updating adaboost

2019-11-04 11:01:16 +01:00
parent fb9515fdf0
commit 9bc330e85b
9 changed files with 63 additions and 8 deletions
@@ -235,7 +235,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Nov 3, 2019</h4></center> <!-- date -->
+<center><h4>Nov 4, 2019</h4></center> <!-- date -->
 <br>
 <p>

@@ -235,7 +235,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Nov 3, 2019</h4></center> <!-- date -->
+<center><h4>Nov 4, 2019</h4></center> <!-- date -->
 <br>
 <p>

@@ -148,7 +148,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>&nbsp;<br>
-<center><h4>Nov 3, 2019</h4></center> <!-- date -->
+<center><h4>Nov 4, 2019</h4></center> <!-- date -->
 <br>
 <p>

@@ -1847,6 +1847,17 @@ where the function \( I() \) is one if we misclassify and zero if we classify co

 <p>
 With the above definitions we are now ready to set up the algorithm for AdaBoost.
+The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
+
+<ol>
+<p><li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is to see then that \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
+<p><li> We rewrite the misclassification error as</li> 
+</ol>
+<p>&nbsp;<br>
+$$
+\mathrm{err}=\frac{\sum_{i=0}^{n-1}w_iI(y_i\ne G(\boldsymbol{X}_{i*})}{\sum_{i=0}^{n-1}w_i},
+$$
+<p>&nbsp;<br>
 </section>


@@ -175,7 +175,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Nov 3, 2019</h4></center> <!-- date -->
+<center><h4>Nov 4, 2019</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1823,6 +1823,16 @@ where the function \( I() \) is one if we misclassify and zero if we classify co

 <p>
 With the above definitions we are now ready to set up the algorithm for AdaBoost.
+The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
+
+<ol>
+<li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is to see then that \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
+<li> We rewrite the misclassification error as</li> 
+</ol>
+
+$$
+\mathrm{err}=\frac{\sum_{i=0}^{n-1}w_iI(y_i\ne G(\boldsymbol{X}_{i*})}{\sum_{i=0}^{n-1}w_i},
+$$

 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -180,7 +180,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Nov 3, 2019</h4></center> <!-- date -->
+<center><h4>Nov 4, 2019</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1828,6 +1828,16 @@ where the function \( I() \) is one if we misclassify and zero if we classify co

 <p>
 With the above definitions we are now ready to set up the algorithm for AdaBoost.
+The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
+
+<ol>
+<li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is to see then that \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
+<li> We rewrite the misclassification error as</li> 
+</ol>
+
+$$
+\mathrm{err}=\frac{\sum_{i=0}^{n-1}w_iI(y_i\ne G(\boldsymbol{X}_{i*})}{\sum_{i=0}^{n-1}w_i},
+$$

 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -10,7 +10,7 @@
    "<!-- Author: -->  \n",
    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
    "\n",
-    "Date: **Nov 3, 2019**\n",
+    "Date: **Nov 4, 2019**\n",
    "\n",
    "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
    "\n",
@@ -1875,9 +1875,25 @@
    "## Basic Steps of AdaBoost\n",
    "\n",
    "With the above definitions we are now ready to set up the algorithm for AdaBoost.\n",
+    "The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.\n",
+    "1. We start by initializing all weights to $w_i = 1/n$, with $i=0,1,2,\\dots n-1$. It is to see then that $\\sum_{i=0}^{n-1}w_i = 1$.\n",
    "\n",
-    "\n",
-    "\n",
+    "2. We rewrite the misclassification error as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathrm{err}=\\frac{\\sum_{i=0}^{n-1}w_iI(y_i\\ne G(\\boldsymbol{X}_{i*})}{\\sum_{i=0}^{n-1}w_i},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
    "## AdaBoost Examples"
   ]
  },
@@ -1501,6 +1501,14 @@ where the function $I()$ is one if we misclassify and zero if we classify correc
 ===== Basic Steps of AdaBoost =====

 With the above definitions we are now ready to set up the algorithm for AdaBoost.
+The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
+o We start by initializing all weights to $w_i = 1/n$, with $i=0,1,2,\dots n-1$. It is to see then that $\sum_{i=0}^{n-1}w_i = 1$.
+o We rewrite the misclassification error as 
+!bt
+\[
+\mathrm{err}=\frac{\sum_{i=0}^{n-1}w_iI(y_i\ne G(\bm{X}_{i*})}{\sum_{i=0}^{n-1}w_i},
+\]
+!et