From 99a8a9d91e6e375c7824afefe6ca9e76c9f9a0f0 Mon Sep 17 00:00:00 2001
From: Jan Benda <jan.benda@uni-tuebingen.de>
Date: Thu, 17 Dec 2020 22:38:07 +0100
Subject: [PATCH] [regression] improved cost function figure
---
regression/lecture/cubiccost.py | 12 +++++++-----
regression/lecture/regression.tex | 16 ++++++++--------
2 files changed, 15 insertions(+), 13 deletions(-)
diff --git a/regression/lecture/cubiccost.py b/regression/lecture/cubiccost.py
index 0b8d2dc..30d9575 100644
--- a/regression/lecture/cubiccost.py
+++ b/regression/lecture/cubiccost.py
@@ -49,16 +49,18 @@ def plot_mse_min(ax, x, y, c):
mses = np.zeros(len(ccs))
for i, cc in enumerate(ccs):
mses[i] = np.mean((y-(cc*x**3.0))**2.0)
- di = 20
- i0 = 14
- imin = np.argmin(mses[i0::di])*di + i0
+ imin = np.argmin(mses)
+ di = 25
+ i0 = 16
+ dimin = np.argmin(mses[i0::di])*di + i0
ax.plot(c, 500.0, **psB)
ax.plot(ccs, mses, **lsAm)
ax.plot(ccs[i0::di], mses[i0::di], **psAm)
- ax.plot(ccs[imin], mses[imin], **psC)
+ ax.plot(ccs[dimin], mses[dimin], **psD)
+ #ax.plot(ccs[imin], mses[imin], **psCm)
ax.annotate('Estimated\nminimum of\ncost\nfunction',
- xy=(ccs[imin], mses[imin]*1.2), xycoords='data',
+ xy=(ccs[dimin], mses[dimin]*1.2), xycoords='data',
xytext=(4, 6700), textcoords='data', ha='left',
arrowprops=dict(arrowstyle="->", relpos=(0.8,0.0),
connectionstyle="angle3,angleA=0,angleB=85") )
diff --git a/regression/lecture/regression.tex b/regression/lecture/regression.tex
index 8867744..2990aef 100644
--- a/regression/lecture/regression.tex
+++ b/regression/lecture/regression.tex
@@ -154,6 +154,14 @@ function $f_{cost}(c)$ that maps the parameter value $c$ to a scalar
error value. For a given data set we thus can simply plot the cost
function as a function of $c$ (\figref{cubiccostfig}).
+\begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise}
+ Then calculate the mean squared error between the data and straight
+ lines for a range of slopes and intercepts using the
+ \varcode{meanSquaredErrorCubic()} function from the previous
+ exercise. Illustrate the error surface using the \code{surface()}
+ function.
+\end{exercise}
+
\begin{figure}[t]
\includegraphics{cubiccost}
\titlecaption{Minimum of the cost function.}{For a given data set
@@ -167,14 +175,6 @@ function as a function of $c$ (\figref{cubiccostfig}).
the computed range.}\label{cubiccostfig}
\end{figure}
-\begin{exercise}{errorSurface.m}{}\label{errorsurfaceexercise}
- Then calculate the mean squared error between the data and straight
- lines for a range of slopes and intercepts using the
- \varcode{meanSquaredErrorCubic()} function from the previous
- exercise. Illustrate the error surface using the \code{surface()}
- function.
-\end{exercise}
-
By looking at the plot of the cost function we can visually identify
the position of the minimum and thus estimate the optimal value for
the parameter $c$. How can we use the error surface to guide an