{ "cells": [ { "cell_type": "markdown", "id": "25890abd", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# SciKit Learn\n", "\n", "The [sklearn package](https://scikit-learn.org/stable/) provides a broad collection of data analysis and machine learning tools:\n", " - cover the whole process, data manipulation, fitting models, evaluating the results\n", " - Sklearn is based on **numpy**: data and results as numpy arrays. \n", "\n", "Classes and functions are provided in an high-level API:\n", " - allows application without requiring (too much) knowledge about the algorithm itself\n", " - API allows to use the same syntax for very different algorithms" ] }, { "cell_type": "markdown", "id": "99ee232b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Basic syntax for creating a model:\n", "\n", "- instantiate the respective (algorithm's) object with hyper parameters and options\n", "\n", "- fit the data using this object's built-in methods\n", "\n", "- evaluate the model or use the model for prediction \n", "\n", "\n", "Note: we import classes specifically from the `scikit-learn` package instead of importing the package as a whole " ] }, { "cell_type": "markdown", "id": "fcc68b89", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Regression\n", "\n", "### Linear Regression\n", "\n", "- in LR, we model the the influence of some independent numerical variables on the value of a dependent numerical variable (the target). \n", "\n", "- widely used in economics\n", "\n", "The ordinary least squares (OLS) regression is found in module `linear_model` as the `LinearRegression` class.\n", "\n", "NOTE: by default, sklearn will fit an intercept. To exclude the intercept, set `fit_intercept=False` when instantiating the `LinearRegression()` object.\n", "\n", "To demonstrate the procedure, we will use a [health insurance data set](https://www.kaggle.com/mirichoi0218/insurance/version/1#) trying to explain the insurance charges.\n", "\n", "The data includes some categorical variables, for which we need to create dummy variables" ] }, { "cell_type": "markdown", "id": "4234c7d9", "metadata": {}, "source": [ "- intercept\n", "y = $\\alpha$ + $\\beta$ $\\cdot$ x \n", "\n", "- no intercept\n", "y = $\\beta$ $\\cdot$ x " ] }, { "cell_type": "code", "execution_count": 1, "id": "c7be2dd7", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "
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agesexbmichildrensmokerregioncharges
019female27.900yessouthwest16884.9240
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" ], "text/plain": [ " age sex bmi children smoker region charges\n", "0 19 female 27.90 0 yes southwest 16884.9240\n", "1 18 male 33.77 1 no southeast 1725.5523\n", "2 28 male 33.00 3 no southeast 4449.4620" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "df = pd.read_csv(\"data/insurance.csv\")\n", "#df = df.select_dtypes(include=['int64', 'float64'])\n", "df.head(3)" ] }, { "cell_type": "markdown", "id": "c7b2c3f5", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- transform the pandas Series for independent and dependent variable to a numpy array, which we reshape to 2D\n", "\n", "- instantiate the object (default option `fit_intercept=True` included for illustrative reasons)\n", "\n", "- call the `.fit()` method with positional arguments: first the independent variable(s) X, then target y\n", "\n", "After the fit, we can access the parameters: intercept and coefficient(s). Again, the syntax is similar as above for the StandardScaler.\n", "\n", "In this example, we regress the charges for a policy on the age of the customer. " ] }, { "cell_type": "code", "execution_count": 2, "id": "26b84731", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "intercept: [3165.88500606], coefficient: [[257.72261867]]\n" ] } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "\n", "X = np.array(df.age).reshape(-1,1)\n", "y = np.array(df.charges).reshape(-1,1)\n", "\n", "linreg = LinearRegression(fit_intercept=True)\n", "linreg.fit(X,y)\n", "\n", "print(f\"intercept: {linreg.intercept_}, coefficient: {linreg.coef_}\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "23ba103d", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[257.72261867]])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "linreg.coef_" ] }, { "cell_type": "markdown", "id": "1f0c6345", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "What we find is a positive slope, `linreg.coef_` > 0, meaning that a higher bmi results in higher charges. To be precise, if your bmi increases by one unit, you will, on average, be charged about 394 more units.\n", "\n", "We can also see that the estimated parameters are returned as (nested) arrays. To get to the values, we must hence extract them accordingly." ] }, { "cell_type": "code", "execution_count": 4, "id": "b1e8b865", "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "intercept: 3165.8850060630284, coefficient: 257.72261866689547\n" ] } ], "source": [ "print(f\"intercept: {linreg.intercept_[0]}, coefficient: {linreg.coef_[0][0]}\")" ] }, { "cell_type": "markdown", "id": "da51975c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now, we can generate fitted values and plot these together with the data to get a visualisation of the regression results\n", "\n", "To do so, we pass the `X` values to the `.predict()` method and save the result as `y_pred`. \n", "\n", "We then use matplotlib to create a scatter plot of the data and add a line plot of the regression line." ] }, { "cell_type": "code", "execution_count": 5, "id": "2427228c", "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "y_pred = linreg.predict(X)\n", "\n", "plt.scatter(X, y)\n", "plt.plot(X,y_pred, color='red')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c659c75f", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In the case above, we used the data \"seen\" for prediction. We can easily extrapolate this to unseen data, by simply predicting for a larger value range." ] }, { "cell_type": "code", "execution_count": 6, "id": "06083217", "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_plot = np.linspace(0,80).reshape(-1,1)\n", "y_extrapol = linreg.predict(x_plot)\n", "\n", "plt.scatter(X, y)\n", "plt.plot(x_plot,y_extrapol, color='red')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8f15e0e5", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Digression: statsmodels\n", "\n", "At this point, we shortly discuss an important point when it comes to regression: significance.\n", "\n", "We skipped this above, because sklearn has its shortcomings when it comes to this kind of 'classical statistics'. The calculation of p-values for example is not included and would have to be implemented by oneself.\n", "\n", "For such statistics, we can switch to the [statsmodels package](https://www.statsmodels.org/stable/index.html):\n", " - maybe a better choice for regression modelling because of detailed output\n", "\n", "Below, an example is given for the regression from above.\n", "The syntax is just slightly different:\n", " - we call `add_constant` on the data (!) to fit an intercept\n", " - we instantiate an `OLS` object, providign the data here, not in the subsequent\n", " - `fit` call\n", " - using `.summary()` automatically outputs a table of information about the model" ] }, { "cell_type": "markdown", "id": "4c21fe43", "metadata": {}, "source": [ "- intercept\n", "y = $\\alpha$ + $\\beta$ $\\cdot$ x \n", "\n", "- no intercept\n", "y = $\\beta$ $\\cdot$ x " ] }, { "cell_type": "code", "execution_count": 7, "id": "f10698e5", "metadata": { "scrolled": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: charges R-squared: 0.089\n", "Model: OLS Adj. R-squared: 0.089\n", "Method: Least Squares F-statistic: 131.2\n", "Date: Wed, 17 Jul 2024 Prob (F-statistic): 4.89e-29\n", "Time: 19:02:33 Log-Likelihood: -14415.\n", "No. Observations: 1338 AIC: 2.883e+04\n", "Df Residuals: 1336 BIC: 2.884e+04\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 3165.8850 937.149 3.378 0.001 1327.440 5004.330\n", "age 257.7226 22.502 11.453 0.000 213.579 301.866\n", "==============================================================================\n", "Omnibus: 399.600 Durbin-Watson: 2.033\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 864.239\n", "Skew: 1.733 Prob(JB): 2.15e-188\n", "Kurtosis: 4.869 Cond. No. 124.\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "import statsmodels.api as sm\n", "\n", "X = sm.add_constant(df.age)\n", "y = df.charges\n", "\n", "res = sm.OLS(y, X).fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "markdown", "id": "c96bafbe", "metadata": {}, "source": [ "$H_0$ : $\\beta =0$" ] }, { "cell_type": "markdown", "id": "e18dde54", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "We can access the quantities from the table specifically, using the names listed when running `dir(res_smoker)`." ] }, { "cell_type": "code", "execution_count": 8, "id": "2c0b97b4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "const 7.506030e-04\n", "age 4.886693e-29\n", "dtype: float64" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.pvalues" ] }, { "cell_type": "code", "execution_count": 9, "id": "0d0767a8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "const 3165.885006\n", "age 257.722619\n", "dtype: float64" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.params" ] }, { "cell_type": "code", "execution_count": 10, "id": "8483a22d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[257.72261867]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "linreg.coef_" ] }, { "cell_type": "code", "execution_count": 11, "id": "b9c4b8d2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3165.88500606])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "linreg.intercept_" ] }, { "cell_type": "markdown", "id": "00a9dd9d", "metadata": {}, "source": [ "# Clustering" ] }, { "cell_type": "markdown", "id": "6e9872c0", "metadata": {}, "source": [ "Clustering is unsupervised learning. Instead of knowing results that you want to model, like in linear regression, where the target variable has been observed, one lets the algorithm decide the outcome.\n", "\n", "For our example of clustering, we want to assign data point to clusters, based on some characteristics. These could for example be the number of employees or the market cap. What the user needs to enter before, is the number of clusters to assign the data to. So, for an example of three clusters, companies of high market cap and many employees would possibly be in the same cluster. The other cluster might contain low market cap and relatively few employees. The third cluster then might just catch all mixed and not so extreme characteristics.\n", "\n", "We can look at this with an example, that uses the k-means algorithm. The data below shows data points, that are characterised by two features: `x_1` and `x_2`\n", "We try to find clusters, i.e., groups, in that data. Remeber that we are talking about unsupervised learning: a \"true\" number of groups does not exist, like a true, or observed, value exists in regression or classification tasks, which are from the realm of supervides learning. (In this toy example, actually, there is one: we crete data with a given number of centers). However, just from looking at the scatterplot below, we might already guess what number of clusters make sense." ] }, { "cell_type": "code", "execution_count": 12, "id": "3dce72d8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "\n", "X, clusters = make_blobs(n_samples=300, n_features=2, centers=4, random_state=42, cluster_std=2)\n", "df = pd.DataFrame(X, columns=[\"x_1\", \"x_2\"])\n", "df.plot.scatter(x = \"x_1\", y = \"x_2\")" ] }, { "cell_type": "markdown", "id": "b56f5d97", "metadata": {}, "source": [ "Without going into detail, we can use the k-means algorithm by the regular sklearn syntax: instantiate object, fit (and evaluate). In order to assess how many clusters might be justified, we can use the silhouette score. Broadly speaking, it calculates how the distances between points in one cluster compare to the distances to all points in the closest of all other clusters. We can use it to decide the number of cluster that could be appropriate by running k-means for an increasing number of clusters and each time calculating the silhouette score. We can choose that number of clusters, that achieves the highest silhouette score:" ] }, { "cell_type": "code", "execution_count": 13, "id": "6f453230", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "import pandas as pd\n", "import numpy as np\n", "from sklearn.cluster import KMeans\n", "from sklearn.metrics import silhouette_samples\n", "import matplotlib.pylab as plt\n", "\n", "colors = [\"#1f77b4\", \"#ff7f0e\", \"#2ca02c\" , 'red']\n", "X, clusters = make_blobs(n_samples=300, n_features=2, centers=4, random_state=42, cluster_std=2)\n", "df = pd.DataFrame(X, columns=[\"x_1\", \"x_2\"])\n", "\n", "scores = []\n", "max_clusters = 7\n", "for n_cluster in range(2, max_clusters): \n", " kmeans = KMeans(n_clusters = n_cluster, n_init = \"auto\", random_state = 42)\n", " kmeans.fit(X)\n", " silhouette_scores = silhouette_samples(X, kmeans.labels_, metric = \"euclidean\")\n", " scores.append(silhouette_scores.mean())\n", "\n", "fig, axs = plt.subplots(1, 2, figsize = (12, 5))\n", "axs[0].plot(scores)\n", "axs[0].set_xticks([0, 1, 2, 3, 4], [\"2\", \"3\", \"4\", \"5\", \"6\"])\n", "axs[0].set_xlabel(\"Number of clusters\")\n", "axs[0].set_ylabel(\"Average silhouette score\")\n", "\n", "\n", "kmeans = KMeans(n_clusters=3, n_init = \"auto\")\n", "kmeans.fit(X)\n", "df.loc[:, \"cluster\"] = kmeans.labels_\n", "for i in range(3):\n", " df[df.cluster == i].plot.scatter(x = \"x_1\", y = \"x_2\", c = colors[i], ax = axs[1], label = f\"Cluster {i}\")\n", "axs[1].set_xlabel(r\"$x_1$\")\n", "axs[1].set_ylabel(r\"$x_2$\")\n", "axs[1].set_title(r\"Estimated cluster assignments for $K=3$\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "82b4d871", "metadata": {}, "source": [ "Interestingly enough, the inital setting for our data was four centers. However, the silhouette score was the highest for just three clusters. The reason can be seen in the right plot: two of the created clusters are so close to each other, that it makes more sense (in terms of the silhouette score) to regard them as one." ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.0" } }, "nbformat": 4, "nbformat_minor": 5 }