      \includegraphics[width=\columnwidth]{figs/fit_overparamfit_abs2.pdf}
+    \end{column}
+    \begin{column}{0.5\textwidth}
+      \includegraphics[width=\columnwidth]{figs/fit_bias-variance_abs2.pdf}
+    \end{column}
+  \end{columns}
 \end{frame}
 
 \begin{frame}
-- 
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