From 0e718bc2695409539ead8ecc9a460b66f1da4d55 Mon Sep 17 00:00:00 2001
From: Uwe Schmitt <uwe.schmitt@id.ethz.ch>
Date: Sun, 28 Apr 2019 00:24:45 +0200
Subject: [PATCH] polished layout
---
07_regression.ipynb | 171 +++++++++++++++++++++++++++++++++++++-------
1 file changed, 144 insertions(+), 27 deletions(-)
diff --git a/07_regression.ipynb b/07_regression.ipynb
index ff46724..63af2b3 100644
--- a/07_regression.ipynb
+++ b/07_regression.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
@@ -108,7 +108,7 @@
"<IPython.core.display.HTML object>"
]
},
- "execution_count": 3,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -131,7 +131,7 @@
"\n",
"Regression belongs like classification to the field of supervised learning. \n",
"\n",
- "<div class=\"alert alert-block alert-warning\">\n",
+ "<div class=\"alert alert-block alert-info\">\n",
"<i class=\"fa fa-info-circle\"></i> \n",
"<strong>Regression predicts numerical values</strong> \n",
"in contrast to classification which predicts categories.\n",
@@ -160,7 +160,7 @@
},
{
"cell_type": "code",
- "execution_count": 206,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -239,7 +239,7 @@
"4 24.5 74.5 atlantic 24.2"
]
},
- "execution_count": 206,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -253,7 +253,7 @@
},
{
"cell_type": "code",
- "execution_count": 207,
+ "execution_count": 11,
"metadata": {},
"outputs": [
{
@@ -332,7 +332,7 @@
"99 27.5 86.5 sockeye 43.4"
]
},
- "execution_count": 207,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -350,7 +350,7 @@
},
{
"cell_type": "code",
- "execution_count": 210,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -380,18 +380,108 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Before we show how to use a regression method, we have to convert the `kind` column to numerical values (`sklearn.preprocessing.LabelEncoder` was mentioned in chapter 6.) first:"
+ "In contrast to our previous examples, our data set contains a non-numerical text column `kind`.\n",
+ "\n",
+ "<div class=\"alert alert-block alert-warning\">\n",
+ "<i class=\"fa fa-info-circle\"></i> \n",
+ " <code>sklearn.preprocessing.LabelEncoder</code> is a preprocessor which encodes text values to according categorical numbers.\n",
+ "</div>\n",
+ "\n",
+ "\n"
]
},
{
"cell_type": "code",
- "execution_count": 211,
+ "execution_count": 26,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "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>circumference</th>\n",
+ " <th>length</th>\n",
+ " <th>kind</th>\n",
+ " <th>weight</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>95</th>\n",
+ " <td>19.0</td>\n",
+ " <td>69.5</td>\n",
+ " <td>1</td>\n",
+ " <td>18.8</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>96</th>\n",
+ " <td>18.5</td>\n",
+ " <td>67.0</td>\n",
+ " <td>1</td>\n",
+ " <td>18.9</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>97</th>\n",
+ " <td>24.5</td>\n",
+ " <td>67.5</td>\n",
+ " <td>1</td>\n",
+ " <td>24.7</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>98</th>\n",
+ " <td>21.0</td>\n",
+ " <td>66.5</td>\n",
+ " <td>1</td>\n",
+ " <td>26.0</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>99</th>\n",
+ " <td>27.5</td>\n",
+ " <td>86.5</td>\n",
+ " <td>1</td>\n",
+ " <td>43.4</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " circumference length kind weight\n",
+ "95 19.0 69.5 1 18.8\n",
+ "96 18.5 67.0 1 18.9\n",
+ "97 24.5 67.5 1 24.7\n",
+ "98 21.0 66.5 1 26.0\n",
+ "99 27.5 86.5 1 43.4"
+ ]
+ },
+ "execution_count": 26,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"from sklearn.preprocessing import LabelEncoder\n",
"\n",
- "df.iloc[:, 2] = LabelEncoder().fit_transform(df.iloc[:, 2]) * 1"
+ "df.iloc[:, 2] = LabelEncoder().fit_transform(df.iloc[:, 2]) \n",
+ "\n",
+ "df.tail()"
]
},
{
@@ -403,7 +493,7 @@
},
{
"cell_type": "code",
- "execution_count": 212,
+ "execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
@@ -426,7 +516,7 @@
},
{
"cell_type": "code",
- "execution_count": 213,
+ "execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
@@ -438,12 +528,15 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Regression methods in `scikit-learn` also have `fit` and `predict` methods:"
+ "<div class=\"alert alert-block alert-info\">\n",
+ " <i class=\"fa fa-info-circle\"></i> Regression methods in <code>scikit-learn</code> also have <code>fit</code> and <code>predict</code> methods. Thus cross validation, pipelines and hyperparameter-optimization will be available.\n",
+ " \n",
+ "</div>"
]
},
{
"cell_type": "code",
- "execution_count": 214,
+ "execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
@@ -460,7 +553,7 @@
},
{
"cell_type": "code",
- "execution_count": 219,
+ "execution_count": 28,
"metadata": {},
"outputs": [
{
@@ -517,18 +610,16 @@
"source": [
"For assessing the quality of the predictions of a regression method, we can use multiple methods which we will discuss later in this script.\n",
"\n",
- "For our current example we compute the average absolute difference between given values $y_i$ and predicted values $\\hat{y}_i$. Thus\n",
+ "For our current example we compute the average absolute difference between given values $y_i$ and predicted values $\\hat{y}_i$:\n",
"\n",
"$$\n",
"\\frac{1}{n} \\left(|y_1 - \\hat{y}_1| + |y_2 - \\hat{y}_2| + ... + |y_n - \\hat{y}_n| \\right)\n",
- "$$\n",
- "\n",
- "This is called **mean absolute error**."
+ "$$\n"
]
},
{
"cell_type": "code",
- "execution_count": 220,
+ "execution_count": 29,
"metadata": {},
"outputs": [
{
@@ -597,12 +688,19 @@
"\n",
"### 1. Mean absolute error\n",
"\n",
- "This is the metric we used before. Formula is\n",
+ "This is the metric we used before.\n",
+ "<div class=\"alert alert-block alert-info\">\n",
+ " <i class=\"fa fa-info-circle\"></i> <strong>mean absolute error</strong> is defined as \n",
"\n",
"$$\n",
"\\frac{1}{n} \\left(|y_1 - \\hat{y}_1| + |y_2 - \\hat{y}_2| + ... + |y_n - \\hat{y}_n| \\right)\n",
"$$\n",
"\n",
+ "\n",
+ "\n",
+ "</div>\n",
+ "\n",
+ "\n",
"The name of the corresponding score in `scikit-learn` is `neg_mean_absolute_error`.\n",
"\n",
"\n",
@@ -610,10 +708,20 @@
"\n",
"Here we replace the absolute difference by its squared value.\n",
"\n",
+ "\n",
+ "<div class=\"alert alert-block alert-info\">\n",
+ " <i class=\"fa fa-info-circle\"></i> <strong>mean squared error</strong> is defined as \n",
+ "\n",
+ "\n",
"$$\n",
"\\frac{1}{n} \\left((y_1 - \\hat{y}_1)^2 + (y_2 - \\hat{y}_2)^2 + ... + (y_n - \\hat{y}_n)^2 \\right)\n",
"$$\n",
"\n",
+ "\n",
+ "</div>\n",
+ "\n",
+ "\n",
+ "\n",
"This measure is more sensitive to outliers: A few larger differences contribute more significantly to a larger mean squared error. The name of the corresponding score in `scikit-learn` is `neg_mean_squared_error`.\n",
"\n",
"\n",
@@ -621,10 +729,19 @@
"\n",
"Here we replace mean calculation by median:\n",
"\n",
+ "<div class=\"alert alert-block alert-info\">\n",
+ " <i class=\"fa fa-info-circle\"></i> <strong>median absolute error</strong> is defined as \n",
+ "\n",
+ "\n",
+ "\n",
"$$\n",
- "median\\left(|y_1 - \\hat{y}_1|, |y_2 - \\hat{y}_2|, ..., |y_n - \\hat{y}_n| \\right)\n",
+ "\\text{median}\\left(|y_1 - \\hat{y}_1|, |y_2 - \\hat{y}_2|, ..., |y_n - \\hat{y}_n| \\right)\n",
"$$\n",
"\n",
+ "\n",
+ "</div>\n",
+ "\n",
+ "\n",
"This measure is less sensitive to outliers than the metrics we discussed before: A few larger differences will not contribute significantly to a larger error value. The name of the corresponding score in `scikit-learn` is `neg_median_absolute_error`.\n",
"\n",
"### 4. Mean squared log error\n",
@@ -681,7 +798,7 @@
},
{
"cell_type": "code",
- "execution_count": 221,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -730,7 +847,7 @@
},
{
"cell_type": "code",
- "execution_count": 222,
+ "execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
@@ -743,7 +860,7 @@
},
{
"cell_type": "code",
- "execution_count": 223,
+ "execution_count": 21,
"metadata": {},
"outputs": [
{
--
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