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Machine Learning with Scikit-Learn.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Machine Learning with Scikit-Learn.ipynb",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/JonasSchroeder/a1813f3b23439939987af55f049f8463/machine-learning-with-scikit-learn.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "55gDWCjOrVPc",
"colab_type": "text"
},
"source": [
"# Machine Learning with Scikit-Learn\n",
"\n",
"# Data representation\n",
"\n",
"Simplest representation: table with n_samples (rows) and n_features (columns)."
]
},
{
"cell_type": "code",
"metadata": {
"id": "gTtgKyMYrdmc",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 204
},
"outputId": "d9f00736-d057-471d-b537-643121f49fa3"
},
"source": [
"import seaborn as sns\n",
"iris = sns.load_dataset('iris')\n",
"iris.head()"
],
"execution_count": 1,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>sepal_length</th>\n",
" <th>sepal_width</th>\n",
" <th>petal_length</th>\n",
" <th>petal_width</th>\n",
" <th>species</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>5.1</td>\n",
" <td>3.5</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4.9</td>\n",
" <td>3.0</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4.7</td>\n",
" <td>3.2</td>\n",
" <td>1.3</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4.6</td>\n",
" <td>3.1</td>\n",
" <td>1.5</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5.0</td>\n",
" <td>3.6</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" sepal_length sepal_width petal_length petal_width species\n",
"0 5.1 3.5 1.4 0.2 setosa\n",
"1 4.9 3.0 1.4 0.2 setosa\n",
"2 4.7 3.2 1.3 0.2 setosa\n",
"3 4.6 3.1 1.5 0.2 setosa\n",
"4 5.0 3.6 1.4 0.2 setosa"
]
},
"metadata": {
"tags": []
},
"execution_count": 1
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "YggOKfFYtBGw",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 485
},
"outputId": "b3bf7299-f808-49d6-b0bd-c0af291ef9b0"
},
"source": [
"%matplotlib inline\n",
"sns.set()\n",
"sns.pairplot(iris, hue='species', size=1.5)"
],
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/seaborn/axisgrid.py:2065: UserWarning: The `size` parameter has been renamed to `height`; pleaes update your code.\n",
" warnings.warn(msg, UserWarning)\n"
],
"name": "stderr"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<seaborn.axisgrid.PairGrid at 0x7f0cf0f91ac8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 2
},
{
"output_type": "display_data",
"data": {
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IsyHLnbtxeDIZxM4zohlYVLnF59mS6zFSo5N30QIwDDB0kCQq17yF++jx6CE/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mw2M2vWLBwOx2k8Tu1H0zXyyGHOpgVkurJx2BNITx1OrBKPqtatlAqKIom6qAY0XScztwgoOttF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\np3Vdxz+/gb0U0zmdK+1TWl+MeugP1KM7MV3gPntqe+Yu1hxaT6layoWh5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AAAEtJJREFU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\n",
"text/plain": [
"<Figure size 525.85x432 with 20 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "X353FxU9r9bC",
"colab_type": "text"
},
"source": [
"**Features Matrix:** two dimensional numerical array or matrix that stores the information, often as X with the shape [n_samples, n_features].\n",
"\n",
"**Target Vector** one dimensional array or matrix with the length n_samples. Could be seen as a special feature column like 'species' from above, which is what you want to predict based on the data (dependent variable). The target array is often described as y."
]
},
{
"cell_type": "code",
"metadata": {
"id": "3IgghTcItchU",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "290f1575-fc56-4434-c261-9d29b054988a"
},
"source": [
"X_iris = iris.drop('species', axis=1)\n",
"#X_iris.shape (150,4)\n",
"\n",
"y_iris = iris['species']\n",
"#y_iris.shape (150,)"
],
"execution_count": 6,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(150,)"
]
},
"metadata": {
"tags": []
},
"execution_count": 6
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jrqKc0iluoy4",
"colab_type": "text"
},
"source": [
"# Estimator API\n",
"\n",
"Scikit-Learn API is designed with the following guidelines in mind:\n",
"\n",
"\n",
"1. **Consistency** (all objects share common interface, methods, documentation...)\n",
"2. **Inspection** (public parameter values)\n",
"3. **Limited object history** (algorithms as classes, everything else as standard python formats like arrays, dataframes, ...)\n",
"4. **Composition** (more complex tasks represented as sequence of fundamental algorithsms)\n",
"5. **Sensible defaults** (library define appropriate defaults)\n",
"\n",
"\n",
"**Common steps to go through using the estimator API**\n",
"\n",
"1. Choose a class of model by importing the appropriate estimator class from Scikit-Learn\n",
"2. Choose model hyperparameter by instantiating this class with desired values\n",
"3. Arrange data into feature matrix and target vector\n",
"4. Fit the model to data using fit()\n",
"5. Apply the model to new data using predict() for supervised data or transform() / predict() for unsupervised data"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "g75KNdBKyRAa",
"colab_type": "text"
},
"source": [
"# Example 1: Simple linear regression"
]
},
{
"cell_type": "code",
"metadata": {
"id": "izNusyUnyZyA",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 285
},
"outputId": "6586e83f-6bd3-4a8a-fd1f-1ff7f8c4f147"
},
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"rng = np.random.RandomState(42)\n",
"x = 10*rng.rand(50)\n",
"y = 2 * x -1 + rng.randn(50)\n",
"plt.scatter(x, y)"
],
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x7f0cec073438>"
]
},
"metadata": {
"tags": []
},
"execution_count": 8
},
{
"output_type": "display_data",
"data": {
"image/png": 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xZ84c/PznP0dHR4fcw5LF7t278a1vfQufffaZ3EOR1MOHD1FSUoJZs2Zhzpw5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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "d887YbvSy7oE",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "37d46f8f-182e-4369-855c-e5c906c5d013"
},
"source": [
"# 1. Choose model\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"# 2. Choose model parameters and initiate the model\n",
"model = LinearRegression(fit_intercept=True)\n",
"model"
],
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "-kJqOuznz5YJ",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "a590c85d-f86e-4916-8cc6-098207f52569"
},
"source": [
"# 3. Arrange data into a feature matrix and target vector\n",
"x\n",
"X = x[:, np.newaxis]\n",
"X.shape"
],
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(50, 1)"
]
},
"metadata": {
"tags": []
},
"execution_count": 12
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "BxyXKOR40VrP",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "009ad6b9-9945-4768-9858-f5e4f4ae8e07"
},
"source": [
"# 4. Fit the model to the data\n",
"model.fit(X, y)"
],
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
]
},
"metadata": {
"tags": []
},
"execution_count": 13
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "IambEzjB0ju3",
"colab_type": "text"
},
"source": [
"Note: Results of the fit() command will be stored in model-specific attributes. Such learned model parameters have trailing underscores at the end.\n",
"\n",
"Examples:"
]
},
{
"cell_type": "code",
"metadata": {
"id": "aKpCzDpe04-m",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "74e0a803-e2b6-4f88-ac13-515a99ed6620"
},
"source": [
"model.coef_"
],
"execution_count": 14,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([1.9776566])"
]
},
"metadata": {
"tags": []
},
"execution_count": 14
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "81k73P6P0ZcS",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "b26d9ce5-49a7-4d69-b70c-44665f2583ec"
},
"source": [
"model.intercept_"
],
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-0.9033107255311146"
]
},
"metadata": {
"tags": []
},
"execution_count": 15
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "t5Px2O9L0_jO",
"colab_type": "text"
},
"source": [
"These two learned parameters represent the slope and intercept of a simple linear fit to the data.\n",
"\n",
"Note: Uncertainty about the internal model parameters and interpretation is a more statistical modeling question than a machine learning task. Thus, Scikit-Learn does not provide tools to draw conclusions from internal model parameters themselves; thy StatsModel package might support here"
]
},
{
"cell_type": "code",
"metadata": {
"id": "f2D0_pNK1-JQ",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 285
},
"outputId": "6d3c871d-74e3-4101-e118-7933ff5468c4"
},
"source": [
"# 5. Predict labels for unknown data\n",
"xfit = np.linspace(-1,11)\n",
"Xfit = xfit[:, np.newaxis]\n",
"yfit = model.predict(Xfit)\n",
"\n",
"plt.scatter(x,y)\n",
"plt.plot(xfit, yfit)"
],
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f0ce8894668>]"
]
},
"metadata": {
"tags": []
},
"execution_count": 16
},
{
"output_type": "display_data",
"data": {
"image/png": 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8XfuBE0qF6ZE7G24REQPdBj0dz2aNmnodvsjIxcX8KgwP88NryXH4v//+2ewp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\nRK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3PIEo6zx2g9B",
"colab_type": "text"
},
"source": [
"# Example 2: Supervised learning with Iris classification\n",
"\n",
"Train a model on part of the iris dataset and use it to predict the remaining labels. How well did it perform?\n",
"\n",
"*Naive Gaussian Bayes*: assuming that each class is drawn from an axis-aligned Gaussian distribution (strong assumption); fast and doesn't need hyperparameter to choose; thus a good model to use as baseline classification. https://www.youtube.com/watch?v=CPqOCI0ahss"
]
},
{
"cell_type": "code",
"metadata": {
"id": "k5_smBdt2xfG",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "ad805b2f-b9df-42ee-a94d-6fbad6ee48ca"
},
"source": [
"import seaborn as sns\n",
"from sklearn.model_selection import train_test_split\n",
"\n",
"# 0. Data preparation\n",
"iris = sns.load_dataset('iris')\n",
"X_iris = iris.drop('species', axis=1)\n",
"y_iris = iris['species']\n",
"\n",
"Xtrain, Xtest, ytrain, ytest = train_test_split(X_iris, y_iris, random_state=1)\n",
"\n",
"# 1.Choice of model\n",
"from sklearn.naive_bayes import GaussianNB\n",
"\n",
"# 2. Model hyperparameter at instantiation (none)\n",
"model = GaussianNB()\n",
"\n",
"# 3. Arrange data (see above)\n",
"\n",
"# 4. Fit the model\n",
"model.fit(Xtrain, ytrain)\n",
"\n",
"# 5. Predict new data (result stored as y_model)\n",
"y_model = model.predict(Xtest) \n",
"\n",
"# Check accuracy of prediction\n",
"from sklearn.metrics import accuracy_score\n",
"accuracy_score(ytest, y_model)"
],
"execution_count": 29,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0.9736842105263158"
]
},
"metadata": {
"tags": []
},
"execution_count": 29
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "s_vuPigO71Ey",
"colab_type": "text"
},
"source": [
"# Example 3: Unsupervised learning for Iris Dimensionality (PCA)\n",
"\n",
"The iris data has four dimensions which makes it hard to visualize the data. Unsupervised learning like Principal component analysis (PCA) can be used to reduce the dimensionality without losing the essential features of the data.\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "y1713pOI78fa",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 419
},
"outputId": "afd61459-c030-4a22-c649-e4957a58e367"
},
"source": [
"iris"
],
"execution_count": 30,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>sepal_length</th>\n",
" <th>sepal_width</th>\n",
" <th>petal_length</th>\n",
" <th>petal_width</th>\n",
" <th>species</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>5.1</td>\n",
" <td>3.5</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4.9</td>\n",
" <td>3.0</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4.7</td>\n",
" <td>3.2</td>\n",
" <td>1.3</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4.6</td>\n",
" <td>3.1</td>\n",
" <td>1.5</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5.0</td>\n",
" <td>3.6</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>145</th>\n",
" <td>6.7</td>\n",
" <td>3.0</td>\n",
" <td>5.2</td>\n",
" <td>2.3</td>\n",
" <td>virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>146</th>\n",
" <td>6.3</td>\n",
" <td>2.5</td>\n",
" <td>5.0</td>\n",
" <td>1.9</td>\n",
" <td>virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>147</th>\n",
" <td>6.5</td>\n",
" <td>3.0</td>\n",
" <td>5.2</td>\n",
" <td>2.0</td>\n",
" <td>virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>148</th>\n",
" <td>6.2</td>\n",
" <td>3.4</td>\n",
" <td>5.4</td>\n",
" <td>2.3</td>\n",
" <td>virginica</td>\n",
" </tr>\n",
" <tr>\n",
" <th>149</th>\n",
" <td>5.9</td>\n",
" <td>3.0</td>\n",
" <td>5.1</td>\n",
" <td>1.8</td>\n",
" <td>virginica</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>150 rows × 5 columns</p>\n",
"</div>"
],
"text/plain": [
" sepal_length sepal_width petal_length petal_width species\n",
"0 5.1 3.5 1.4 0.2 setosa\n",
"1 4.9 3.0 1.4 0.2 setosa\n",
"2 4.7 3.2 1.3 0.2 setosa\n",
"3 4.6 3.1 1.5 0.2 setosa\n",
"4 5.0 3.6 1.4 0.2 setosa\n",
".. ... ... ... ... ...\n",
"145 6.7 3.0 5.2 2.3 virginica\n",
"146 6.3 2.5 5.0 1.9 virginica\n",
"147 6.5 3.0 5.2 2.0 virginica\n",
"148 6.2 3.4 5.4 2.3 virginica\n",
"149 5.9 3.0 5.1 1.8 virginica\n",
"\n",
"[150 rows x 5 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 30
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "8LsaAUQ3BP3I",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 382
},
"outputId": "4891311b-5f26-42b1-f070-32ad765aefb6"
},
"source": [
"import seaborn as sns\n",
"from sklearn.decomposition import PCA\n",
"\n",
"iris = sns.load_dataset('iris')\n",
"X_iris = iris.drop('species', axis=1)\n",
"y_iris = iris['species']\n",
"\n",
"model = PCA(n_components=2)\n",
"model.fit(X_iris)\n",
"X_2D = model.transform(X_iris)\n",
"\n",
"# Plot data with reduced dimensionality\n",
"iris['PCA1'] = X_2D[:,0]\n",
"iris['PCA2'] = X_2D[:,1]\n",
"sns.lmplot(\"PCA1\", \"PCA2\", hue='species', data=iris, fit_reg=False)"
],
"execution_count": 33,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<seaborn.axisgrid.FacetGrid at 0x7f0ce83a2748>"
]
},
"metadata": {
"tags": []
},
"execution_count": 33
},
{
"output_type": "display_data",
"data": {
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raxrsvzeJWCUO0TPLJLBkffvb3+aGG27AbrezadMmfvjDH/Lqq68yZMiQpF+jvr4VwzBT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\nOQrD/hASUqgAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 453.85x360 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "dp-NXZVFFch7",
"colab_type": "text"
},
"source": [
"**Another example: PCA for handwritten digits**\n",
"\n",
"Use PCA or 8x8 pixel images of handwritten digits with 64 dimensions to reduce dimensionality to two. How well does the model work?"
]
},
{
"cell_type": "code",
"metadata": {
"id": "RkQh6qRQFkGK",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 51
},
"outputId": "36a7082b-6ab3-4fb4-e5d3-49e6ebad3ace"
},
"source": [
"import matplotlib.pyplot as plt\n",
"from sklearn.decomposition import PCA\n",
"from sklearn.datasets import load_digits\n",
"digits = load_digits()\n",
"\n",
"pca = PCA(2)\n",
"projected = pca.fit_transform(digits.data)\n",
"print(digits.data.shape)\n",
"print(projected.shape)"
],
"execution_count": 35,
"outputs": [
{
"output_type": "stream",
"text": [
"(1797, 64)\n",
"(1797, 2)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "F33FbjUZGhNO",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 306
},
"outputId": "f0f703d5-4d52-4547-9965-12327403764d"
},
"source": [
"plt.scatter(projected[:,0], projected[:,1],\n",
" c=digits.target, edgecolor='none', alpha=0.5,\n",
" cmap=plt.cm.get_cmap('Spectral', 10))\n",
"plt.xlabel('Component 1')\n",
"plt.ylabel('Component 2')\n",
"plt.colorbar()"
],
"execution_count": 38,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.colorbar.Colorbar at 0x7f0ce595b2e8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 38
},
{
"output_type": "display_data",
"data": {
"image/png": 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WjcCfiVKK7373u7znPe9hcnKSgYGBpdc6OjpQSlEsFs9pdP9iOjvPXrD5ldLd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QxVFHSurbPc22FmrkJ2Yx9z8XVEr3/Q70CCgsMVRkQoru1SrO2jalXcmx7A2VlMNEQ6LVQ6REUB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\nC7xGo9GMU7TAazQazTjl/wNJI/vC05aPOQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "dxNVNYJEIXYi",
"colab_type": "text"
},
"source": [
"**Choosing the number of components: Cumulative Explained Variance**\n",
"\n",
"How many components should we use to not lose too much? We can take a look at the *cumulative explained variance ration* as a function of the number of components to determine the optimum.\n",
"\n",
"This curve qunatifies how much of the total 64-dimensional variance is contained within the first N components, e.g. first 10 components explain 75% of the variance. To retain 90% of the variance (rule of thumb?), we would need about 20 components.\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "Y2ER8fLhIscS",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 302
},
"outputId": "50ce49ed-2c77-4195-dcef-434c2bc8b458"
},
"source": [
"pca = PCA().fit(digits.data)\n",
"plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
"plt.xlabel('number of components')\n",
"plt.ylabel('cumulative explained variance')"
],
"execution_count": 41,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0, 0.5, 'cumulative explained variance')"
]
},
"metadata": {
"tags": []
},
"execution_count": 41
},
{
"output_type": "display_data",
"data": {
"image/png": 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44QUcOXLErAFtQXF5NVKuFSOuT1teG0FETYqkIvHtt9/C3r7uKZ0jR45Er169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\ngoiITGKRICIik/4/99e688KJrXgAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "bKinnGIn75O1",
"colab_type": "text"
},
"source": [
"#Example 4: Unsupervised Learning with Iris Clustering (GMM)\n",
"\n",
"Find distinct groups of data without reference to any labels using Gaussian Mixture Model (GMM). GMM can be seen as an extension to k-means clustering, where cluster membership is assigned based on distance-from-cluster-center.\n",
"\n",
"The k-means model has no intrinsic measure of probability or uncertainty of cluster assignments. Furthermore, k-means is not flexible enough to account for non-circular clusters and unnecessary cluster overlap can occur.\n",
"\n",
"Gaussian Mixture Model, on the other hand, attempts to find a mixture of multidimensional Gaussian probability distributions that best model any dataset. GMM contains a probabilistic model and allows for non-circular clusters."
]
},
{
"cell_type": "code",
"metadata": {
"id": "VIeK3whJj-I5",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 386
},
"outputId": "241edbd8-0488-42b1-85b4-d51e91372384"
},
"source": [
"from sklearn.mixture import GaussianMixture as GMM\n",
"from sklearn.decomposition import PCA\n",
"import seaborn as sns\n",
"\n",
"iris = sns.load_dataset('iris')\n",
"X_iris = iris.drop('species', axis=1)\n",
"y_iris = iris['species']\n",
"\n",
"# PCA to reduce dimensionality\n",
"model = PCA(n_components=2)\n",
"model.fit(X_iris)\n",
"X_2D = model.transform(X_iris)\n",
"\n",
"iris['PCA1'] = X_2D[:,0]\n",
"iris['PCA2'] = X_2D[:,1]\n",
"\n",
"# Gaussian Mixture Model for clustering\n",
"model = GMM(n_components = 3, covariance_type = 'full')\n",
"model.fit(X_iris)\n",
"ygmm = model.predict(X_iris)\n",
"iris['cluster'] = ygmm\n",
"\n",
"\n",
"# plot\n",
"sns.lmplot(\"PCA1\", \"PCA2\", data=iris, hue='species', col='cluster', fit_reg=False)"
],
"execution_count": 17,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<seaborn.axisgrid.FacetGrid at 0x7f38ae9634e0>"
]
},
"metadata": {
"tags": []
},
"execution_count": 17
},
{
"output_type": "display_data",
"data": {
"image/png": 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FJBwhVhHDzIhVxIiEI3T1dBV6ayIiIsuibUMjN7W9mJAZoxmnImycvzpKtCKsiWIiImVO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\n",
"text/plain": [
"<Figure size 1164.75x360 with 3 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LOqtrTFCnGIG",
"colab_type": "text"
},
"source": [
"# Hypermeters and Model Validation\n",
"\n",
"A model can be validated by applying it to training data and comparing the outcome to the known real value. Note: Don't evaluate a model using the same data that was used for model fitting. Common methods include holdout sets and cross validation.\n",
"\n",
"\n",
"\n",
"**Holdout sets**\n",
"\n",
"Hold back a subset of the data to check the model's performance. Take a look at the basic example below. However, using holdout sets has the disadvantage that we lose a part of the data that could otherwise been used for training the model. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "PIrH5t00sHMA",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.model_selection import train_test_split\n",
"from sklearn.metrics import accuracy_score\n",
"\n",
"# split 50:50\n",
"X1, X2, y1, y2 = train_test_split(X, y, random_state=0, train_size=0.5)\n",
"\n",
"# fit the model \n",
"model.fit(X1, y1)\n",
"\n",
"# evaluate the model\n",
"y2_model = model.predict(X2)\n",
"accuracy_score(y2, y2_model)\n",
"\n",
"# Output: 0.90000066666"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "kqppeDv7tPAq",
"colab_type": "text"
},
"source": [
"**Cross-validation**\n",
"\n",
"Cross-validation can be understand as a sequence of the procedure with holdout sets. Each subset is used as training and test data. The result is multiple accuracy scores which we could combine and take the mean to get a better measure for the global model performance."
]
},
{
"cell_type": "code",
"metadata": {
"id": "TAQyvcBxuFVR",
"colab_type": "code",
"colab": {}
},
"source": [
"# two-fold cross-validation\n",
"y2_model = model.fit(X1, y2).predict(X2)\n",
"y1_model = model.fit(X2, y1).predict(X1)\n",
"accuracy_score(y1, y1_model), accuracy_score(y2, y2_model)\n",
"\n",
"# Output: (0.900000066666, 0.90500000001)\n",
"\n",
"# evaluation of accuracy for five-fold cross-validation\n",
"from sklearn.model_selection import cross_val_score\n",
"cross_val_score(model, X, y, cv=5)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "q-r9mUqYy8_o",
"colab_type": "text"
},
"source": [
"**Underperforming estimator? What should you do**\n",
"\n",
"Options:\n",
"1. Use a more complicated/flexible model\n",
"2. Use a less complicated/flexible model\n",
"3. Gather more training samples (rows)\n",
"4. Gather more data to add features to each sample (columns)\n",
"\n",
"This leads to the **bias-variance trade-off**, where bias is the result of an underfitted model (gaps to real data) and high variance is the result of an overfitted model that is so flexibel that it even accounts for noise.\n",
"\n",
"**Validation curves** can help to find the balance between the two extremes. Here is an example in sklearn where we will use a two-degree polynomial regression model (= polynomial pre-processing and simple linear regression)."
]
},
{
"cell_type": "code",
"metadata": {
"id": "LLAmjE6z0ng4",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 289
},
"outputId": "749f9e26-e5be-459d-cfd0-27c08989954c"
},
"source": [
"from sklearn.preprocessing import PolynomialFeatures\n",
"from sklearn.linear_model import LinearRegression\n",
"from sklearn.pipeline import make_pipeline\n",
"\n",
"def PolynomialRegression(degree=2, **kwargs):\n",
" return make_pipeline(PolynomialFeatures(degree),\n",
" LinearRegression(**kwargs))\n",
"\n",
"# Create data for testing\n",
"import numpy as np\n",
"\n",
"def make_data(N, err=1.0, rseed=1):\n",
" rng = np.random.RandomState(rseed)\n",
" X = rng.rand(N, 1) ** 2\n",
" y = 10 -1. / (X.ravel() + 0.1)\n",
" if err > 0:\n",
" y += err * rng.randn(N)\n",
" return X, y\n",
"\n",
"X, y = make_data(40)\n",
"\n",
"# Visualize\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import seaborn; seaborn.set()\n",
"\n",
"X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n",
"\n",
"plt.scatter(X.ravel(), y, color='black')\n",
"axis = plt.axis()\n",
"for degree in [1, 3, 5]:\n",
" y_test = PolynomialRegression(degree).fit(X, y).predict(X_test)\n",
" plt.plot(X_test.ravel(), y_test, label='degree={0}'.format(degree))\n",
"plt.xlim(-0.1, 1.0)\n",
"plt.ylim(-2, 12)\n",
"plt.legend(loc='best')"
],
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa450eed828>"
]
},
"metadata": {
"tags": []
},
"execution_count": 8
},
{
"output_type": "display_data",
"data": {
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lx93TDzoDmvghaBKHoY4diCog7JLP9+R0wNkPt6LiIoITwghPiyY8LZqIAX0I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\nQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "MbBd3-kH6F10",
"colab_type": "text"
},
"source": [
"What degree of polynomial provides a suitable trade-off between bias (underfitting) and viance (overfitting)? \n",
"\n",
"We can visualize the validation curve for this data and model as well as compute the training score and validation score using the code below.\n",
"\n",
"It turns out that a polynomial degree of 3 leads to the optimal trade-off (highest validation score)"
]
},
{
"cell_type": "code",
"metadata": {
"id": "pp_F3WU06gwD",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 306
},
"outputId": "c52846aa-d085-409c-a7d7-678c865ad9a9"
},
"source": [
"from sklearn.model_selection import validation_curve\n",
"degree = np.arange(0, 21)\n",
"train_score, val_score = validation_curve(PolynomialRegression(), X, y,\n",
" 'polynomialfeatures__degree',\n",
" degree, cv=7)\n",
"plt.plot(degree, np.median(train_score, 1), color='blue', label='training score')\n",
"plt.plot(degree, np.median(val_score, 1), color='red', label='validation score')\n",
"plt.legend(loc='best')\n",
"plt.ylim(0, 1)\n",
"plt.xlabel('degree')\n",
"plt.ylabel('score')"
],
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0, 0.5, 'score')"
]
},
"metadata": {
"tags": []
},
"execution_count": 12
},
{
"output_type": "display_data",
"data": {
"image/png": 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MTpkg4IiSHHkH5HqEEM1kGzIMw+/7MOzeFexQRAs0u7spNTWV3bt3+zOWdqHB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\nGiVJQgghRKP+P9/XdL9xy0xZAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tQnaDbtD8AFQ",
"colab_type": "text"
},
"source": [
"**Learning curve**\n",
"\n",
"Note that the behavior of the validation curve has two important inputs: the model complexity and the number of training points. It is therefore useful to explore the behavior of the model as a function of the number of training points. A plot of the training/validation score with respect to the size of the training set is known as the learning curve.\n",
"\n",
"Usually with increasing sample size the curve for training score and validation score converge to signal a good fit. From that point on, adding more training data won't help."
]
},
{
"cell_type": "code",
"metadata": {
"id": "0kqtOs9T9nVd",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 411
},
"outputId": "f5dde15d-1719-4cf3-e797-2b21e9daafe5"
},
"source": [
"from sklearn.model_selection import learning_curve\n",
"\n",
"fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n",
"fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n",
"\n",
"for i, degree in enumerate([2, 9]):\n",
" N, train_lc, val_lc = learning_curve(PolynomialRegression(degree),\n",
" X, y, cv=7,\n",
" train_sizes=np.linspace(0.3, 1, 25))\n",
" ax[i].plot(N, np.mean(train_lc, 1), color='blue', label='training score')\n",
" ax[i].plot(N, np.mean(val_lc, 1), color='red', label='validation score')\n",
" ax[i].hlines(np.mean([train_lc[-1], val_lc[-1]]), N[0], N[-1], color='gray', linestyle='dashed')\n",
" ax[i].set_ylim(0,1)\n",
" ax[i].set_xlim(N[0], N[-1])\n",
" ax[i].set_xlabel('training size')\n",
" ax[i].set_ylabel('score')\n",
" ax[i].set_title('degree = {0}'.format(degree), size=14)\n",
" ax[i].legend(loc='best')"
],
"execution_count": 16,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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8HtMSMDkhbzDoBEzBoGmZOuvT+6QDqi3NV1RYmjixe4yOS/uisPBvZuHhmBQm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\nSUlJat26tUJDQyVJ5513njIyMrRt2zZNnTr1pFu5xcXF+Tli66utT0a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"text/plain": [
"<Figure size 1152x432 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "IjMTGdGg_-6Y",
"colab_type": "text"
},
"source": [
"**Grid Search**\n",
"\n",
"Validation and learning curves change not only with sample size. Sklearn provides automated tools to find the optimal hyperparameter settings for maximum validation."
]
},
{
"cell_type": "code",
"metadata": {
"id": "v62_gXwbBHhu",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 122
},
"outputId": "f5ad6a01-47ba-4dd3-d89b-01a4d15d5e05"
},
"source": [
"from sklearn.model_selection import GridSearchCV\n",
"\n",
"param_grid = {'polynomialfeatures__degree': np.arange(21),\n",
" 'linearregression__fit_intercept': [True, False],\n",
" 'linearregression__normalize': [True, False]}\n",
"grid = GridSearchCV(PolynomialRegression(), param_grid, cv=7)\n",
"\n",
"grid.fit(X, y)\n",
"\n",
"grid.best_params_"
],
"execution_count": 18,
"outputs": [
{
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/sklearn/model_selection/_search.py:814: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
" DeprecationWarning)\n"
],
"name": "stderr"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'linearregression__fit_intercept': False,\n",
" 'linearregression__normalize': True,\n",
" 'polynomialfeatures__degree': 4}"
]
},
"metadata": {
"tags": []
},
"execution_count": 18
}
]
}
]
}
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