[regression] improved cost function figure

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") )

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