Big update of chapter 5 for 3rd edition
Aurélien Geron
parent
608d9ce815
commit
8e97aab84b
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@ -125,6 +125,13 @@
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"# Linear SVM Classification"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The book starts with a few figures, before the first code example, so the next three cells generate and save these figures. You can skip them if you want."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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@ -168,12 +175,13 @@
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" margin = 1/w[1]\n",
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" gutter_up = decision_boundary + margin\n",
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" gutter_down = decision_boundary - margin\n",
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"\n",
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" svs = svm_clf.support_vectors_\n",
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" plt.scatter(svs[:, 0], svs[:, 1], s=180, facecolors='#FFAAAA')\n",
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" plt.plot(x0, decision_boundary, \"k-\", linewidth=2)\n",
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" plt.plot(x0, gutter_up, \"k--\", linewidth=2)\n",
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" plt.plot(x0, gutter_down, \"k--\", linewidth=2)\n",
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"\n",
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" plt.plot(x0, decision_boundary, \"k-\", linewidth=2, zorder=-2)\n",
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" plt.plot(x0, gutter_up, \"k--\", linewidth=2, zorder=-2)\n",
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" plt.plot(x0, gutter_down, \"k--\", linewidth=2, zorder=-2)\n",
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" plt.scatter(svs[:, 0], svs[:, 1], s=180, facecolors='#AAA',\n",
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" zorder=-1)\n",
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"\n",
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"fig, axes = plt.subplots(ncols=2, figsize=(10,2.7), sharey=True)\n",
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"\n",
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@ -187,6 +195,7 @@
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"plt.ylabel(\"Petal width\")\n",
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"plt.legend(loc=\"upper left\")\n",
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"plt.axis([0, 5.5, 0, 2])\n",
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"plt.gca().set_aspect(\"equal\")\n",
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"plt.grid()\n",
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"\n",
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"plt.sca(axes[1])\n",
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@ -195,6 +204,7 @@
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"plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\")\n",
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"plt.xlabel(\"Petal length\")\n",
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"plt.axis([0, 5.5, 0, 2])\n",
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"plt.gca().set_aspect(\"equal\")\n",
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"plt.grid()\n",
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"\n",
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"save_fig(\"large_margin_classification_plot\")\n",
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@ -320,17 +330,17 @@
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from sklearn import datasets\n",
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"from sklearn.datasets import load_iris\n",
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"from sklearn.pipeline import make_pipeline\n",
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"from sklearn.preprocessing import StandardScaler\n",
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"from sklearn.svm import LinearSVC\n",
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"\n",
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"iris = datasets.load_iris(as_frame=True)\n",
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"iris = load_iris(as_frame=True)\n",
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"X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
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"y = (iris.target == 2) # Iris virginica\n",
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"\n",
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"svm_clf = make_pipeline(StandardScaler(),\n",
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" LinearSVC(C=1, loss=\"hinge\", random_state=42))\n",
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" LinearSVC(C=1, random_state=42))\n",
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"svm_clf.fit(X, y)"
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]
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},
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@ -340,7 +350,8 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"svm_clf.predict([[5.5, 1.7]])"
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"X_new = [[5.5, 1.7], [5.0, 1.5]]\n",
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"svm_clf.predict(X_new)"
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]
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},
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{
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@ -348,12 +359,21 @@
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"svm_clf.decision_function(X_new)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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"# not in the book – this cell generates and saves Figure 5–4\n",
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"\n",
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"scaler = StandardScaler()\n",
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"svm_clf1 = LinearSVC(C=1, loss=\"hinge\", max_iter=10_000, random_state=42)\n",
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"svm_clf2 = LinearSVC(C=100, loss=\"hinge\", max_iter=10_000, random_state=42)\n",
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"svm_clf1 = LinearSVC(C=1, max_iter=10_000, random_state=42)\n",
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"svm_clf2 = LinearSVC(C=100, max_iter=10_000, random_state=42)\n",
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"\n",
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"scaled_svm_clf1 = make_pipeline(scaler, svm_clf1)\n",
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"scaled_svm_clf2 = make_pipeline(scaler, svm_clf2)\n",
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@ -387,7 +407,7 @@
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"plt.xlabel(\"Petal length\")\n",
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"plt.ylabel(\"Petal width\")\n",
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"plt.legend(loc=\"upper left\")\n",
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"plt.title(\"$C = {}$\".format(svm_clf1.C))\n",
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"plt.title(f\"$C = {svm_clf1.C}$\")\n",
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"plt.axis([4, 5.9, 0.8, 2.8])\n",
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"plt.grid()\n",
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"\n",
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@ -396,7 +416,7 @@
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"plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
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"plot_svc_decision_boundary(svm_clf2, 4, 5.99)\n",
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"plt.xlabel(\"Petal length\")\n",
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"plt.title(\"$C = {}$\".format(svm_clf2.C))\n",
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"plt.title(f\"$C = {svm_clf2.C}$\")\n",
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"plt.axis([4, 5.9, 0.8, 2.8])\n",
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"plt.grid()\n",
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"\n",
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@ -413,7 +433,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -461,12 +481,11 @@
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sklearn.datasets import make_moons\n",
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"from sklearn.pipeline import make_pipeline\n",
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"from sklearn.preprocessing import PolynomialFeatures\n",
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"\n",
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"X, y = make_moons(n_samples=100, noise=0.15, random_state=42)\n",
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@ -474,14 +493,14 @@
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"polynomial_svm_clf = make_pipeline(\n",
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" PolynomialFeatures(degree=3),\n",
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" StandardScaler(),\n",
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" LinearSVC(C=10, loss=\"hinge\", max_iter=10_000, random_state=42)\n",
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" LinearSVC(C=10, max_iter=10_000, random_state=42)\n",
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")\n",
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"polynomial_svm_clf.fit(X, y)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -528,7 +547,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": 15,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -543,7 +562,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"execution_count": 16,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -581,7 +600,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"execution_count": 17,
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"metadata": {
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"scrolled": true
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},
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@ -651,18 +670,6 @@
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [],
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"source": [
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"x1_example = X1D[3, 0]\n",
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"for landmark in (-2, 1):\n",
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" k = gaussian_rbf(np.array([[x1_example]]), np.array([[landmark]]), gamma)\n",
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" print(\"Phi({}, {}) = {}\".format(x1_example, landmark, k))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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@ -722,7 +729,7 @@
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" plot_predictions(svm_clf, [-1.5, 2.45, -1, 1.5])\n",
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" plot_dataset(X, y, [-1.5, 2.45, -1, 1.5])\n",
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" gamma, C = hyperparams[i]\n",
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" plt.title(r\"$\\gamma = {}, C = {}$\".format(gamma, C))\n",
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" plt.title(fr\"$\\gamma = {gamma}, C = {C}$\")\n",
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" if i in (0, 1):\n",
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" plt.xlabel(\"\")\n",
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" if i in (1, 3):\n",
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@ -745,6 +752,7 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"# not in the book – this code generates a simple linear dataset\n",
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"np.random.seed(42)\n",
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"m = 50\n",
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"X = 2 * np.random.rand(m, 1)\n",
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@ -766,7 +774,8 @@
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"source": [
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"from sklearn.svm import LinearSVR\n",
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"\n",
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"svm_reg = LinearSVR(epsilon=1.5, random_state=42)\n",
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"svm_reg = make_pipeline(StandardScaler(),\n",
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" LinearSVR(epsilon=0.5, random_state=42))\n",
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"svm_reg.fit(X, y)"
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]
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},
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@ -780,47 +789,49 @@
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"\n",
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"def find_support_vectors(svm_reg, X, y):\n",
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" y_pred = svm_reg.predict(X)\n",
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" off_margin = (np.abs(y - y_pred) >= svm_reg.epsilon)\n",
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" epsilon = svm_reg[-1].epsilon\n",
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" off_margin = np.abs(y - y_pred) >= epsilon\n",
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" return np.argwhere(off_margin)\n",
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"\n",
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"def plot_svm_regression(svm_reg, X, y, axes):\n",
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" x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)\n",
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" y_pred = svm_reg.predict(x1s)\n",
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" plt.plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
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" plt.plot(x1s, y_pred + svm_reg.epsilon, \"k--\")\n",
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" plt.plot(x1s, y_pred - svm_reg.epsilon, \"k--\")\n",
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" plt.scatter(X[svm_reg.support_], y[svm_reg.support_], s=180, facecolors='#FFAAAA')\n",
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" epsilon = svm_reg[-1].epsilon\n",
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" plt.plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\", zorder=-2)\n",
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" plt.plot(x1s, y_pred + epsilon, \"k--\", zorder=-2)\n",
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" plt.plot(x1s, y_pred - epsilon, \"k--\", zorder=-2)\n",
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" plt.scatter(X[svm_reg._support], y[svm_reg._support], s=180,\n",
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" facecolors='#AAA', zorder=-1)\n",
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" plt.plot(X, y, \"bo\")\n",
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" plt.xlabel(r\"$x_1$\")\n",
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" plt.legend(loc=\"upper left\")\n",
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" plt.axis(axes)\n",
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"\n",
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"svm_reg1 = LinearSVR(epsilon=1.5, random_state=42)\n",
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"svm_reg2 = LinearSVR(epsilon=0.5, random_state=42)\n",
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"svm_reg1.fit(X, y)\n",
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"svm_reg2 = make_pipeline(StandardScaler(),\n",
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" LinearSVR(epsilon=1.2, random_state=42))\n",
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"svm_reg2.fit(X, y)\n",
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"\n",
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"svm_reg1.support_ = find_support_vectors(svm_reg1, X, y)\n",
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"svm_reg2.support_ = find_support_vectors(svm_reg2, X, y)\n",
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"svm_reg._support = find_support_vectors(svm_reg, X, y)\n",
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"svm_reg2._support = find_support_vectors(svm_reg2, X, y)\n",
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"\n",
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"eps_x1 = 1\n",
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"eps_y_pred = svm_reg1.predict([[eps_x1]])\n",
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"eps_y_pred = svm_reg2.predict([[eps_x1]])\n",
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"\n",
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"fig, axes = plt.subplots(ncols=2, figsize=(9, 4), sharey=True)\n",
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"plt.sca(axes[0])\n",
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"plot_svm_regression(svm_reg1, X, y, [0, 2, 3, 11])\n",
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"plt.title(r\"$\\epsilon = {}$\".format(svm_reg1.epsilon))\n",
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"plot_svm_regression(svm_reg, X, y, [0, 2, 3, 11])\n",
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"plt.title(fr\"$\\epsilon = {svm_reg[-1].epsilon}$\")\n",
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"plt.ylabel(r\"$y$\", rotation=0)\n",
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"plt.grid()\n",
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"plt.annotate(\n",
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" '', xy=(eps_x1, eps_y_pred), xycoords='data',\n",
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" xytext=(eps_x1, eps_y_pred - svm_reg1.epsilon),\n",
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" textcoords='data', arrowprops={'arrowstyle': '<->', 'linewidth': 1.5}\n",
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" )\n",
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"plt.text(0.91, 5.6, r\"$\\epsilon$\", fontsize=16)\n",
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"plt.sca(axes[1])\n",
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"plot_svm_regression(svm_reg2, X, y, [0, 2, 3, 11])\n",
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"plt.title(r\"$\\epsilon = {}$\".format(svm_reg2.epsilon))\n",
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"plt.title(fr\"$\\epsilon = {svm_reg2[-1].epsilon}$\")\n",
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"plt.annotate(\n",
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" '', xy=(eps_x1, eps_y_pred), xycoords='data',\n",
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" xytext=(eps_x1, eps_y_pred - svm_reg2[-1].epsilon),\n",
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" textcoords='data', arrowprops={'arrowstyle': '<->', 'linewidth': 1.5}\n",
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" )\n",
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"plt.text(0.90, 5.4, r\"$\\epsilon$\", fontsize=16)\n",
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"plt.grid()\n",
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"save_fig(\"svm_regression_plot\")\n",
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"plt.show()"
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"metadata": {},
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"outputs": [],
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"source": [
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"# not in the book – this code generates a simple quadratic dataset\n",
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"np.random.seed(42)\n",
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"m = 100\n",
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"m = 50\n",
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"X = 2 * np.random.rand(m, 1) - 1\n",
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"y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10).ravel()"
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"y = (0.2 + 0.1 * X + 0.5 * X ** 2 + np.random.randn(m, 1) / 10).ravel()"
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]
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},
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{
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"source": [
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"from sklearn.svm import SVR\n",
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"\n",
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"svm_poly_reg = SVR(kernel=\"poly\", degree=2, C=100)\n",
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"svm_poly_reg = make_pipeline(StandardScaler(),\n",
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" SVR(kernel=\"poly\", degree=2, C=0.01, epsilon=0.1))\n",
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"svm_poly_reg.fit(X, y)"
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]
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},
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"execution_count": 25,
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"metadata": {},
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"outputs": [],
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"source": [
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"svm_poly_reg1 = SVR(kernel=\"poly\", degree=2, C=100)\n",
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"svm_poly_reg2 = SVR(kernel=\"poly\", degree=2, C=0.01)\n",
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"svm_poly_reg1.fit(X, y)\n",
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"svm_poly_reg2.fit(X, y)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"source": [
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"# not in the book – this cell generates and saves Figure 5–11\n",
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"\n",
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"svm_poly_reg2 = make_pipeline(StandardScaler(),\n",
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" SVR(kernel=\"poly\", degree=2, C=100))\n",
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"svm_poly_reg2.fit(X, y)\n",
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"\n",
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"svm_poly_reg._support = find_support_vectors(svm_poly_reg, X, y)\n",
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"svm_poly_reg2._support = find_support_vectors(svm_poly_reg2, X, y)\n",
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"\n",
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"fig, axes = plt.subplots(ncols=2, figsize=(9, 4), sharey=True)\n",
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"plt.sca(axes[0])\n",
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"plot_svm_regression(svm_poly_reg1, X, y, [-1, 1, 0, 1])\n",
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"plt.title(f\"$degree={svm_poly_reg1.degree}, \"\n",
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" f\"C={svm_poly_reg1.C}, \"\n",
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" f\"\\\\epsilon={svm_poly_reg1.epsilon}$\")\n",
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"plot_svm_regression(svm_poly_reg, X, y, [-1, 1, 0, 1])\n",
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"plt.title(f\"$degree={svm_poly_reg[-1].degree}, \"\n",
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" f\"C={svm_poly_reg[-1].C}, \"\n",
|
||||
" fr\"\\epsilon={svm_poly_reg[-1].epsilon}$\")\n",
|
||||
"plt.ylabel(r\"$y$\", rotation=0)\n",
|
||||
"plt.grid()\n",
|
||||
"\n",
|
||||
"plt.sca(axes[1])\n",
|
||||
"plot_svm_regression(svm_poly_reg2, X, y, [-1, 1, 0, 1])\n",
|
||||
"plt.title(f\"$degree={svm_poly_reg2.degree}, \"\n",
|
||||
" f\"C={svm_poly_reg2.C}, \"\n",
|
||||
" f\"\\\\epsilon={svm_poly_reg2.epsilon}$\")\n",
|
||||
"plt.title(f\"$degree={svm_poly_reg2[-1].degree}, \"\n",
|
||||
" f\"C={svm_poly_reg2[-1].C}, \"\n",
|
||||
" fr\"\\epsilon={svm_poly_reg2[-1].epsilon}$\")\n",
|
||||
"plt.grid()\n",
|
||||
"save_fig(\"svm_with_polynomial_kernel_plot\")\n",
|
||||
"plt.show()"
|
||||
|
|
@ -900,90 +908,46 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Extra Material – Under the Hood"
|
||||
"# Under the hood"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 27,
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
|
||||
"y = (iris.target == 2)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||||
"# not in the book – this cell generates and saves Figure 5–12\n",
|
||||
"\n",
|
||||
"def plot_3D_decision_function(ax, w, b, x1_lim=[4, 6], x2_lim=[0.8, 2.8]):\n",
|
||||
" x1_in_bounds = (X[:, 0] > x1_lim[0]) & (X[:, 0] < x1_lim[1])\n",
|
||||
" X_crop = X[x1_in_bounds]\n",
|
||||
" y_crop = y[x1_in_bounds]\n",
|
||||
" x1s = np.linspace(x1_lim[0], x1_lim[1], 20)\n",
|
||||
" x2s = np.linspace(x2_lim[0], x2_lim[1], 20)\n",
|
||||
" x1, x2 = np.meshgrid(x1s, x2s)\n",
|
||||
" xs = np.c_[x1.ravel(), x2.ravel()]\n",
|
||||
" df = (xs.dot(w) + b).reshape(x1.shape)\n",
|
||||
" m = 1 / np.linalg.norm(w)\n",
|
||||
" boundary_x2s = -x1s * (w[0] / w[1]) - b / w[1]\n",
|
||||
" margin_x2s_1 = -x1s * (w[0] / w[1]) - (b - 1) / w[1]\n",
|
||||
" margin_x2s_2 = -x1s * (w[0] / w[1]) - (b + 1) / w[1]\n",
|
||||
" ax.plot_surface(x1s, x2, np.zeros_like(x1),\n",
|
||||
" color=\"b\", alpha=0.2, cstride=100, rstride=100)\n",
|
||||
" ax.plot(x1s, boundary_x2s, 0, \"k-\", linewidth=2, label=r\"$h=0$\")\n",
|
||||
" ax.plot(x1s, margin_x2s_1, 0, \"k--\", linewidth=2, label=r\"$h=\\pm 1$\")\n",
|
||||
" ax.plot(x1s, margin_x2s_2, 0, \"k--\", linewidth=2)\n",
|
||||
" ax.plot(X_crop[:, 0][y_crop==1], X_crop[:, 1][y_crop==1], 0, \"g^\")\n",
|
||||
" ax.plot_wireframe(x1, x2, df, alpha=0.3, color=\"k\")\n",
|
||||
" ax.plot(X_crop[:, 0][y_crop==0], X_crop[:, 1][y_crop==0], 0, \"bs\")\n",
|
||||
" ax.axis(x1_lim + x2_lim)\n",
|
||||
" ax.text(4.5, 2.5, 3.8, \"Decision function $h$\", fontsize=14)\n",
|
||||
" ax.set_xlabel(r\"Petal length\", labelpad=10)\n",
|
||||
" ax.set_ylabel(r\"Petal width\", labelpad=10)\n",
|
||||
" ax.set_zlabel(r\"$h = \\mathbf{w}^T \\mathbf{x} + b$\", labelpad=5)\n",
|
||||
" ax.legend(loc=\"upper left\")\n",
|
||||
"\n",
|
||||
"fig = plt.figure(figsize=(11, 6))\n",
|
||||
"ax1 = fig.add_subplot(111, projection='3d')\n",
|
||||
"plot_3D_decision_function(ax1, w=svm_clf2.coef_[0], b=svm_clf2.intercept_[0])\n",
|
||||
"\n",
|
||||
"save_fig(\"iris_3D_plot\")\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 29,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import matplotlib.patches as patches\n",
|
||||
"\n",
|
||||
"def plot_2D_decision_function(w, b, ylabel=True, x1_lim=[-3, 3]):\n",
|
||||
" x1 = np.linspace(x1_lim[0], x1_lim[1], 200)\n",
|
||||
" y = w * x1 + b\n",
|
||||
" m = 1 / w\n",
|
||||
" half_margin = 1 / w\n",
|
||||
"\n",
|
||||
" plt.plot(x1, y)\n",
|
||||
" plt.axhline(y=0, color='k')\n",
|
||||
" plt.axvline(x=0, color='k')\n",
|
||||
" rect = patches.Rectangle((-3, -1), 6, 2, edgecolor='none', facecolor='blue',\n",
|
||||
" alpha=0.1)\n",
|
||||
" plt.plot(x1, y, \"b-\", linewidth=2, label=r\"$s = w_1 x_1$\")\n",
|
||||
" plt.axhline(y=0, color='k', linewidth=1)\n",
|
||||
" plt.axvline(x=0, color='k', linewidth=1)\n",
|
||||
" rect = patches.Rectangle((-half_margin, -2), 2 * half_margin, 4,\n",
|
||||
" edgecolor='none', facecolor='gray', alpha=0.2)\n",
|
||||
" plt.gca().add_patch(rect)\n",
|
||||
" plt.plot([m, m], [0, 1], \"b--\")\n",
|
||||
" plt.plot([-m, -m], [0, -1], \"b--\")\n",
|
||||
" plt.plot([-m, m], [0, 0], \"k-o\", linewidth=3)\n",
|
||||
" plt.plot([-3, 3], [1, 1], \"k--\", linewidth=1)\n",
|
||||
" plt.plot([-3, 3], [-1, -1], \"k--\", linewidth=1)\n",
|
||||
" plt.plot(half_margin, 1, \"k.\")\n",
|
||||
" plt.plot(-half_margin, -1, \"k.\")\n",
|
||||
" plt.axis(x1_lim + [-2, 2])\n",
|
||||
" plt.xlabel(r\"$x_1$\")\n",
|
||||
" if ylabel:\n",
|
||||
" plt.ylabel(r\"$w_1 x_1$ \", rotation=0)\n",
|
||||
" plt.title(r\"$w_1 = {}$\".format(w))\n",
|
||||
" plt.ylabel(\"$s$\", rotation=0, labelpad=5)\n",
|
||||
" plt.legend()\n",
|
||||
" plt.text(1.02, -1.6, \"Margin\", ha=\"left\", va=\"center\",\n",
|
||||
" color=\"k\", fontsize=14)\n",
|
||||
" plt.annotate(\n",
|
||||
" '', xy=(-half_margin, -1.6), xytext=(half_margin, -1.6),\n",
|
||||
" arrowprops={'ec': 'k', 'arrowstyle': '<->', 'linewidth': 1.5}\n",
|
||||
" )\n",
|
||||
" plt.title(fr\"$w_1 = {w}$\")\n",
|
||||
"\n",
|
||||
"fig, axes = plt.subplots(ncols=2, figsize=(9, 3.2), sharey=True)\n",
|
||||
"plt.sca(axes[0])\n",
|
||||
|
|
@ -996,31 +960,36 @@
|
|||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**Code to generate the Hinge Loss figure:**"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 30,
|
||||
"execution_count": 27,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"t = np.linspace(-2, 4, 200)\n",
|
||||
"h = np.where(1 - t < 0, 0, 1 - t) # max(0, 1-t)\n",
|
||||
"# not in the book – this cell generates and saves Figure 5–13\n",
|
||||
"\n",
|
||||
"s = np.linspace(-2.5, 2.5, 200)\n",
|
||||
"hinge_pos = np.where(1 - s < 0, 0, 1 - s) # max(0, 1 - s)\n",
|
||||
"hinge_neg = np.where(1 + s < 0, 0, 1 + s) # max(0, 1 + s)\n",
|
||||
"\n",
|
||||
"titles = (r\"Hinge loss = $max(0, 1 - s\\,t)$\", r\"Squared Hinge loss\")\n",
|
||||
"\n",
|
||||
"fix, axs = plt.subplots(1, 2, sharey=True, figsize=(8.2, 3))\n",
|
||||
"\n",
|
||||
"for ax, loss_pos, loss_neg, title in zip(\n",
|
||||
" axs, (hinge_pos, hinge_pos ** 2), (hinge_neg, hinge_neg ** 2), titles):\n",
|
||||
" ax.plot(s, loss_pos, \"g-\", linewidth=2, zorder=10, label=\"$t=1$\")\n",
|
||||
" ax.plot(s, loss_neg, \"r--\", linewidth=2, zorder=10, label=\"$t=-1$\")\n",
|
||||
" ax.grid(True, which='both')\n",
|
||||
" ax.axhline(y=0, color='k')\n",
|
||||
" ax.axvline(x=0, color='k')\n",
|
||||
" ax.set_xlabel(r\"$s = \\mathbf{w}^\\intercal \\mathbf{x} + b$\")\n",
|
||||
" ax.axis([-2.5, 2.5, -0.5, 2.5])\n",
|
||||
" ax.legend(loc=\"center right\")\n",
|
||||
" ax.set_title(title)\n",
|
||||
" ax.set_yticks(np.arange(0, 2.5, 1))\n",
|
||||
" ax.set_aspect(\"equal\")\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(5,2.8))\n",
|
||||
"plt.plot(t, h, \"b-\", linewidth=2, label=\"$max(0, 1 - t)$\", zorder=10)\n",
|
||||
"plt.grid(True, which='both')\n",
|
||||
"plt.axhline(y=0, color='k')\n",
|
||||
"plt.axvline(x=0, color='k')\n",
|
||||
"plt.yticks(np.arange(-1, 2.5, 1))\n",
|
||||
"plt.xlabel(\"$t$\")\n",
|
||||
"plt.axis([-2, 4, -1, 2.5])\n",
|
||||
"plt.legend(loc=\"upper right\")\n",
|
||||
"save_fig(\"hinge_plot\")\n",
|
||||
"plt.show()"
|
||||
]
|
||||
|
|
@ -1029,59 +998,19 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Extra material – Training Time"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"X, y = make_moons(n_samples=1000, noise=0.4, random_state=42)\n",
|
||||
"\n",
|
||||
"plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
|
||||
"plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n",
|
||||
"plt.grid()\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 32,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import time\n",
|
||||
"\n",
|
||||
"tol = 0.1\n",
|
||||
"tols = []\n",
|
||||
"times = []\n",
|
||||
"for i in range(10):\n",
|
||||
" svm_clf = SVC(kernel=\"poly\", gamma=3, C=10, tol=tol)\n",
|
||||
" t1 = time.time()\n",
|
||||
" svm_clf.fit(X, y)\n",
|
||||
" t2 = time.time()\n",
|
||||
" times.append(t2-t1)\n",
|
||||
" tols.append(tol)\n",
|
||||
" tol /= 10\n",
|
||||
"plt.semilogx(tols, times, \"bo-\")\n",
|
||||
"plt.xlabel(\"Tolerance\")\n",
|
||||
"plt.ylabel(\"Time (seconds)\")\n",
|
||||
"plt.grid()\n",
|
||||
"plt.show()"
|
||||
"# Extra Material"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Extra Material – Linear SVM classifier implementation using Batch Gradient Descent"
|
||||
"## Linear SVM classifier implementation using Batch Gradient Descent"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 33,
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1091,7 +1020,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 34,
|
||||
"execution_count": 29,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1152,7 +1081,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 35,
|
||||
"execution_count": 30,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1165,7 +1094,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 36,
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1179,7 +1108,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 37,
|
||||
"execution_count": 32,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1188,7 +1117,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 38,
|
||||
"execution_count": 33,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1199,7 +1128,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 39,
|
||||
"execution_count": 34,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1230,7 +1159,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 40,
|
||||
"execution_count": 35,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
|
|
@ -1275,7 +1204,7 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## 1. to 7."
|
||||
"## 1. to 8."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1289,14 +1218,14 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# 8."
|
||||
"# 9."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"_Exercise: train a `LinearSVC` on a linearly separable dataset. Then train an `SVC` and a `SGDClassifier` on the same dataset. See if you can get them to produce roughly the same model._"
|
||||
"_Exercise: Train a `LinearSVC` on a linearly separable dataset. Then train an `SVC` and a `SGDClassifier` on the same dataset. See if you can get them to produce roughly the same model._"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1308,7 +1237,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 41,
|
||||
"execution_count": 36,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1323,9 +1252,19 @@
|
|||
"y = y[setosa_or_versicolor]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Now let's build and train 3 models:\n",
|
||||
"* Remember that `LinearSVC` uses `loss=\"squared_hinge\"` by default, so if we want all 3 models to produce similar results, we need to set `loss=\"hinge\"`.\n",
|
||||
"* Also, the `SVC` class uses an RBF kernel by default, so we need to set `kernel=\"linear\"` to get similar results as the other two models.\n",
|
||||
"* Lastly, the `SGDClassifier` class does not have a `C` hyperparameter, but it has another regularization hyperparameter called `alpha`, so we can tweak it to get similar results as the other two models."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 42,
|
||||
"execution_count": 37,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1334,24 +1273,14 @@
|
|||
"from sklearn.preprocessing import StandardScaler\n",
|
||||
"\n",
|
||||
"C = 5\n",
|
||||
"alpha = 1 / (C * len(X))\n",
|
||||
"\n",
|
||||
"lin_clf = LinearSVC(loss=\"hinge\", C=C, random_state=42)\n",
|
||||
"svm_clf = SVC(kernel=\"linear\", C=C)\n",
|
||||
"sgd_clf = SGDClassifier(loss=\"hinge\", learning_rate=\"constant\", eta0=0.001,\n",
|
||||
" alpha=alpha, max_iter=1000, tol=1e-3, random_state=42)\n",
|
||||
"alpha = 0.05\n",
|
||||
"\n",
|
||||
"scaler = StandardScaler()\n",
|
||||
"X_scaled = scaler.fit_transform(X)\n",
|
||||
"\n",
|
||||
"lin_clf.fit(X_scaled, y)\n",
|
||||
"svm_clf.fit(X_scaled, y)\n",
|
||||
"sgd_clf.fit(X_scaled, y)\n",
|
||||
"\n",
|
||||
"print(\"LinearSVC: \", lin_clf.intercept_, lin_clf.coef_)\n",
|
||||
"print(\"SVC: \", svm_clf.intercept_, svm_clf.coef_)\n",
|
||||
"print(f\"SGDClassifier(alpha={sgd_clf.alpha:.1e}):\",\n",
|
||||
" sgd_clf.intercept_, sgd_clf.coef_)"
|
||||
"lin_clf = LinearSVC(loss=\"hinge\", C=C, random_state=42).fit(X_scaled, y)\n",
|
||||
"svc_clf = SVC(kernel=\"linear\", C=C).fit(X_scaled, y)\n",
|
||||
"sgd_clf = SGDClassifier(alpha=alpha, random_state=42).fit(X_scaled, y)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1363,28 +1292,24 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 43,
|
||||
"execution_count": 38,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Compute the slope and bias of each decision boundary\n",
|
||||
"w1 = -lin_clf.coef_[0, 0] / lin_clf.coef_[0, 1]\n",
|
||||
"b1 = -lin_clf.intercept_[0] / lin_clf.coef_[0, 1]\n",
|
||||
"w2 = -svm_clf.coef_[0, 0] / svm_clf.coef_[0, 1]\n",
|
||||
"b2 = -svm_clf.intercept_[0] / svm_clf.coef_[0, 1]\n",
|
||||
"w3 = -sgd_clf.coef_[0, 0] / sgd_clf.coef_[0, 1]\n",
|
||||
"b3 = -sgd_clf.intercept_[0] / sgd_clf.coef_[0, 1]\n",
|
||||
"def compute_decision_boundary(model):\n",
|
||||
" w = -model.coef_[0, 0] / model.coef_[0, 1]\n",
|
||||
" b = -model.intercept_[0] / model.coef_[0, 1]\n",
|
||||
" return scaler.inverse_transform([[-10, -10 * w + b], [10, 10 * w + b]])\n",
|
||||
"\n",
|
||||
"# Transform the decision boundary lines back to the original scale\n",
|
||||
"line1 = scaler.inverse_transform([[-10, -10 * w1 + b1], [10, 10 * w1 + b1]])\n",
|
||||
"line2 = scaler.inverse_transform([[-10, -10 * w2 + b2], [10, 10 * w2 + b2]])\n",
|
||||
"line3 = scaler.inverse_transform([[-10, -10 * w3 + b3], [10, 10 * w3 + b3]])\n",
|
||||
"lin_line = compute_decision_boundary(lin_clf)\n",
|
||||
"svc_line = compute_decision_boundary(svc_clf)\n",
|
||||
"sgd_line = compute_decision_boundary(sgd_clf)\n",
|
||||
"\n",
|
||||
"# Plot all three decision boundaries\n",
|
||||
"plt.figure(figsize=(11, 4))\n",
|
||||
"plt.plot(line1[:, 0], line1[:, 1], \"k:\", label=\"LinearSVC\")\n",
|
||||
"plt.plot(line2[:, 0], line2[:, 1], \"b--\", linewidth=2, label=\"SVC\")\n",
|
||||
"plt.plot(line3[:, 0], line3[:, 1], \"r-\", label=\"SGDClassifier\")\n",
|
||||
"plt.plot(lin_line[:, 0], lin_line[:, 1], \"k:\", label=\"LinearSVC\")\n",
|
||||
"plt.plot(svc_line[:, 0], svc_line[:, 1], \"b--\", linewidth=2, label=\"SVC\")\n",
|
||||
"plt.plot(sgd_line[:, 0], sgd_line[:, 1], \"r-\", label=\"SGDClassifier\")\n",
|
||||
"plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\") # label=\"Iris versicolor\"\n",
|
||||
"plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\") # label=\"Iris setosa\"\n",
|
||||
"plt.xlabel(\"Petal length\")\n",
|
||||
|
|
@ -1407,14 +1332,14 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# 9."
|
||||
"# 10."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"_Exercise: train an SVM classifier on the Wine dataset, which you can load using `sklearn.datasets.load_wine()`. This dataset contains the chemical analysis of 178 wine samples produced by 3 different cultivators: the goal is to train a classification model capable of predicting the cultivator based on the wine's chemical analysis. Since SVM classifiers are binary classifiers, you will need to use one-versus-all to classify all 3 classes. You may want to tune the hyperparameters using small validation sets to speed up the process. What accuracy can you reach?_"
|
||||
"_Exercise: Train an SVM classifier on the Wine dataset, which you can load using `sklearn.datasets.load_wine()`. This dataset contains the chemical analysis of 178 wine samples produced by 3 different cultivators: the goal is to train a classification model capable of predicting the cultivator based on the wine's chemical analysis. Since SVM classifiers are binary classifiers, you will need to use one-versus-all to classify all 3 classes. What accuracy can you reach?_"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1426,7 +1351,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 44,
|
||||
"execution_count": 39,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1437,7 +1362,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 45,
|
||||
"execution_count": 40,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1446,7 +1371,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 46,
|
||||
"execution_count": 41,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1458,7 +1383,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 47,
|
||||
"execution_count": 42,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1467,7 +1392,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 48,
|
||||
"execution_count": 43,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1483,7 +1408,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 49,
|
||||
"execution_count": 44,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1500,7 +1425,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 50,
|
||||
"execution_count": 45,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1519,7 +1444,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 51,
|
||||
"execution_count": 46,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1539,7 +1464,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 52,
|
||||
"execution_count": 47,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1557,7 +1482,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 53,
|
||||
"execution_count": 48,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1582,7 +1507,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 54,
|
||||
"execution_count": 49,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1599,7 +1524,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 55,
|
||||
"execution_count": 50,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1618,7 +1543,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 56,
|
||||
"execution_count": 51,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1634,7 +1559,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 57,
|
||||
"execution_count": 52,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1652,14 +1577,14 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## 10."
|
||||
"## 11."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"_Exercise: Train and fine-tune an SVM regressor on the California housing dataset. You can use the original dataset rather than the tweaked version we used in Chapter 2. The original dataset can be fetched using `sklearn.datasets.fetch_california_housing()`. Since there are over 20,000 instances, SVMs can be slow, so for hyperparameter tuning you should use much less instances (e.g., 2,000), to test many more hyperparameter combinations._"
|
||||
"_Exercise: Train and fine-tune an SVM regressor on the California housing dataset. You can use the original dataset rather than the tweaked version we used in Chapter 2. The original dataset can be fetched using `sklearn.datasets.fetch_california_housing()`. The labels represent hundreds of thousands of dollars. Since there are over 20,000 instances, SVMs can be slow, so for hyperparameter tuning you should use much less instances (e.g., 2,000), to test many more hyperparameter combinations. What is your best model's RMSE?_"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1671,7 +1596,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 58,
|
||||
"execution_count": 53,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1691,13 +1616,14 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 59,
|
||||
"execution_count": 54,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from sklearn.model_selection import train_test_split\n",
|
||||
"\n",
|
||||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
|
||||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2,\n",
|
||||
" random_state=42)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1716,7 +1642,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 60,
|
||||
"execution_count": 55,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1735,7 +1661,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 61,
|
||||
"execution_count": 56,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1753,7 +1679,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 62,
|
||||
"execution_count": 57,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1773,7 +1699,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 63,
|
||||
"execution_count": 58,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1789,7 +1715,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 64,
|
||||
"execution_count": 59,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1810,7 +1736,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 65,
|
||||
"execution_count": 60,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1819,7 +1745,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 66,
|
||||
"execution_count": 61,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1836,7 +1762,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 67,
|
||||
"execution_count": 62,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
|
|||
Loading…
Reference in New Issue