From 661d591b040773bfc5c5a9c2ce2332ac1a648b73 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Aur=C3=A9lien=20Geron?= <ageron@users.noreply.github.com>
Date: Thu, 27 May 2021 17:05:34 +1200
Subject: [PATCH] Clarify the Decision Tree instability section, fixes #422

---
 06_decision_trees.ipynb | 29 ++++++++++++-----------------
 1 file changed, 12 insertions(+), 17 deletions(-)

diff --git a/06_decision_trees.ipynb b/06_decision_trees.ipynb
index 5994c42..ab7f00a 100644
--- a/06_decision_trees.ipynb
+++ b/06_decision_trees.ipynb
@@ -206,7 +206,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Sensitivity to training set details"
+    "# High Variance"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We've seen that small changes in the dataset (such as a rotation) may produce a very different Decision Tree.\n",
+    "Now let's show that training the same model on the same data may produce a very different model every time, since the CART training algorithm used by Scikit-Learn is stochastic. To show this, we will set `random_state` to a different value than earlier:"
    ]
   },
   {
@@ -215,7 +223,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "X[(X[:, 1]==X[:, 1][y==1].max()) & (y==1)] # widest Iris versicolor flower"
+    "tree_clf_tweaked = DecisionTreeClassifier(max_depth=2, random_state=40)\n",
+    "tree_clf_tweaked.fit(X, y)"
    ]
   },
   {
@@ -223,23 +232,9 @@
    "execution_count": 8,
    "metadata": {},
    "outputs": [],
-   "source": [
-    "not_widest_versicolor = (X[:, 1]!=1.8) | (y==2)\n",
-    "X_tweaked = X[not_widest_versicolor]\n",
-    "y_tweaked = y[not_widest_versicolor]\n",
-    "\n",
-    "tree_clf_tweaked = DecisionTreeClassifier(max_depth=2, random_state=40)\n",
-    "tree_clf_tweaked.fit(X_tweaked, y_tweaked)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [],
    "source": [
     "plt.figure(figsize=(8, 4))\n",
-    "plot_decision_boundary(tree_clf_tweaked, X_tweaked, y_tweaked, legend=False)\n",
+    "plot_decision_boundary(tree_clf_tweaked, X, y, legend=False)\n",
     "plt.plot([0, 7.5], [0.8, 0.8], \"k-\", linewidth=2)\n",
     "plt.plot([0, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
     "plt.text(1.0, 0.9, \"Depth=0\", fontsize=15)\n",