diff --git a/anno3/apprendimento_automatico/esercizi/marco/AdaBoost-checkpoint.ipynb b/anno3/apprendimento_automatico/esercizi/marco/AdaBoost-checkpoint.ipynb
new file mode 100644
index 0000000..662bc58
--- /dev/null
+++ b/anno3/apprendimento_automatico/esercizi/marco/AdaBoost-checkpoint.ipynb
@@ -0,0 +1,365 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 81,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import math\n",
+ "from copy import deepcopy\n",
+ "import sklearn.datasets\n",
+ "from sklearn.svm import SVC"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "X,y = sklearn.datasets.make_hastie_10_2()\n",
+ "X_train = X[0:8000,:]\n",
+ "y_train = y[0:8000]\n",
+ "X_test = X[8000:,:]\n",
+ "y_test = y[8000:]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 72,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class SVC_:\n",
+ " def __init__(self, kernel=\"rbf\", degree=\"3\"):\n",
+ " self.svc = SVC(kernel=kernel, degree=degree)\n",
+ "\n",
+ " def fit(self, X, y, sample_weight=None):\n",
+ " if sample_weight is not None:\n",
+ " sample_weight = sample_weight * len(X)\n",
+ "\n",
+ " self.svc.fit(X,y,sample_weight=sample_weight)\n",
+ " return self\n",
+ "\n",
+ " def predict(self, X):\n",
+ " return self.svc.predict(X)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 1\n",
+ "\n",
+ "1. Implement the AdaBoost ensemble algorithm by completing the following code:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 226,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class AdaBoost:\n",
+ " def __init__(self, weakModel, T):\n",
+ " self.model = weakModel\n",
+ " self.models = []\n",
+ " self.T = T\n",
+ " self.a = []\n",
+ "\n",
+ " def fit(self, X, y):\n",
+ " w = [1 / len(X) for x in X]\n",
+ " for t in range(self.T):\n",
+ " model = deepcopy(self.model)\n",
+ " model.fit(X, y, sample_weight = w)\n",
+ " predictions = model.predict(X)\n",
+ " self.models.append(model)\n",
+ " e = sum([w[i] if predictions[i] != y[i] else 0 for i in range(len(y))])\n",
+ " if t%10 == 0:\n",
+ " print(\"Weighted Error:\", e)\n",
+ " a = np.log((1 - e) / e) / 2\n",
+ " self.a.append(a)\n",
+ " w = [w[i] * np.exp(-a * y[i] * predictions[i]) for i in range(len(w))]\n",
+ " w /= sum(w)\n",
+ " return self\n",
+ "\n",
+ " def predict(self, X):\n",
+ " return np.sign(sum([self.a[t] * self.models[t].predict(X) for t in range(self.T)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the implementation you are free to assume:\n",
+ "- that the problem is a binary classification problem with labels in $\\{-1, +1\\}$.\n",
+ "- that the weakModel can fit a weighted sample set by means of the call `weakModel.fit(X,y,sample_weight=w)` where `w` is a vector of length $|y|$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "2. Test your implementation on the dataset loaded above and using an SVC with a polynomial kernel. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 227,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Weighted Error: 0.49512499999995935\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n"
+ ]
+ }
+ ],
+ "source": [
+ "weakModel = SVC(kernel=\"poly\", degree=3)\n",
+ "adaboost = AdaBoost(weakModel, 10)\n",
+ "adaboost.fit(X_train, y_train)\n",
+ "y_test_ = adaboost.predict(X_test)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 123,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.49425\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(0.5 - (y_test.dot(y_test_)) / (2 * len(y_test)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "3. evaluate the AdaBoost performances as usual by calculating the classification error and compare it with the classification error of the weak model.\n",
+ "\n",
+ "**Note 1**: \n",
+ "since the labels are bound to be in ${+1, -1}$, the classification error (i.e., the number of incorrectly classified examples over the total number of examples) can be easily computed as:\n",
+ "$$\n",
+ " error(y,y') = \\frac{N - y \\cdot y'}{2N} = \\frac{1}{2} - \\frac{y \\cdot y'}{2N},\n",
+ "$$\n",
+ "where $N$ is the total number of examples. The formula can be derived noticing that $y \\cdot y'$ calculates the number $N_c$ of examples correctly classified minus the number $N_{\\bar c}$ of examples incorrectly classified. We have then $y \\cdot y' = N_c - N_{\\bar c}$ and by noticing that $N = N_c + N_{\\bar c}$:\n",
+ "$$\n",
+ " N - y \\cdot y' = N_c + N_{\\bar c} - N_c + N_{\\bar c} = 2 N_{\\bar c} \\Rightarrow \\frac{N - y \\cdot y'}{2 N} = \\frac{N_{\\bar c}}{N}\n",
+ "$$\n",
+ "\n",
+ "**Note 2**:\n",
+ "do not forget to deepcopy your base model before fitting it to the new data\n",
+ "\n",
+ "**Note 3**:\n",
+ "The SVC model allows specifying weights, but it *does not* work well when weights are normalized (it works well when the weights are larger). The following class takes normalized weights and denormalize them before passing them to the SVC classifier:\n",
+ "\n",
+ "```python\n",
+ " class SVC_:\n",
+ " def __init__(self, kernel=\"rbf\", degree=\"3\"):\n",
+ " self.svc = SVC(kernel=kernel, degree=degree)\n",
+ "\n",
+ " def fit(self, X,y,sample_weight=None):\n",
+ " if sample_weight is not None:\n",
+ " sample_weight = sample_weight * len(X)\n",
+ "\n",
+ " self.svc.fit(X,y,sample_weight=sample_weight)\n",
+ " return self\n",
+ "\n",
+ " def predict(self, X):\n",
+ " return self.svc.predict(X)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "1. Write a weak learner to be used with the AdaBoost algorithm you just wrote. The weak learner that you will implement is the most inaccurate weak learner possible: it basically works by extracting a linear model at random and trying to use that model to classify the examples. Being extracted at random the models it generates do not guarantee that the weighted error $\\epsilon_t$ is smaller than $0.5$. The algorithm solves this problem by flipping the decisions whenever it finds out that $\\epsilon_t > 0.5$ (i.e., if the weighted error is larger than $0.5$ it reverses the sign of all the weights so that the decision surface stays the same, but the regions where it predicts $+1$ and $-1$ are reversed).\n",
+ "\n",
+ " It shall work as follows:\n",
+ "\n",
+ " - it creates a random linear model by generating the needed weight vector $\\mathbf{w}$ at random (**note**: these are the weights of the linear model, they are *NOT* related in any way to the weights of the examples); each weight shall be sampled from U(-1,1);\n",
+ " - it evaluates the weighted loss $\\epsilon_t$ on the given dataset and flip the linear model if $\\epsilon_t > 0.5$;\n",
+ " - at prediction time it predicts +1 if $\\mathbf{x} \\cdot \\mathbf{w} > 0$; it predicts -1 otherwise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 222,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class RandomLinearModel:\n",
+ " def loss(self, y, y_, sample_weight):\n",
+ " return sum([sample_weight[i] if y[i] != y_[i] else 0 for i in range(len(y))])\n",
+ " \n",
+ " def fit(self,X,y,sample_weight=[]):\n",
+ " self.w = np.random.rand(len(X[0])) * 2 - 1\n",
+ " if len(sample_weight) == 0:\n",
+ " sample_weight = [1 / len(X) for x in X]\n",
+ " if self.loss(y, self.predict(X), sample_weight) > 0.5:\n",
+ " self.w *= -1\n",
+ " return self\n",
+ " \n",
+ " def predict(self,X):\n",
+ " return np.sign(X.dot(self.w))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 228,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.487\n"
+ ]
+ }
+ ],
+ "source": [
+ "rs = RandomLinearModel()\n",
+ "rs.fit(X_train, y_train)\n",
+ "predictions = rs.predict(X_test)\n",
+ "print(0.5 - y_test.dot(predictions)/(2 * len(y_test)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "2. Learn an AdaBoost model using the RandomLinearModel weak learner printing every $K$ iterations the weighted error and the current error of the ensemble (you are free to choose $K$ so to make your output just frequent enough to let you know what is happening but without flooding the console with messages). Evaluate the training and test error of the final ensemble model."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 229,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Weighted Error: 0.49524999999995933\n",
+ "Weighted Error: 0.4948541341954795\n",
+ "Weighted Error: 0.49729398392530305\n",
+ "Weighted Error: 0.49980867302257964\n",
+ "Weighted Error: 0.49683487146024025\n",
+ "Weighted Error: 0.49790489175815233\n",
+ "Weighted Error: 0.4940625587347454\n",
+ "Weighted Error: 0.4950371378338745\n",
+ "Weighted Error: 0.4909255291281916\n",
+ "Weighted Error: 0.4960331784908466\n"
+ ]
+ }
+ ],
+ "source": [
+ "rs = RandomLinearModel()\n",
+ "a = AdaBoost(rs,100)\n",
+ "a.fit(X_train,y_train)\n",
+ "\n",
+ "y_train_ = a.predict(X_train)\n",
+ "y_test_ = a.predict(X_test)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 232,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Training Error: 0.462125\n",
+ "Test Error: 0.49375\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Training Error:\", 0.5 - y_train.dot(y_train_)/(2 * len(y_train)))\n",
+ "print(\"Test Error:\", 0.5 - y_test.dot(y_test_)/(2 * len(y_test)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "3. Write few paragraphs about what you think about the experiment and about the results you obtained."
+ ]
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/anno3/apprendimento_automatico/esercizi/marco/AdaBoost.ipynb b/anno3/apprendimento_automatico/esercizi/marco/AdaBoost.ipynb
new file mode 100644
index 0000000..3543b22
--- /dev/null
+++ b/anno3/apprendimento_automatico/esercizi/marco/AdaBoost.ipynb
@@ -0,0 +1,385 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import math\n",
+ "from copy import deepcopy\n",
+ "import sklearn.datasets\n",
+ "from sklearn.svm import SVC"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "X,y = sklearn.datasets.make_hastie_10_2()\n",
+ "X_train = X[0:8000,:]\n",
+ "y_train = y[0:8000]\n",
+ "X_test = X[8000:,:]\n",
+ "y_test = y[8000:]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class SVC_:\n",
+ " def __init__(self, kernel=\"rbf\", degree=\"3\"):\n",
+ " self.svc = SVC(kernel=kernel, degree=degree)\n",
+ "\n",
+ " def fit(self, X, y, sample_weight=None):\n",
+ " if sample_weight is not None:\n",
+ " sample_weight = sample_weight * len(X)\n",
+ "\n",
+ " self.svc.fit(X,y,sample_weight=sample_weight)\n",
+ " return self\n",
+ "\n",
+ " def predict(self, X):\n",
+ " return self.svc.predict(X)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 1\n",
+ "\n",
+ "1. Implement the AdaBoost ensemble algorithm by completing the following code:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class AdaBoost:\n",
+ " def __init__(self, weakModel, T):\n",
+ " self.model = weakModel\n",
+ " self.models = []\n",
+ " self.T = T\n",
+ " self.a = []\n",
+ "\n",
+ " def fit(self, X, y):\n",
+ " w = np.array([1 / len(X) for x in X])\n",
+ " for t in range(self.T):\n",
+ " model = deepcopy(self.model)\n",
+ " model.fit(X, y, sample_weight = w)\n",
+ " predictions = model.predict(X)\n",
+ " self.models.append(model)\n",
+ " e = sum([w[i] if predictions[i] != y[i] else 0 for i in range(len(y))])\n",
+ " if t%10 == 0:\n",
+ " print(\"Weighted Error:\", e)\n",
+ " a = np.log((1 - e) / e) / 2\n",
+ " self.a.append(a)\n",
+ " w = np.array([w[i] * np.exp(-a * y[i] * predictions[i]) for i in range(len(w))])\n",
+ " w /= sum(w)\n",
+ " return self\n",
+ "\n",
+ " def predict(self, X):\n",
+ " return np.sign(sum([self.a[t] * self.models[t].predict(X) for t in range(self.T)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the implementation you are free to assume:\n",
+ "- that the problem is a binary classification problem with labels in $\\{-1, +1\\}$.\n",
+ "- that the weakModel can fit a weighted sample set by means of the call `weakModel.fit(X,y,sample_weight=w)` where `w` is a vector of length $|y|$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "2. Test your implementation on the dataset loaded above and using an SVC with a polynomial kernel. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "8000"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(X_train)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Weighted Error: 0.3538749999999749\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n",
+ "C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\n",
+ " \"avoid this warning.\", FutureWarning)\n"
+ ]
+ }
+ ],
+ "source": [
+ "weakModel = SVC_(kernel=\"poly\", degree=3)\n",
+ "adaboost = AdaBoost(weakModel, 10)\n",
+ "adaboost.fit(X_train, y_train)\n",
+ "y_test_ = adaboost.predict(X_test)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.22525\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(0.5 - (y_test.dot(y_test_)) / (2 * len(y_test)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "3. evaluate the AdaBoost performances as usual by calculating the classification error and compare it with the classification error of the weak model.\n",
+ "\n",
+ "**Note 1**: \n",
+ "since the labels are bound to be in ${+1, -1}$, the classification error (i.e., the number of incorrectly classified examples over the total number of examples) can be easily computed as:\n",
+ "$$\n",
+ " error(y,y') = \\frac{N - y \\cdot y'}{2N} = \\frac{1}{2} - \\frac{y \\cdot y'}{2N},\n",
+ "$$\n",
+ "where $N$ is the total number of examples. The formula can be derived noticing that $y \\cdot y'$ calculates the number $N_c$ of examples correctly classified minus the number $N_{\\bar c}$ of examples incorrectly classified. We have then $y \\cdot y' = N_c - N_{\\bar c}$ and by noticing that $N = N_c + N_{\\bar c}$:\n",
+ "$$\n",
+ " N - y \\cdot y' = N_c + N_{\\bar c} - N_c + N_{\\bar c} = 2 N_{\\bar c} \\Rightarrow \\frac{N - y \\cdot y'}{2 N} = \\frac{N_{\\bar c}}{N}\n",
+ "$$\n",
+ "\n",
+ "**Note 2**:\n",
+ "do not forget to deepcopy your base model before fitting it to the new data\n",
+ "\n",
+ "**Note 3**:\n",
+ "The SVC model allows specifying weights, but it *does not* work well when weights are normalized (it works well when the weights are larger). The following class takes normalized weights and denormalize them before passing them to the SVC classifier:\n",
+ "\n",
+ "```python\n",
+ " class SVC_:\n",
+ " def __init__(self, kernel=\"rbf\", degree=\"3\"):\n",
+ " self.svc = SVC(kernel=kernel, degree=degree)\n",
+ "\n",
+ " def fit(self, X,y,sample_weight=None):\n",
+ " if sample_weight is not None:\n",
+ " sample_weight = sample_weight * len(X)\n",
+ "\n",
+ " self.svc.fit(X,y,sample_weight=sample_weight)\n",
+ " return self\n",
+ "\n",
+ " def predict(self, X):\n",
+ " return self.svc.predict(X)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "1. Write a weak learner to be used with the AdaBoost algorithm you just wrote. The weak learner that you will implement is the most inaccurate weak learner possible: it basically works by extracting a linear model at random and trying to use that model to classify the examples. Being extracted at random the models it generates do not guarantee that the weighted error $\\epsilon_t$ is smaller than $0.5$. The algorithm solves this problem by flipping the decisions whenever it finds out that $\\epsilon_t > 0.5$ (i.e., if the weighted error is larger than $0.5$ it reverses the sign of all the weights so that the decision surface stays the same, but the regions where it predicts $+1$ and $-1$ are reversed).\n",
+ "\n",
+ " It shall work as follows:\n",
+ "\n",
+ " - it creates a random linear model by generating the needed weight vector $\\mathbf{w}$ at random (**note**: these are the weights of the linear model, they are *NOT* related in any way to the weights of the examples); each weight shall be sampled from U(-1,1);\n",
+ " - it evaluates the weighted loss $\\epsilon_t$ on the given dataset and flip the linear model if $\\epsilon_t > 0.5$;\n",
+ " - at prediction time it predicts +1 if $\\mathbf{x} \\cdot \\mathbf{w} > 0$; it predicts -1 otherwise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 222,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class RandomLinearModel:\n",
+ " def loss(self, y, y_, sample_weight):\n",
+ " return sum([sample_weight[i] if y[i] != y_[i] else 0 for i in range(len(y))])\n",
+ " \n",
+ " def fit(self,X,y,sample_weight=[]):\n",
+ " self.w = np.random.rand(len(X[0])) * 2 - 1\n",
+ " if len(sample_weight) == 0:\n",
+ " sample_weight = [1 / len(X) for x in X]\n",
+ " if self.loss(y, self.predict(X), sample_weight) > 0.5:\n",
+ " self.w *= -1\n",
+ " return self\n",
+ " \n",
+ " def predict(self,X):\n",
+ " return np.sign(X.dot(self.w))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 228,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.487\n"
+ ]
+ }
+ ],
+ "source": [
+ "rs = RandomLinearModel()\n",
+ "rs.fit(X_train, y_train)\n",
+ "predictions = rs.predict(X_test)\n",
+ "print(0.5 - y_test.dot(predictions)/(2 * len(y_test)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "2. Learn an AdaBoost model using the RandomLinearModel weak learner printing every $K$ iterations the weighted error and the current error of the ensemble (you are free to choose $K$ so to make your output just frequent enough to let you know what is happening but without flooding the console with messages). Evaluate the training and test error of the final ensemble model."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 229,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Weighted Error: 0.49524999999995933\n",
+ "Weighted Error: 0.4948541341954795\n",
+ "Weighted Error: 0.49729398392530305\n",
+ "Weighted Error: 0.49980867302257964\n",
+ "Weighted Error: 0.49683487146024025\n",
+ "Weighted Error: 0.49790489175815233\n",
+ "Weighted Error: 0.4940625587347454\n",
+ "Weighted Error: 0.4950371378338745\n",
+ "Weighted Error: 0.4909255291281916\n",
+ "Weighted Error: 0.4960331784908466\n"
+ ]
+ }
+ ],
+ "source": [
+ "rs = RandomLinearModel()\n",
+ "a = AdaBoost(rs,100)\n",
+ "a.fit(X_train,y_train)\n",
+ "\n",
+ "y_train_ = a.predict(X_train)\n",
+ "y_test_ = a.predict(X_test)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 232,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Training Error: 0.462125\n",
+ "Test Error: 0.49375\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Training Error:\", 0.5 - y_train.dot(y_train_)/(2 * len(y_train)))\n",
+ "print(\"Test Error:\", 0.5 - y_test.dot(y_test_)/(2 * len(y_test)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "3. Write few paragraphs about what you think about the experiment and about the results you obtained."
+ ]
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/anno3/apprendimento_automatico/esercizi/marco/Datasets/3-clusters.csv b/anno3/apprendimento_automatico/esercizi/marco/Datasets/3-clusters.csv
new file mode 100644
index 0000000..646d43f
--- /dev/null
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\ No newline at end of file
diff --git a/anno3/apprendimento_automatico/esercizi/marco/Datasets/CURE-complete.csv b/anno3/apprendimento_automatico/esercizi/marco/Datasets/CURE-complete.csv
new file mode 100644
index 0000000..67f5c98
--- /dev/null
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\ No newline at end of file
diff --git a/anno3/apprendimento_automatico/esercizi/marco/Datasets/dataset-DBSCAN.csv b/anno3/apprendimento_automatico/esercizi/marco/Datasets/dataset-DBSCAN.csv
new file mode 100644
index 0000000..e0d6984
--- /dev/null
+++ b/anno3/apprendimento_automatico/esercizi/marco/Datasets/dataset-DBSCAN.csv
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\ No newline at end of file
diff --git a/anno3/apprendimento_automatico/esercizi/marco/aaut-merged.pdf b/anno3/apprendimento_automatico/esercizi/marco/aaut-merged.pdf
new file mode 100644
index 0000000..ad57e5a
Binary files /dev/null and b/anno3/apprendimento_automatico/esercizi/marco/aaut-merged.pdf differ
diff --git a/anno3/apprendimento_automatico/esercizi/marco/classification_iris_aa_19_20-checkpoint.ipynb b/anno3/apprendimento_automatico/esercizi/marco/classification_iris_aa_19_20-checkpoint.ipynb
new file mode 100644
index 0000000..8c888af
--- /dev/null
+++ b/anno3/apprendimento_automatico/esercizi/marco/classification_iris_aa_19_20-checkpoint.ipynb
@@ -0,0 +1,1810 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# # Classifiers introduction\n",
+ "\n",
+ "In the following program we introduce the basic steps of classification of a dataset in a matrix"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Import the package for learning and modeling trees"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "from sklearn import tree"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Define the matrix containing the data (one example per row)\n",
+ "and the vector containing the corresponding target value"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "X = [[0, 0, 0], [1, 1, 1], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1]]\n",
+ "Y = [1, 0, 0, 0, 1, 1]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Declare the classification model you want to use and then fit the model to the data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "clf = tree.DecisionTreeClassifier()\n",
+ "clf = clf.fit(X, Y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Predict the target value (and print it) for the passed data, using the fitted model currently in clf"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(clf.predict([[0, 1, 1]]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 0]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(clf.predict([[1, 0, 1],[0, 0, 1]]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "import os\n",
+ "os.environ[\"PATH\"] += os.pathsep + 'C:/Users/galat/.conda/envs/aaut/Library/bin/graphviz'\n",
+ "import graphviz\n",
+ "dot_data = tree.export_graphviz(clf, out_file=None) \n",
+ "graph = graphviz.Source(dot_data) \n",
+ "graph"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the following we start using a dataset (from UCI Machine Learning repository)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from sklearn.datasets import load_iris\n",
+ "iris = load_iris()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Declare the type of prediction model and the working criteria for the model induction algorithm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "clf = tree.DecisionTreeClassifier(criterion=\"entropy\",random_state=300,min_samples_leaf=5,class_weight={0:1,1:1,2:1})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Split the dataset in training and test set"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate a random permutation of the indices of examples that will be later used \n",
+ "# for the training and the test set\n",
+ "import numpy as np\n",
+ "np.random.seed(1231)\n",
+ "indices = np.random.permutation(len(iris.data))\n",
+ "\n",
+ "# We now decide to keep the last 10 indices for test set, the remaining for the training set\n",
+ "indices_training=indices[:-10]\n",
+ "indices_test=indices[-10:]\n",
+ "\n",
+ "iris_X_train = iris.data[indices_training] # keep for training all the matrix elements with the exception of the last 10 \n",
+ "iris_y_train = iris.target[indices_training]\n",
+ "iris_X_test = iris.data[indices_test] # keep the last 10 elements for test set\n",
+ "iris_y_test = iris.target[indices_test]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Fit the learning model on training set"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# fit the model to the training data\n",
+ "clf = clf.fit(iris_X_train, iris_y_train)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Obtain predictions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Predictions:\n",
+ "[0 0 0 1 0 0 1 2 0 0]\n",
+ "True classes:\n",
+ "[0 0 0 2 0 0 1 1 0 0]\n",
+ "['setosa' 'versicolor' 'virginica']\n"
+ ]
+ }
+ ],
+ "source": [
+ "# apply fitted model \"clf\" to the test set \n",
+ "predicted_y_test = clf.predict(iris_X_test)\n",
+ "\n",
+ "# print the predictions (class numbers associated to classes names in target names)\n",
+ "print(\"Predictions:\")\n",
+ "print(predicted_y_test)\n",
+ "print(\"True classes:\")\n",
+ "print(iris_y_test) \n",
+ "print(iris.target_names)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Print the index of the test instances and the corresponding predictions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Look at the specific examples"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Instance # 33: \n",
+ "sepal length (cm)=5.5, sepal width (cm)=4.2, petal length (cm)=1.4, petal width (cm)=0.2\n",
+ "Predicted: setosa\t True: setosa\n",
+ "\n",
+ "Instance # 2: \n",
+ "sepal length (cm)=4.7, sepal width (cm)=3.2, petal length (cm)=1.3, petal width (cm)=0.2\n",
+ "Predicted: setosa\t True: setosa\n",
+ "\n",
+ "Instance # 11: \n",
+ "sepal length (cm)=4.8, sepal width (cm)=3.4, petal length (cm)=1.6, petal width (cm)=0.2\n",
+ "Predicted: setosa\t True: setosa\n",
+ "\n",
+ "Instance # 126: \n",
+ "sepal length (cm)=6.2, sepal width (cm)=2.8, petal length (cm)=4.8, petal width (cm)=1.8\n",
+ "Predicted: versicolor\t True: virginica\n",
+ "\n",
+ "Instance # 49: \n",
+ "sepal length (cm)=5.0, sepal width (cm)=3.3, petal length (cm)=1.4, petal width (cm)=0.2\n",
+ "Predicted: setosa\t True: setosa\n",
+ "\n",
+ "Instance # 10: \n",
+ "sepal length (cm)=5.4, sepal width (cm)=3.7, petal length (cm)=1.5, petal width (cm)=0.2\n",
+ "Predicted: setosa\t True: setosa\n",
+ "\n",
+ "Instance # 85: \n",
+ "sepal length (cm)=6.0, sepal width (cm)=3.4, petal length (cm)=4.5, petal width (cm)=1.6\n",
+ "Predicted: versicolor\t True: versicolor\n",
+ "\n",
+ "Instance # 52: \n",
+ "sepal length (cm)=6.9, sepal width (cm)=3.1, petal length (cm)=4.9, petal width (cm)=1.5\n",
+ "Predicted: virginica\t True: versicolor\n",
+ "\n",
+ "Instance # 5: \n",
+ "sepal length (cm)=5.4, sepal width (cm)=3.9, petal length (cm)=1.7, petal width (cm)=0.4\n",
+ "Predicted: setosa\t True: setosa\n",
+ "\n",
+ "Instance # 21: \n",
+ "sepal length (cm)=5.1, sepal width (cm)=3.7, petal length (cm)=1.5, petal width (cm)=0.4\n",
+ "Predicted: setosa\t True: setosa\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "for i in range(len(iris_y_test)): \n",
+ " print(\"Instance # \"+str(indices_test[i])+\": \")\n",
+ " s=\"\"\n",
+ " for j in range(len(iris.feature_names)):\n",
+ " s=s+iris.feature_names[j]+\"=\"+str(iris_X_test[i][j])\n",
+ " if (j\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dot_data = tree.export_graphviz(clf, out_file=None, \n",
+ " feature_names=iris.feature_names, \n",
+ " class_names=iris.target_names, \n",
+ " filled=True, rounded=True, \n",
+ " special_characters=True) \n",
+ "graph = graphviz.Source(dot_data) \n",
+ "graph"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 1. Artificial inflation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "# Generate a random permutation of the indices of examples that will be later used \n",
+ "# for the training and the test set\n",
+ "import numpy as np\n",
+ "np.random.seed(1231)\n",
+ "indices = np.random.permutation(len(iris.data))\n",
+ "\n",
+ "# We now decide to keep the last 10 indices for test set, the remaining for the training set\n",
+ "indices_training=indices[:-10]\n",
+ "indices_test=indices[-10:]\n",
+ "\n",
+ "iris_X_train = iris.data[indices_training] # keep for training all the matrix elements with the exception of the last 10 \n",
+ "iris_y_train = iris.target[indices_training]\n",
+ "iris_X_test = iris.data[indices_test] # keep the last 10 elements for test set\n",
+ "iris_y_test = iris.target[indices_test]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "samples_x = []\n",
+ "samples_y = []\n",
+ "for i in range(0, len(iris_y_train)):\n",
+ " if iris_y_train[i] == 1:\n",
+ " for _ in range(9):\n",
+ " samples_x.append(iris_X_train[i])\n",
+ " samples_y.append(1)\n",
+ " elif iris_y_train[i] == 2:\n",
+ " for _ in range(9):\n",
+ " samples_x.append(iris_X_train[i])\n",
+ " samples_y.append(2)\n",
+ "\n",
+ "#Samples inflation\n",
+ "iris_X_train = np.append(iris_X_train, samples_x, axis = 0)\n",
+ "iris_y_train = np.append(iris_y_train, samples_y, axis = 0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Accuracy: 1.0\n",
+ "F1: 1.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "clf = tree.DecisionTreeClassifier(criterion=\"entropy\",random_state=300,min_samples_leaf=10,class_weight={0:1,1:1,2:1})\n",
+ "clf = clf.fit(iris_X_train, iris_y_train)\n",
+ "predicted_y_test = clf.predict(iris_X_test)\n",
+ "acc_score = accuracy_score(iris_y_test, predicted_y_test)\n",
+ "f1 = f1_score(iris_y_test, predicted_y_test, average='macro')\n",
+ "print(\"Accuracy: \", acc_score)\n",
+ "print(\"F1: \", f1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dot_data = tree.export_graphviz(clf, out_file=None, \n",
+ " feature_names=iris.feature_names, \n",
+ " class_names=iris.target_names, \n",
+ " filled=True, rounded=True, \n",
+ " special_characters=True) \n",
+ "graph = graphviz.Source(dot_data) \n",
+ "graph"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Class weights"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate a random permutation of the indices of examples that will be later used \n",
+ "# for the training and the test set\n",
+ "import numpy as np\n",
+ "np.random.seed(1231)\n",
+ "indices = np.random.permutation(len(iris.data))\n",
+ "\n",
+ "# We now decide to keep the last 10 indices for test set, the remaining for the training set\n",
+ "indices_training=indices[:-10]\n",
+ "indices_test=indices[-10:]\n",
+ "\n",
+ "iris_X_train = iris.data[indices_training] # keep for training all the matrix elements with the exception of the last 10 \n",
+ "iris_y_train = iris.target[indices_training]\n",
+ "iris_X_test = iris.data[indices_test] # keep the last 10 elements for test set\n",
+ "iris_y_test = iris.target[indices_test]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Accuracy: 0.8\n",
+ "F1: 0.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "clf = tree.DecisionTreeClassifier(criterion=\"entropy\",random_state=300,min_samples_leaf=5,class_weight={0:1,1:10,2:10})\n",
+ "clf = clf.fit(iris_X_train, iris_y_train)\n",
+ "predicted_y_test = clf.predict(iris_X_test)\n",
+ "acc_score = accuracy_score(iris_y_test, predicted_y_test)\n",
+ "f1 = f1_score(iris_y_test, predicted_y_test, average='macro')\n",
+ "print(\"Accuracy: \", acc_score)\n",
+ "print(\"F1: \", f1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 27,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dot_data = tree.export_graphviz(clf, out_file=None, \n",
+ " feature_names=iris.feature_names, \n",
+ " class_names=iris.target_names, \n",
+ " filled=True, rounded=True, \n",
+ " special_characters=True) \n",
+ "graph = graphviz.Source(dot_data) \n",
+ "graph"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 3. Avoid overfitting"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate a random permutation of the indices of examples that will be later used \n",
+ "# for the training and the test set\n",
+ "import numpy as np\n",
+ "np.random.seed(1231)\n",
+ "indices = np.random.permutation(len(iris.data))\n",
+ "\n",
+ "# We now decide to keep the last 10 indices for test set, the remaining for the training set\n",
+ "indices_training=indices[:-10]\n",
+ "indices_test=indices[-10:]\n",
+ "\n",
+ "iris_X_train = iris.data[indices_training] # keep for training all the matrix elements with the exception of the last 10 \n",
+ "iris_y_train = iris.target[indices_training]\n",
+ "iris_X_test = iris.data[indices_test] # keep the last 10 elements for test set\n",
+ "iris_y_test = iris.target[indices_test]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Accuracy: 1.0\n",
+ "F1: 1.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "clf = tree.DecisionTreeClassifier(criterion=\"entropy\",random_state=300,min_samples_leaf=3,class_weight={0:1,1:10,2:10}, min_impurity_decrease = 0.005, max_depth = 4, max_leaf_nodes = 6)\n",
+ "clf = clf.fit(iris_X_train, iris_y_train)\n",
+ "predicted_y_test = clf.predict(iris_X_test)\n",
+ "acc_score = accuracy_score(iris_y_test, predicted_y_test)\n",
+ "f1 = f1_score(iris_y_test, predicted_y_test, average='macro')\n",
+ "print(\"Accuracy: \", acc_score)\n",
+ "print(\"F1: \", f1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n",
+ "\r\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dot_data = tree.export_graphviz(clf, out_file=None, \n",
+ " feature_names=iris.feature_names, \n",
+ " class_names=iris.target_names, \n",
+ " filled=True, rounded=True, \n",
+ " special_characters=True) \n",
+ "graph = graphviz.Source(dot_data) \n",
+ "graph"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 4. Confusion Matrix"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[7, 0, 0],\n",
+ " [0, 2, 0],\n",
+ " [0, 0, 1]])"
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# initializes the confusion matrix\n",
+ "confusion = np.zeros([3, 3], dtype = int)\n",
+ "\n",
+ "# print the corresponding instances indexes and class names\n",
+ "for i in range(len(iris_y_test)): \n",
+ " #increments the indexed cell value\n",
+ " confusion[iris_y_test[i], predicted_y_test[i]]+=1\n",
+ "confusion"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 5. ROC Curves"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[(0.0, 43.0), (30.0, 0.0), (30.0, 0.0), (40.0, 0.0), (430.0, 0.0), (440.0, 0.0)], [(0.0, 440.0), (10.0, 20.0), (20.0, 10.0), (30.0, 10.0), (43.0, 0.0), (430.0, 0.0)], [(0.0, 430.0), (10.0, 30.0), (10.0, 20.0), (20.0, 10.0), (43.0, 0.0), (440.0, 0.0)]]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "[[[0, 0.0, 30.0, 60.0, 100.0, 530.0, 970.0],\n",
+ " [0, 43.0, 43.0, 43.0, 43.0, 43.0, 43.0]],\n",
+ " [[0, 0.0, 10.0, 30.0, 60.0, 103.0, 533.0],\n",
+ " [0, 440.0, 460.0, 470.0, 480.0, 480.0, 480.0]],\n",
+ " [[0, 0.0, 10.0, 20.0, 40.0, 83.0, 523.0],\n",
+ " [0, 430.0, 460.0, 480.0, 490.0, 490.0, 490.0]]]"
+ ]
+ },
+ "execution_count": 32,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Calculates the ROC curves (x, y)\n",
+ "leafs = []\n",
+ "class_pairs = [[],[],[]]\n",
+ "roc_curves = [[[0], [0]], [[0], [0]], [[0], [0]]]\n",
+ "for i in range(clf.tree_.node_count):\n",
+ " if (clf.tree_.feature[i] == -2):\n",
+ " leafs.append(i)\n",
+ "\n",
+ "# c = class index\n",
+ "for leaf in leafs:\n",
+ " for c in range(3):\n",
+ " #pairs(neg, pos)\n",
+ " class_pairs[c].append((clf.tree_.value[leaf][0].sum() - clf.tree_.value[leaf][0][c], clf.tree_.value[leaf][0][c]))\n",
+ "\n",
+ "#pairs sorting\n",
+ "for c in range(3):\n",
+ " class_pairs[c] = sorted(class_pairs[c], key=lambda t: t[0]/max(1,t[1]))\n",
+ "print(class_pairs)\n",
+ "\n",
+ "for i in range(1, len(leafs) + 1):\n",
+ " for c in range(3):\n",
+ " roc_curves[c][0].append(class_pairs[c][i - 1][0] + roc_curves[c][0][i - 1])\n",
+ " roc_curves[c][1].append(class_pairs[c][i - 1][1] + roc_curves[c][1][i - 1])\n",
+ "\n",
+ "roc_curves"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "