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Created August 23, 2017 01:06
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GA DSI Instructor Challenge
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GA_DSI_instructor_challenge_Emma.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Part 1: Modeling"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import seaborn as sns\n",
"import requests\n",
"import statistics\n",
"\n",
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn.feature_selection import f_classif, SelectKBest, SelectFromModel\n",
"from sklearn.model_selection import train_test_split, GridSearchCV, ShuffleSplit\n",
"from sklearn.pipeline import Pipeline\n",
"from sklearn.ensemble import RandomForestClassifier\n",
"from sklearn.linear_model import Lasso, Ridge, LogisticRegression"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# read in data file\n",
"url = 'https://gist.githubusercontent.com/jeff-boykin/b5c536467c30d66ab97cd1f5c9a3497d/raw/5233c792af49c9b78f20c35d5cd729e1307a7df7/breast-cancer.csv'"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"bc_data = pd.read_csv(url, header=None)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" <th>7</th>\n",
" <th>8</th>\n",
" <th>9</th>\n",
" <th>...</th>\n",
" <th>22</th>\n",
" <th>23</th>\n",
" <th>24</th>\n",
" <th>25</th>\n",
" <th>26</th>\n",
" <th>27</th>\n",
" <th>28</th>\n",
" <th>29</th>\n",
" <th>30</th>\n",
" <th>31</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>842302</td>\n",
" <td>M</td>\n",
" <td>17.99</td>\n",
" <td>10.38</td>\n",
" <td>122.80</td>\n",
" <td>1001.0</td>\n",
" <td>0.11840</td>\n",
" <td>0.27760</td>\n",
" <td>0.3001</td>\n",
" <td>0.14710</td>\n",
" <td>...</td>\n",
" <td>25.38</td>\n",
" <td>17.33</td>\n",
" <td>184.60</td>\n",
" <td>2019.0</td>\n",
" <td>0.1622</td>\n",
" <td>0.6656</td>\n",
" <td>0.7119</td>\n",
" <td>0.2654</td>\n",
" <td>0.4601</td>\n",
" <td>0.11890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>842517</td>\n",
" <td>M</td>\n",
" <td>20.57</td>\n",
" <td>17.77</td>\n",
" <td>132.90</td>\n",
" <td>1326.0</td>\n",
" <td>0.08474</td>\n",
" <td>0.07864</td>\n",
" <td>0.0869</td>\n",
" <td>0.07017</td>\n",
" <td>...</td>\n",
" <td>24.99</td>\n",
" <td>23.41</td>\n",
" <td>158.80</td>\n",
" <td>1956.0</td>\n",
" <td>0.1238</td>\n",
" <td>0.1866</td>\n",
" <td>0.2416</td>\n",
" <td>0.1860</td>\n",
" <td>0.2750</td>\n",
" <td>0.08902</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>84300903</td>\n",
" <td>M</td>\n",
" <td>19.69</td>\n",
" <td>21.25</td>\n",
" <td>130.00</td>\n",
" <td>1203.0</td>\n",
" <td>0.10960</td>\n",
" <td>0.15990</td>\n",
" <td>0.1974</td>\n",
" <td>0.12790</td>\n",
" <td>...</td>\n",
" <td>23.57</td>\n",
" <td>25.53</td>\n",
" <td>152.50</td>\n",
" <td>1709.0</td>\n",
" <td>0.1444</td>\n",
" <td>0.4245</td>\n",
" <td>0.4504</td>\n",
" <td>0.2430</td>\n",
" <td>0.3613</td>\n",
" <td>0.08758</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>84348301</td>\n",
" <td>M</td>\n",
" <td>11.42</td>\n",
" <td>20.38</td>\n",
" <td>77.58</td>\n",
" <td>386.1</td>\n",
" <td>0.14250</td>\n",
" <td>0.28390</td>\n",
" <td>0.2414</td>\n",
" <td>0.10520</td>\n",
" <td>...</td>\n",
" <td>14.91</td>\n",
" <td>26.50</td>\n",
" <td>98.87</td>\n",
" <td>567.7</td>\n",
" <td>0.2098</td>\n",
" <td>0.8663</td>\n",
" <td>0.6869</td>\n",
" <td>0.2575</td>\n",
" <td>0.6638</td>\n",
" <td>0.17300</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>84358402</td>\n",
" <td>M</td>\n",
" <td>20.29</td>\n",
" <td>14.34</td>\n",
" <td>135.10</td>\n",
" <td>1297.0</td>\n",
" <td>0.10030</td>\n",
" <td>0.13280</td>\n",
" <td>0.1980</td>\n",
" <td>0.10430</td>\n",
" <td>...</td>\n",
" <td>22.54</td>\n",
" <td>16.67</td>\n",
" <td>152.20</td>\n",
" <td>1575.0</td>\n",
" <td>0.1374</td>\n",
" <td>0.2050</td>\n",
" <td>0.4000</td>\n",
" <td>0.1625</td>\n",
" <td>0.2364</td>\n",
" <td>0.07678</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 32 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6 7 8 \\\n",
"0 842302 M 17.99 10.38 122.80 1001.0 0.11840 0.27760 0.3001 \n",
"1 842517 M 20.57 17.77 132.90 1326.0 0.08474 0.07864 0.0869 \n",
"2 84300903 M 19.69 21.25 130.00 1203.0 0.10960 0.15990 0.1974 \n",
"3 84348301 M 11.42 20.38 77.58 386.1 0.14250 0.28390 0.2414 \n",
"4 84358402 M 20.29 14.34 135.10 1297.0 0.10030 0.13280 0.1980 \n",
"\n",
" 9 ... 22 23 24 25 26 27 28 \\\n",
"0 0.14710 ... 25.38 17.33 184.60 2019.0 0.1622 0.6656 0.7119 \n",
"1 0.07017 ... 24.99 23.41 158.80 1956.0 0.1238 0.1866 0.2416 \n",
"2 0.12790 ... 23.57 25.53 152.50 1709.0 0.1444 0.4245 0.4504 \n",
"3 0.10520 ... 14.91 26.50 98.87 567.7 0.2098 0.8663 0.6869 \n",
"4 0.10430 ... 22.54 16.67 152.20 1575.0 0.1374 0.2050 0.4000 \n",
"\n",
" 29 30 31 \n",
"0 0.2654 0.4601 0.11890 \n",
"1 0.1860 0.2750 0.08902 \n",
"2 0.2430 0.3613 0.08758 \n",
"3 0.2575 0.6638 0.17300 \n",
"4 0.1625 0.2364 0.07678 \n",
"\n",
"[5 rows x 32 columns]"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bc_data.head()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"B 357\n",
"M 212\n",
"Name: 1, dtype: int64"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bc_data[1].value_counts()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### (note that there are a lot more benign than malignant samples - this could affect our predictive model)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# read in header file\n",
"header = requests.get('https://gist.githubusercontent.com/jeff-boykin/b5c536467c30d66ab97cd1f5c9a3497d/raw/5233c792af49c9b78f20c35d5cd729e1307a7df7/field_names.txt')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"header = header.text.splitlines()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# assign headers to dataframe\n",
"bc_data.columns=header"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>ID</th>\n",
" <th>diagnosis</th>\n",
" <th>radius_mean</th>\n",
" <th>radius_sd_error</th>\n",
" <th>radius_worst</th>\n",
" <th>texture_mean</th>\n",
" <th>texture_sd_error</th>\n",
" <th>texture_worst</th>\n",
" <th>perimeter_mean</th>\n",
" <th>perimeter_sd_error</th>\n",
" <th>...</th>\n",
" <th>concavity_worst</th>\n",
" <th>concave_points_mean</th>\n",
" <th>concave_points_sd_error</th>\n",
" <th>concave_points_worst</th>\n",
" <th>symmetry_mean</th>\n",
" <th>symmetry_sd_error</th>\n",
" <th>symmetry_worst</th>\n",
" <th>fractal_dimension_mean</th>\n",
" <th>fractal_dimension_sd_error</th>\n",
" <th>fractal_dimension_worst</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>842302</td>\n",
" <td>M</td>\n",
" <td>17.99</td>\n",
" <td>10.38</td>\n",
" <td>122.80</td>\n",
" <td>1001.0</td>\n",
" <td>0.11840</td>\n",
" <td>0.27760</td>\n",
" <td>0.3001</td>\n",
" <td>0.14710</td>\n",
" <td>...</td>\n",
" <td>25.38</td>\n",
" <td>17.33</td>\n",
" <td>184.60</td>\n",
" <td>2019.0</td>\n",
" <td>0.1622</td>\n",
" <td>0.6656</td>\n",
" <td>0.7119</td>\n",
" <td>0.2654</td>\n",
" <td>0.4601</td>\n",
" <td>0.11890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>842517</td>\n",
" <td>M</td>\n",
" <td>20.57</td>\n",
" <td>17.77</td>\n",
" <td>132.90</td>\n",
" <td>1326.0</td>\n",
" <td>0.08474</td>\n",
" <td>0.07864</td>\n",
" <td>0.0869</td>\n",
" <td>0.07017</td>\n",
" <td>...</td>\n",
" <td>24.99</td>\n",
" <td>23.41</td>\n",
" <td>158.80</td>\n",
" <td>1956.0</td>\n",
" <td>0.1238</td>\n",
" <td>0.1866</td>\n",
" <td>0.2416</td>\n",
" <td>0.1860</td>\n",
" <td>0.2750</td>\n",
" <td>0.08902</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>84300903</td>\n",
" <td>M</td>\n",
" <td>19.69</td>\n",
" <td>21.25</td>\n",
" <td>130.00</td>\n",
" <td>1203.0</td>\n",
" <td>0.10960</td>\n",
" <td>0.15990</td>\n",
" <td>0.1974</td>\n",
" <td>0.12790</td>\n",
" <td>...</td>\n",
" <td>23.57</td>\n",
" <td>25.53</td>\n",
" <td>152.50</td>\n",
" <td>1709.0</td>\n",
" <td>0.1444</td>\n",
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" <td>0.4504</td>\n",
" <td>0.2430</td>\n",
" <td>0.3613</td>\n",
" <td>0.08758</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>84348301</td>\n",
" <td>M</td>\n",
" <td>11.42</td>\n",
" <td>20.38</td>\n",
" <td>77.58</td>\n",
" <td>386.1</td>\n",
" <td>0.14250</td>\n",
" <td>0.28390</td>\n",
" <td>0.2414</td>\n",
" <td>0.10520</td>\n",
" <td>...</td>\n",
" <td>14.91</td>\n",
" <td>26.50</td>\n",
" <td>98.87</td>\n",
" <td>567.7</td>\n",
" <td>0.2098</td>\n",
" <td>0.8663</td>\n",
" <td>0.6869</td>\n",
" <td>0.2575</td>\n",
" <td>0.6638</td>\n",
" <td>0.17300</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>84358402</td>\n",
" <td>M</td>\n",
" <td>20.29</td>\n",
" <td>14.34</td>\n",
" <td>135.10</td>\n",
" <td>1297.0</td>\n",
" <td>0.10030</td>\n",
" <td>0.13280</td>\n",
" <td>0.1980</td>\n",
" <td>0.10430</td>\n",
" <td>...</td>\n",
" <td>22.54</td>\n",
" <td>16.67</td>\n",
" <td>152.20</td>\n",
" <td>1575.0</td>\n",
" <td>0.1374</td>\n",
" <td>0.2050</td>\n",
" <td>0.4000</td>\n",
" <td>0.1625</td>\n",
" <td>0.2364</td>\n",
" <td>0.07678</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 32 columns</p>\n",
"</div>"
],
"text/plain": [
" ID diagnosis radius_mean radius_sd_error radius_worst \\\n",
"0 842302 M 17.99 10.38 122.80 \n",
"1 842517 M 20.57 17.77 132.90 \n",
"2 84300903 M 19.69 21.25 130.00 \n",
"3 84348301 M 11.42 20.38 77.58 \n",
"4 84358402 M 20.29 14.34 135.10 \n",
"\n",
" texture_mean texture_sd_error texture_worst perimeter_mean \\\n",
"0 1001.0 0.11840 0.27760 0.3001 \n",
"1 1326.0 0.08474 0.07864 0.0869 \n",
"2 1203.0 0.10960 0.15990 0.1974 \n",
"3 386.1 0.14250 0.28390 0.2414 \n",
"4 1297.0 0.10030 0.13280 0.1980 \n",
"\n",
" perimeter_sd_error ... concavity_worst \\\n",
"0 0.14710 ... 25.38 \n",
"1 0.07017 ... 24.99 \n",
"2 0.12790 ... 23.57 \n",
"3 0.10520 ... 14.91 \n",
"4 0.10430 ... 22.54 \n",
"\n",
" concave_points_mean concave_points_sd_error concave_points_worst \\\n",
"0 17.33 184.60 2019.0 \n",
"1 23.41 158.80 1956.0 \n",
"2 25.53 152.50 1709.0 \n",
"3 26.50 98.87 567.7 \n",
"4 16.67 152.20 1575.0 \n",
"\n",
" symmetry_mean symmetry_sd_error symmetry_worst fractal_dimension_mean \\\n",
"0 0.1622 0.6656 0.7119 0.2654 \n",
"1 0.1238 0.1866 0.2416 0.1860 \n",
"2 0.1444 0.4245 0.4504 0.2430 \n",
"3 0.2098 0.8663 0.6869 0.2575 \n",
"4 0.1374 0.2050 0.4000 0.1625 \n",
"\n",
" fractal_dimension_sd_error fractal_dimension_worst \n",
"0 0.4601 0.11890 \n",
"1 0.2750 0.08902 \n",
"2 0.3613 0.08758 \n",
"3 0.6638 0.17300 \n",
"4 0.2364 0.07678 \n",
"\n",
"[5 rows x 32 columns]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bc_data.head()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"RangeIndex: 569 entries, 0 to 568\n",
"Data columns (total 32 columns):\n",
"ID 569 non-null int64\n",
"diagnosis 569 non-null object\n",
"radius_mean 569 non-null float64\n",
"radius_sd_error 569 non-null float64\n",
"radius_worst 569 non-null float64\n",
"texture_mean 569 non-null float64\n",
"texture_sd_error 569 non-null float64\n",
"texture_worst 569 non-null float64\n",
"perimeter_mean 569 non-null float64\n",
"perimeter_sd_error 569 non-null float64\n",
"perimeter_worst 569 non-null float64\n",
"area_mean 569 non-null float64\n",
"area_sd_error 569 non-null float64\n",
"area_worst 569 non-null float64\n",
"smoothness_mean 569 non-null float64\n",
"smoothness_sd_error 569 non-null float64\n",
"smoothness_worst 569 non-null float64\n",
"compactness_mean 569 non-null float64\n",
"compactness_sd_error 569 non-null float64\n",
"compactness_worst 569 non-null float64\n",
"concavity_mean 569 non-null float64\n",
"concavity_sd_error 569 non-null float64\n",
"concavity_worst 569 non-null float64\n",
"concave_points_mean 569 non-null float64\n",
"concave_points_sd_error 569 non-null float64\n",
"concave_points_worst 569 non-null float64\n",
"symmetry_mean 569 non-null float64\n",
"symmetry_sd_error 569 non-null float64\n",
"symmetry_worst 569 non-null float64\n",
"fractal_dimension_mean 569 non-null float64\n",
"fractal_dimension_sd_error 569 non-null float64\n",
"fractal_dimension_worst 569 non-null float64\n",
"dtypes: float64(30), int64(1), object(1)\n",
"memory usage: 142.3+ KB\n"
]
}
],
"source": [
"# check for any null values and look at types of columns\n",
"bc_data.info()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# encode 'diagnosis' column\n",
"bc_data['diagnosis'] = bc_data['diagnosis'].astype('category').cat.codes"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>ID</th>\n",
" <th>diagnosis</th>\n",
" <th>radius_mean</th>\n",
" <th>radius_sd_error</th>\n",
" <th>radius_worst</th>\n",
" <th>texture_mean</th>\n",
" <th>texture_sd_error</th>\n",
" <th>texture_worst</th>\n",
" <th>perimeter_mean</th>\n",
" <th>perimeter_sd_error</th>\n",
" <th>...</th>\n",
" <th>concavity_worst</th>\n",
" <th>concave_points_mean</th>\n",
" <th>concave_points_sd_error</th>\n",
" <th>concave_points_worst</th>\n",
" <th>symmetry_mean</th>\n",
" <th>symmetry_sd_error</th>\n",
" <th>symmetry_worst</th>\n",
" <th>fractal_dimension_mean</th>\n",
" <th>fractal_dimension_sd_error</th>\n",
" <th>fractal_dimension_worst</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>5.690000e+02</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>...</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" <td>569.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>3.037183e+07</td>\n",
" <td>0.372583</td>\n",
" <td>14.127292</td>\n",
" <td>19.289649</td>\n",
" <td>91.969033</td>\n",
" <td>654.889104</td>\n",
" <td>0.096360</td>\n",
" <td>0.104341</td>\n",
" <td>0.088799</td>\n",
" <td>0.048919</td>\n",
" <td>...</td>\n",
" <td>16.269190</td>\n",
" <td>25.677223</td>\n",
" <td>107.261213</td>\n",
" <td>880.583128</td>\n",
" <td>0.132369</td>\n",
" <td>0.254265</td>\n",
" <td>0.272188</td>\n",
" <td>0.114606</td>\n",
" <td>0.290076</td>\n",
" <td>0.083946</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>1.250206e+08</td>\n",
" <td>0.483918</td>\n",
" <td>3.524049</td>\n",
" <td>4.301036</td>\n",
" <td>24.298981</td>\n",
" <td>351.914129</td>\n",
" <td>0.014064</td>\n",
" <td>0.052813</td>\n",
" <td>0.079720</td>\n",
" <td>0.038803</td>\n",
" <td>...</td>\n",
" <td>4.833242</td>\n",
" <td>6.146258</td>\n",
" <td>33.602542</td>\n",
" <td>569.356993</td>\n",
" <td>0.022832</td>\n",
" <td>0.157336</td>\n",
" <td>0.208624</td>\n",
" <td>0.065732</td>\n",
" <td>0.061867</td>\n",
" <td>0.018061</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>8.670000e+03</td>\n",
" <td>0.000000</td>\n",
" <td>6.981000</td>\n",
" <td>9.710000</td>\n",
" <td>43.790000</td>\n",
" <td>143.500000</td>\n",
" <td>0.052630</td>\n",
" <td>0.019380</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>...</td>\n",
" <td>7.930000</td>\n",
" <td>12.020000</td>\n",
" <td>50.410000</td>\n",
" <td>185.200000</td>\n",
" <td>0.071170</td>\n",
" <td>0.027290</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.156500</td>\n",
" <td>0.055040</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>8.692180e+05</td>\n",
" <td>0.000000</td>\n",
" <td>11.700000</td>\n",
" <td>16.170000</td>\n",
" <td>75.170000</td>\n",
" <td>420.300000</td>\n",
" <td>0.086370</td>\n",
" <td>0.064920</td>\n",
" <td>0.029560</td>\n",
" <td>0.020310</td>\n",
" <td>...</td>\n",
" <td>13.010000</td>\n",
" <td>21.080000</td>\n",
" <td>84.110000</td>\n",
" <td>515.300000</td>\n",
" <td>0.116600</td>\n",
" <td>0.147200</td>\n",
" <td>0.114500</td>\n",
" <td>0.064930</td>\n",
" <td>0.250400</td>\n",
" <td>0.071460</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>9.060240e+05</td>\n",
" <td>0.000000</td>\n",
" <td>13.370000</td>\n",
" <td>18.840000</td>\n",
" <td>86.240000</td>\n",
" <td>551.100000</td>\n",
" <td>0.095870</td>\n",
" <td>0.092630</td>\n",
" <td>0.061540</td>\n",
" <td>0.033500</td>\n",
" <td>...</td>\n",
" <td>14.970000</td>\n",
" <td>25.410000</td>\n",
" <td>97.660000</td>\n",
" <td>686.500000</td>\n",
" <td>0.131300</td>\n",
" <td>0.211900</td>\n",
" <td>0.226700</td>\n",
" <td>0.099930</td>\n",
" <td>0.282200</td>\n",
" <td>0.080040</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>8.813129e+06</td>\n",
" <td>1.000000</td>\n",
" <td>15.780000</td>\n",
" <td>21.800000</td>\n",
" <td>104.100000</td>\n",
" <td>782.700000</td>\n",
" <td>0.105300</td>\n",
" <td>0.130400</td>\n",
" <td>0.130700</td>\n",
" <td>0.074000</td>\n",
" <td>...</td>\n",
" <td>18.790000</td>\n",
" <td>29.720000</td>\n",
" <td>125.400000</td>\n",
" <td>1084.000000</td>\n",
" <td>0.146000</td>\n",
" <td>0.339100</td>\n",
" <td>0.382900</td>\n",
" <td>0.161400</td>\n",
" <td>0.317900</td>\n",
" <td>0.092080</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>9.113205e+08</td>\n",
" <td>1.000000</td>\n",
" <td>28.110000</td>\n",
" <td>39.280000</td>\n",
" <td>188.500000</td>\n",
" <td>2501.000000</td>\n",
" <td>0.163400</td>\n",
" <td>0.345400</td>\n",
" <td>0.426800</td>\n",
" <td>0.201200</td>\n",
" <td>...</td>\n",
" <td>36.040000</td>\n",
" <td>49.540000</td>\n",
" <td>251.200000</td>\n",
" <td>4254.000000</td>\n",
" <td>0.222600</td>\n",
" <td>1.058000</td>\n",
" <td>1.252000</td>\n",
" <td>0.291000</td>\n",
" <td>0.663800</td>\n",
" <td>0.207500</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>8 rows × 32 columns</p>\n",
"</div>"
],
"text/plain": [
" ID diagnosis radius_mean radius_sd_error radius_worst \\\n",
"count 5.690000e+02 569.000000 569.000000 569.000000 569.000000 \n",
"mean 3.037183e+07 0.372583 14.127292 19.289649 91.969033 \n",
"std 1.250206e+08 0.483918 3.524049 4.301036 24.298981 \n",
"min 8.670000e+03 0.000000 6.981000 9.710000 43.790000 \n",
"25% 8.692180e+05 0.000000 11.700000 16.170000 75.170000 \n",
"50% 9.060240e+05 0.000000 13.370000 18.840000 86.240000 \n",
"75% 8.813129e+06 1.000000 15.780000 21.800000 104.100000 \n",
"max 9.113205e+08 1.000000 28.110000 39.280000 188.500000 \n",
"\n",
" texture_mean texture_sd_error texture_worst perimeter_mean \\\n",
"count 569.000000 569.000000 569.000000 569.000000 \n",
"mean 654.889104 0.096360 0.104341 0.088799 \n",
"std 351.914129 0.014064 0.052813 0.079720 \n",
"min 143.500000 0.052630 0.019380 0.000000 \n",
"25% 420.300000 0.086370 0.064920 0.029560 \n",
"50% 551.100000 0.095870 0.092630 0.061540 \n",
"75% 782.700000 0.105300 0.130400 0.130700 \n",
"max 2501.000000 0.163400 0.345400 0.426800 \n",
"\n",
" perimeter_sd_error ... concavity_worst \\\n",
"count 569.000000 ... 569.000000 \n",
"mean 0.048919 ... 16.269190 \n",
"std 0.038803 ... 4.833242 \n",
"min 0.000000 ... 7.930000 \n",
"25% 0.020310 ... 13.010000 \n",
"50% 0.033500 ... 14.970000 \n",
"75% 0.074000 ... 18.790000 \n",
"max 0.201200 ... 36.040000 \n",
"\n",
" concave_points_mean concave_points_sd_error concave_points_worst \\\n",
"count 569.000000 569.000000 569.000000 \n",
"mean 25.677223 107.261213 880.583128 \n",
"std 6.146258 33.602542 569.356993 \n",
"min 12.020000 50.410000 185.200000 \n",
"25% 21.080000 84.110000 515.300000 \n",
"50% 25.410000 97.660000 686.500000 \n",
"75% 29.720000 125.400000 1084.000000 \n",
"max 49.540000 251.200000 4254.000000 \n",
"\n",
" symmetry_mean symmetry_sd_error symmetry_worst \\\n",
"count 569.000000 569.000000 569.000000 \n",
"mean 0.132369 0.254265 0.272188 \n",
"std 0.022832 0.157336 0.208624 \n",
"min 0.071170 0.027290 0.000000 \n",
"25% 0.116600 0.147200 0.114500 \n",
"50% 0.131300 0.211900 0.226700 \n",
"75% 0.146000 0.339100 0.382900 \n",
"max 0.222600 1.058000 1.252000 \n",
"\n",
" fractal_dimension_mean fractal_dimension_sd_error \\\n",
"count 569.000000 569.000000 \n",
"mean 0.114606 0.290076 \n",
"std 0.065732 0.061867 \n",
"min 0.000000 0.156500 \n",
"25% 0.064930 0.250400 \n",
"50% 0.099930 0.282200 \n",
"75% 0.161400 0.317900 \n",
"max 0.291000 0.663800 \n",
"\n",
" fractal_dimension_worst \n",
"count 569.000000 \n",
"mean 0.083946 \n",
"std 0.018061 \n",
"min 0.055040 \n",
"25% 0.071460 \n",
"50% 0.080040 \n",
"75% 0.092080 \n",
"max 0.207500 \n",
"\n",
"[8 rows x 32 columns]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# look at some summary statistics for the dataset\n",
"bc_data.describe()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"### Compute the mean and median smoothness and compactness for benign and malignant tumors - do they differ? "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"benign = bc_data[bc_data['diagnosis']==0]\n",
"malignant = bc_data[bc_data['diagnosis']==1]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean and median smoothness for benign is 2.0003, 1.851\n",
"mean and median smoothness for malignant is 4.3239, 3.6795\n"
]
}
],
"source": [
"# smoothness\n",
"\n",
"median_smooth_benign = statistics.median(benign['smoothness_mean'])\n",
"median_smooth_malig = statistics.median(malignant['smoothness_mean'])\n",
"\n",
"print('mean and median smoothness for benign is {}, {}'.format(\n",
" round(benign['smoothness_mean'].mean(),4), median_smooth_benign))\n",
"print('mean and median smoothness for malignant is {}, {}'.format(\n",
" round(malignant['smoothness_mean'].mean(),4), median_smooth_malig))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean and median compactness for benign is 0.0214, 0.0163\n",
"mean and median compactness for malignant is 0.0323, 0.02859\n"
]
}
],
"source": [
"# compactness\n",
"\n",
"median_compact_benign = statistics.median(benign['compactness_mean'])\n",
"median_compact_malig = statistics.median(malignant['compactness_mean'])\n",
"\n",
"print('mean and median compactness for benign is {}, {}'.format(\n",
" round(benign['compactness_mean'].mean(),4), round(median_compact_benign,4)))\n",
"print('mean and median compactness for malignant is {}, {}'.format(\n",
" round(malignant['compactness_mean'].mean(),4), median_compact_malig))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Write a function to generate bootstrap samples of the data."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def get_bootstrap(df, num_samples_to_get):\n",
" n = len(df.values)\n",
" bootstrap_df = pd.DataFrame(\n",
" df.values[np.random.randint(n, size=num_samples_to_get)], columns=df.columns)\n",
" return bootstrap_df"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>ID</th>\n",
" <th>diagnosis</th>\n",
" <th>radius_mean</th>\n",
" <th>radius_sd_error</th>\n",
" <th>radius_worst</th>\n",
" <th>texture_mean</th>\n",
" <th>texture_sd_error</th>\n",
" <th>texture_worst</th>\n",
" <th>perimeter_mean</th>\n",
" <th>perimeter_sd_error</th>\n",
" <th>...</th>\n",
" <th>concavity_worst</th>\n",
" <th>concave_points_mean</th>\n",
" <th>concave_points_sd_error</th>\n",
" <th>concave_points_worst</th>\n",
" <th>symmetry_mean</th>\n",
" <th>symmetry_sd_error</th>\n",
" <th>symmetry_worst</th>\n",
" <th>fractal_dimension_mean</th>\n",
" <th>fractal_dimension_sd_error</th>\n",
" <th>fractal_dimension_worst</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>868682.0</td>\n",
" <td>0.0</td>\n",
" <td>11.430</td>\n",
" <td>15.39</td>\n",
" <td>73.06</td>\n",
" <td>399.8</td>\n",
" <td>0.09639</td>\n",
" <td>0.06889</td>\n",
" <td>0.03503</td>\n",
" <td>0.02875</td>\n",
" <td>...</td>\n",
" <td>12.320</td>\n",
" <td>22.02</td>\n",
" <td>79.93</td>\n",
" <td>462.0</td>\n",
" <td>0.1190</td>\n",
" <td>0.16480</td>\n",
" <td>0.13990</td>\n",
" <td>0.08476</td>\n",
" <td>0.2676</td>\n",
" <td>0.06765</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>911384.0</td>\n",
" <td>0.0</td>\n",
" <td>14.920</td>\n",
" <td>14.93</td>\n",
" <td>96.45</td>\n",
" <td>686.9</td>\n",
" <td>0.08098</td>\n",
" <td>0.08549</td>\n",
" <td>0.05539</td>\n",
" <td>0.03221</td>\n",
" <td>...</td>\n",
" <td>17.180</td>\n",
" <td>18.22</td>\n",
" <td>112.00</td>\n",
" <td>906.6</td>\n",
" <td>0.1065</td>\n",
" <td>0.27910</td>\n",
" <td>0.31510</td>\n",
" <td>0.11470</td>\n",
" <td>0.2688</td>\n",
" <td>0.08273</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>924342.0</td>\n",
" <td>0.0</td>\n",
" <td>9.333</td>\n",
" <td>21.94</td>\n",
" <td>59.01</td>\n",
" <td>264.0</td>\n",
" <td>0.09240</td>\n",
" <td>0.05605</td>\n",
" <td>0.03996</td>\n",
" <td>0.01282</td>\n",
" <td>...</td>\n",
" <td>9.845</td>\n",
" <td>25.05</td>\n",
" <td>62.86</td>\n",
" <td>295.8</td>\n",
" <td>0.1103</td>\n",
" <td>0.08298</td>\n",
" <td>0.07993</td>\n",
" <td>0.02564</td>\n",
" <td>0.2435</td>\n",
" <td>0.07393</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>915664.0</td>\n",
" <td>0.0</td>\n",
" <td>14.810</td>\n",
" <td>14.70</td>\n",
" <td>94.66</td>\n",
" <td>680.7</td>\n",
" <td>0.08472</td>\n",
" <td>0.05016</td>\n",
" <td>0.03416</td>\n",
" <td>0.02541</td>\n",
" <td>...</td>\n",
" <td>15.610</td>\n",
" <td>17.58</td>\n",
" <td>101.70</td>\n",
" <td>760.2</td>\n",
" <td>0.1139</td>\n",
" <td>0.10110</td>\n",
" <td>0.11010</td>\n",
" <td>0.07955</td>\n",
" <td>0.2334</td>\n",
" <td>0.06142</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>845636.0</td>\n",
" <td>1.0</td>\n",
" <td>16.020</td>\n",
" <td>23.24</td>\n",
" <td>102.70</td>\n",
" <td>797.8</td>\n",
" <td>0.08206</td>\n",
" <td>0.06669</td>\n",
" <td>0.03299</td>\n",
" <td>0.03323</td>\n",
" <td>...</td>\n",
" <td>19.190</td>\n",
" <td>33.88</td>\n",
" <td>123.80</td>\n",
" <td>1150.0</td>\n",
" <td>0.1181</td>\n",
" <td>0.15510</td>\n",
" <td>0.14590</td>\n",
" <td>0.09975</td>\n",
" <td>0.2948</td>\n",
" <td>0.08452</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 32 columns</p>\n",
"</div>"
],
"text/plain": [
" ID diagnosis radius_mean radius_sd_error radius_worst \\\n",
"0 868682.0 0.0 11.430 15.39 73.06 \n",
"1 911384.0 0.0 14.920 14.93 96.45 \n",
"2 924342.0 0.0 9.333 21.94 59.01 \n",
"3 915664.0 0.0 14.810 14.70 94.66 \n",
"4 845636.0 1.0 16.020 23.24 102.70 \n",
"\n",
" texture_mean texture_sd_error texture_worst perimeter_mean \\\n",
"0 399.8 0.09639 0.06889 0.03503 \n",
"1 686.9 0.08098 0.08549 0.05539 \n",
"2 264.0 0.09240 0.05605 0.03996 \n",
"3 680.7 0.08472 0.05016 0.03416 \n",
"4 797.8 0.08206 0.06669 0.03299 \n",
"\n",
" perimeter_sd_error ... concavity_worst \\\n",
"0 0.02875 ... 12.320 \n",
"1 0.03221 ... 17.180 \n",
"2 0.01282 ... 9.845 \n",
"3 0.02541 ... 15.610 \n",
"4 0.03323 ... 19.190 \n",
"\n",
" concave_points_mean concave_points_sd_error concave_points_worst \\\n",
"0 22.02 79.93 462.0 \n",
"1 18.22 112.00 906.6 \n",
"2 25.05 62.86 295.8 \n",
"3 17.58 101.70 760.2 \n",
"4 33.88 123.80 1150.0 \n",
"\n",
" symmetry_mean symmetry_sd_error symmetry_worst fractal_dimension_mean \\\n",
"0 0.1190 0.16480 0.13990 0.08476 \n",
"1 0.1065 0.27910 0.31510 0.11470 \n",
"2 0.1103 0.08298 0.07993 0.02564 \n",
"3 0.1139 0.10110 0.11010 0.07955 \n",
"4 0.1181 0.15510 0.14590 0.09975 \n",
"\n",
" fractal_dimension_sd_error fractal_dimension_worst \n",
"0 0.2676 0.06765 \n",
"1 0.2688 0.08273 \n",
"2 0.2435 0.07393 \n",
"3 0.2334 0.06142 \n",
"4 0.2948 0.08452 \n",
"\n",
"[5 rows x 32 columns]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"get_bootstrap(bc_data, 5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Identify 2-3 variables that are predictive of a malignant tumor. Display the relationship visually and write 1-2 sentences explaining the relationship."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# split data into X and y (target)\n",
"\n",
"bc_X = bc_data.iloc[:, 2:]\n",
"bc_y = bc_data.iloc[:, 1]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(569, 30)"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bc_X.shape"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(569,)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bc_y.shape"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>feature</th>\n",
" <th>f-score</th>\n",
" <th>p-value</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>fractal_dimension_mean</td>\n",
" <td>964.385393</td>\n",
" <td>1.969100e-124</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>concave_points_sd_error</td>\n",
" <td>897.944219</td>\n",
" <td>5.771397e-119</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>perimeter_sd_error</td>\n",
" <td>861.676020</td>\n",
" <td>7.101150e-116</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>concavity_worst</td>\n",
" <td>860.781707</td>\n",
" <td>8.482292e-116</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>radius_worst</td>\n",
" <td>697.235272</td>\n",
" <td>8.436251e-101</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>concave_points_worst</td>\n",
" <td>661.600206</td>\n",
" <td>2.828848e-97</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>radius_mean</td>\n",
" <td>646.981021</td>\n",
" <td>8.465941e-96</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>texture_mean</td>\n",
" <td>573.060747</td>\n",
" <td>4.734564e-88</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>perimeter_mean</td>\n",
" <td>533.793126</td>\n",
" <td>9.966556e-84</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>symmetry_worst</td>\n",
" <td>436.691939</td>\n",
" <td>2.464664e-72</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>texture_worst</td>\n",
" <td>313.233079</td>\n",
" <td>3.938263e-56</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>symmetry_sd_error</td>\n",
" <td>304.341063</td>\n",
" <td>7.069816e-55</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>area_sd_error</td>\n",
" <td>268.840327</td>\n",
" <td>9.738949e-50</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>smoothness_mean</td>\n",
" <td>253.897392</td>\n",
" <td>1.651905e-47</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>smoothness_sd_error</td>\n",
" <td>243.651586</td>\n",
" <td>5.895521e-46</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>concave_points_mean</td>\n",
" <td>149.596905</td>\n",
" <td>1.078057e-30</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>symmetry_mean</td>\n",
" <td>122.472880</td>\n",
" <td>6.575144e-26</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>fractal_dimension_sd_error</td>\n",
" <td>118.860232</td>\n",
" <td>2.951121e-25</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>radius_sd_error</td>\n",
" <td>118.096059</td>\n",
" <td>4.058636e-25</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>compactness_worst</td>\n",
" <td>113.262760</td>\n",
" <td>3.072309e-24</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>texture_sd_error</td>\n",
" <td>83.651123</td>\n",
" <td>1.051850e-18</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>perimeter_worst</td>\n",
" <td>69.527444</td>\n",
" <td>5.733384e-16</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>fractal_dimension_worst</td>\n",
" <td>66.443961</td>\n",
" <td>2.316432e-15</td>\n",
" </tr>\n",
" <tr>\n",
" <th>23</th>\n",
" <td>compactness_mean</td>\n",
" <td>53.247339</td>\n",
" <td>9.975995e-13</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td>compactness_sd_error</td>\n",
" <td>39.014482</td>\n",
" <td>8.260176e-10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25</th>\n",
" <td>concavity_sd_error</td>\n",
" <td>3.468275</td>\n",
" <td>6.307355e-02</td>\n",
" </tr>\n",
" <tr>\n",
" <th>26</th>\n",
" <td>smoothness_worst</td>\n",
" <td>2.557968</td>\n",
" <td>1.102966e-01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td>area_mean</td>\n",
" <td>0.093459</td>\n",
" <td>7.599368e-01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>28</th>\n",
" <td>area_worst</td>\n",
" <td>0.039095</td>\n",
" <td>8.433320e-01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td>concavity_mean</td>\n",
" <td>0.024117</td>\n",
" <td>8.766418e-01</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" feature f-score p-value\n",
"0 fractal_dimension_mean 964.385393 1.969100e-124\n",
"1 concave_points_sd_error 897.944219 5.771397e-119\n",
"2 perimeter_sd_error 861.676020 7.101150e-116\n",
"3 concavity_worst 860.781707 8.482292e-116\n",
"4 radius_worst 697.235272 8.436251e-101\n",
"5 concave_points_worst 661.600206 2.828848e-97\n",
"6 radius_mean 646.981021 8.465941e-96\n",
"7 texture_mean 573.060747 4.734564e-88\n",
"8 perimeter_mean 533.793126 9.966556e-84\n",
"9 symmetry_worst 436.691939 2.464664e-72\n",
"10 texture_worst 313.233079 3.938263e-56\n",
"11 symmetry_sd_error 304.341063 7.069816e-55\n",
"12 area_sd_error 268.840327 9.738949e-50\n",
"13 smoothness_mean 253.897392 1.651905e-47\n",
"14 smoothness_sd_error 243.651586 5.895521e-46\n",
"15 concave_points_mean 149.596905 1.078057e-30\n",
"16 symmetry_mean 122.472880 6.575144e-26\n",
"17 fractal_dimension_sd_error 118.860232 2.951121e-25\n",
"18 radius_sd_error 118.096059 4.058636e-25\n",
"19 compactness_worst 113.262760 3.072309e-24\n",
"20 texture_sd_error 83.651123 1.051850e-18\n",
"21 perimeter_worst 69.527444 5.733384e-16\n",
"22 fractal_dimension_worst 66.443961 2.316432e-15\n",
"23 compactness_mean 53.247339 9.975995e-13\n",
"24 compactness_sd_error 39.014482 8.260176e-10\n",
"25 concavity_sd_error 3.468275 6.307355e-02\n",
"26 smoothness_worst 2.557968 1.102966e-01\n",
"27 area_mean 0.093459 7.599368e-01\n",
"28 area_worst 0.039095 8.433320e-01\n",
"29 concavity_mean 0.024117 8.766418e-01"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Instantiate SelectKBest with scoring funcion and number of columns we want to select\n",
"\n",
"skb = SelectKBest(score_func=f_classif, k=3)\n",
"\n",
"# Fit X and y\n",
"\n",
"skb.fit(bc_X, bc_y)\n",
"\n",
"# Observe scores in descending order\n",
"\n",
"feat_list = list(zip(bc_X.columns,skb.scores_, skb.pvalues_))\n",
"feat_list.sort(key=lambda x: x[2], reverse=False)\n",
"pd.DataFrame(feat_list, columns=['feature','f-score','p-value'])"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# make a Boolean mask to select only these columns\n",
"\n",
"mask = skb.get_support()\n",
"k_best_features = bc_X.columns[mask]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Index(['perimeter_sd_error', 'concave_points_sd_error',\n",
" 'fractal_dimension_mean'],\n",
" dtype='object')"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k_best_features"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11afaa668>"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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Dg4iIpDE0iIhIGkODiIikMTSIiEgaQ4OIiKQxNIiISBpDg4iIpDE0iIhIGkODiIikMTSI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\nAaCMWnpTxrHnAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ae97a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.lmplot('perimeter_sd_error', 'diagnosis',\n",
" data=bc_data,\n",
" fit_reg=False,\n",
" hue=\"diagnosis\", \n",
" scatter_kws={\"marker\": \"D\",\n",
" \"s\": 100})\n",
"\n",
"plt.xlabel('perimeter_sd_error')\n",
"plt.ylabel('diagnosis')"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11d6b2a90>"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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ekHEaO/bBi33wYh+82Ie6BS00LBYLbDab77KmaVBV1e/y4sWLcfToUSxbtgyK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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ae97ef0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.lmplot('concave_points_sd_error', 'diagnosis',\n",
" data=bc_data,\n",
" fit_reg=False,\n",
" hue=\"diagnosis\", \n",
" scatter_kws={\"marker\": \"D\",\n",
" \"s\": 100})\n",
"\n",
"plt.xlabel('concave_points_sd_error')\n",
"plt.ylabel('diagnosis')"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11d7c0ba8>"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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8+fP5y1/+gt/vp0+fPkyePBmfTx0mItKWefYuvWjRIpLJJHPnzmXixInMnDkz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\nKg0REbGm0hAREWsqDRERsfb/ARqMUp2kMDE5AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11d7457f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.lmplot('fractal_dimension_mean', 'diagnosis',\n",
" data=bc_data,\n",
" fit_reg=False,\n",
" hue=\"diagnosis\", \n",
" scatter_kws={\"marker\": \"D\",\n",
" \"s\": 100})\n",
"\n",
"plt.xlabel('fractal_dimension_mean')\n",
"plt.ylabel('diagnosis')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These plots show, for each of the three most predictive features, the range of values corresponding with 'benign' (0) or 'malignant' (1). (Clearly there is a lot of overlap.) For each feature, as its value gets larger, we are more likely to see a 'malignant' target value. We could also look at a logistic regression to see the likelihood of a tumor being benign or malignant for the range of values for each feature."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Build a model to predict the malignant tumors.\n",
" * Use at least two classification techniques; compare and contrast the advantages and disadvantages of each.\n",
" * Identify how you would control for overfitting in each classification technique.\n",
" * Evaluate the performance of each model.\n",
" * In each model, identify the most important predictive variables and explain how you identified them.\n"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# train test split the features and target data\n",
"\n",
"X_train, X_test, y_train, y_test = train_test_split(bc_X, bc_y)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# We need to standardize the data (to have mean of 0 and std of 1) to allow for equal comparison of variables???\n",
"\n",
"scaler = StandardScaler()\n",
"X_train_sc = scaler.fit(X_train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Logistic Regression model"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"logreg= LogisticRegression(C=10E2).fit(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.98356807511737088"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"logreg.score(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.95104895104895104"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"logreg.score(X_test, y_test)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ -4.89040214e+00, -1.07043962e-01, 1.77156456e-01,\n",
" 4.08181526e-02, 4.78844397e+00, -3.71271262e-01,\n",
" 3.66629580e+00, 7.73872078e+00, 5.10503836e+00,\n",
" -9.55832367e-01, -1.38976254e+00, -2.86400240e+00,\n",
" 1.25043506e+00, 8.34873081e-02, 6.83255599e-01,\n",
" -6.28819993e+00, -7.65296735e+00, 5.85285124e-01,\n",
" -3.41478951e-01, -1.30143805e+00, 1.48126233e+00,\n",
" 5.14966863e-01, -1.34803412e-01, 2.12124601e-03,\n",
" 9.02020268e+00, -4.52930024e+00, 8.77720048e+00,\n",
" 1.53997578e+01, 9.78344021e+00, -1.98603470e+00]])"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"logreg.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Most important predictive variables from logreg - identified by largest absolute value of coefficients. In logistic regression this indicates how much the probability of the target changes in response to the feature."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[('fractal_dimension_mean', 15.399757833548678),\n",
" ('fractal_dimension_sd_error', 9.7834402131332698),\n",
" ('symmetry_mean', 9.0202026754728433),\n",
" ('symmetry_worst', 8.7772004801627173),\n",
" ('perimeter_sd_error', 7.7387207755525829),\n",
" ('compactness_sd_error', 7.6529673475395175),\n",
" ('compactness_mean', 6.2881999286575558),\n",
" ('perimeter_worst', 5.1050383566848723),\n",
" ('radius_mean', 4.8904021429123103),\n",
" ('texture_sd_error', 4.788443970608534),\n",
" ('symmetry_sd_error', 4.5293002380203884),\n",
" ('perimeter_mean', 3.6662957990505372),\n",
" ('area_worst', 2.8640023999202655),\n",
" ('fractal_dimension_worst', 1.9860347048400133),\n",
" ('concavity_worst', 1.4812623280518653),\n",
" ('area_sd_error', 1.3897625413911123),\n",
" ('concavity_sd_error', 1.3014380532400722),\n",
" ('smoothness_mean', 1.2504350619155262),\n",
" ('area_mean', 0.9558323673257948),\n",
" ('smoothness_worst', 0.68325559897317001),\n",
" ('compactness_worst', 0.58528512359556129),\n",
" ('concave_points_mean', 0.51496686329661967),\n",
" ('texture_worst', 0.37127126180280556),\n",
" ('concavity_mean', 0.34147895085529872),\n",
" ('radius_worst', 0.17715645568571733),\n",
" ('concave_points_sd_error', 0.13480341154830128),\n",
" ('radius_sd_error', 0.10704396201040854),\n",
" ('smoothness_sd_error', 0.083487308096107771),\n",
" ('texture_mean', 0.040818152621318229),\n",
" ('concave_points_worst', 0.0021212460138316895)]"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sorted(list(zip(bc_X.columns, abs(logreg.coef_[0]))), key=lambda x: x[1], reverse=True) "
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# make top 5 features to compare below with other model/s\n",
"\n",
"top_5_feats_lr = sorted(list(zip(bc_X.columns, abs(logreg.coef_[0]))), key=lambda x: x[1], reverse=True)[:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Logistic regression is fast to train and predict, scales to large datasets, and works well on sparse data. It is also highly interpretable, but it may not be clear why it sets the coefficients the way it does, especially on a dataset with highly correlated features."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Random Forest model"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ranfor = RandomForestClassifier(max_depth=10).fit(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.99530516431924887"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# train score\n",
"ranfor.score(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.95104895104895104"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# test score\n",
"ranfor.score(X_test, y_test)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Look at feature importances (they sum to 1, and each feature is ranked from 0 if not used at all to 1 if perfectly predicts the target):"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.00664 , 0.01192315, 0.13710448, 0.00716612, 0. ,\n",
" 0.04831478, 0. , 0.18592364, 0. , 0.0050617 ,\n",
" 0.05203602, 0.00125606, 0.00694849, 0.01124793, 0.00541972,\n",
" 0.00069702, 0.00889316, 0.00377655, 0.00682655, 0.00703202,\n",
" 0.07571054, 0.01774287, 0.09602688, 0.1576697 , 0.01514367,\n",
" 0.01134483, 0.0540487 , 0.04214065, 0.0222338 , 0.00167097])"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ranfor.feature_importances_"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[('perimeter_sd_error', 0.18592363887837887),\n",
" ('concave_points_worst', 0.15766970441192482),\n",
" ('radius_worst', 0.13710448289774602),\n",
" ('concave_points_sd_error', 0.096026882456910934),\n",
" ('concavity_worst', 0.075710540823427569),\n",
" ('symmetry_worst', 0.054048696911513136),\n",
" ('area_sd_error', 0.052036024912112247),\n",
" ('texture_worst', 0.048314784282380209),\n",
" ('fractal_dimension_mean', 0.042140651237974232),\n",
" ('fractal_dimension_sd_error', 0.02223379669289666),\n",
" ('concave_points_mean', 0.017742868252507153),\n",
" ('symmetry_mean', 0.015143672818011891),\n",
" ('radius_sd_error', 0.011923151224529921),\n",
" ('symmetry_sd_error', 0.011344834546666903),\n",
" ('smoothness_sd_error', 0.011247927042949152),\n",
" ('compactness_sd_error', 0.0088931642312099438),\n",
" ('texture_mean', 0.0071661187113607958),\n",
" ('concavity_sd_error', 0.0070320153136990112),\n",
" ('smoothness_mean', 0.0069484874326051658),\n",
" ('concavity_mean', 0.0068265506332328531),\n",
" ('radius_mean', 0.0066399987446980561),\n",
" ('smoothness_worst', 0.0054197192837217344),\n",
" ('area_mean', 0.0050616961119502018),\n",
" ('compactness_worst', 0.0037765493654083209),\n",
" ('fractal_dimension_worst', 0.0016709683632497841),\n",
" ('area_worst', 0.0012560563799112593),\n",
" ('compactness_mean', 0.00069701803902319298),\n",
" ('texture_sd_error', 0.0),\n",
" ('perimeter_mean', 0.0),\n",
" ('perimeter_worst', 0.0)]"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sorted(list(zip(bc_X.columns, ranfor.feature_importances_)), key=lambda x: x[1], reverse=True) "
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"top_5_feats_rf = sorted(list(zip(bc_X.columns, ranfor.feature_importances_)), key=lambda x: x[1], reverse=True)[:5]"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"([('fractal_dimension_mean', 15.399757833548678),\n",
" ('fractal_dimension_sd_error', 9.7834402131332698),\n",
" ('symmetry_mean', 9.0202026754728433),\n",
" ('symmetry_worst', 8.7772004801627173),\n",
" ('perimeter_sd_error', 7.7387207755525829)],\n",
" [('perimeter_sd_error', 0.18592363887837887),\n",
" ('concave_points_worst', 0.15766970441192482),\n",
" ('radius_worst', 0.13710448289774602),\n",
" ('concave_points_sd_error', 0.096026882456910934),\n",
" ('concavity_worst', 0.075710540823427569)])"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"top_5_feats_lr, top_5_feats_rf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Interesting, the models selected totally different features! Could explore making more trees in the RF model and setting a random state, see if the top features change."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Build a pipeline and compare results with baseline Random Forest"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"rf_pipe = Pipeline([\n",
" ('skb', SelectKBest(score_func=f_classif, k=20)),\n",
" ('scaler', StandardScaler()),\n",
" ('rf', RandomForestClassifier())\n",
"])"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"params = {\n",
" 'rf__n_estimators':[10,100],\n",
" 'rf__max_depth':[10, 20, 40, 50, None]\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"gs_pipe = GridSearchCV(rf_pipe,\n",
" param_grid=params,\n",
" n_jobs=-1,\n",
" cv=ShuffleSplit()\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"GridSearchCV(cv=ShuffleSplit(n_splits=10, random_state=None, test_size=0.1, train_size=None),\n",
" error_score='raise',\n",
" estimator=Pipeline(steps=[('skb', SelectKBest(k=20, score_func=<function f_classif at 0x119e5dbf8>)), ('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('rf', RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
" max_depth=None, max_features='auto', max_leaf_nodes=...imators=10, n_jobs=1, oob_score=False, random_state=None,\n",
" verbose=0, warm_start=False))]),\n",
" fit_params={}, iid=True, n_jobs=-1,\n",
" param_grid={'rf__n_estimators': [10, 100], 'rf__max_depth': [10, 20, 40, 50, None]},\n",
" pre_dispatch='2*n_jobs', refit=True, return_train_score=True,\n",
" scoring=None, verbose=0)"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gs_pipe.fit(bc_X, bc_y)"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.96842105263157896"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gs_pipe.best_score_"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"{'rf__max_depth': None, 'rf__n_estimators': 100}"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gs_pipe.best_params_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The pipeline did slightly better but not much."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Random Forests reduce overfitting that might occur with tree-based models by averaging the results of lots of shallow trees. They are very powerful, don't require scaling of the data, and usually work well without much parameter tuning. But they don't wok well on high dimensions, sparse data, and they require more memory and take longer to train and predict than linear models."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How to prevent overfitting a model?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use regularization (L2 Ridge or L1 Lasso) to restrict linear models and prevent overfitting. Controlling the strength of the regularization by increasing alpha (with Ridge and Lasso) or decreasing C (with Logistic Regression) also helps prevent overfitting by further restricting the coefficients. Using Lasso has the additional benefit of performing automatic feature selection by restricting the coefficients of some features to zero, thus revealing the most important features in the dataset and making the model easier to interpret.\n",
"\n",
"We can also increase the size of the training data (in this case by bootstrapping) to make it harder for the model to overfit.\n",
"\n",
"For the Random Forest model, we can control for overfitting by limiting the max depth of the trees and setting a smaller max_features."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Discussion:\n",
"\n",
"These models could be further improved by tuning hyperparameters via grid search, more feature engineering, and combining different models in ensemble learning. After doing this, we could look at other model evaluation metrics such as a confusion matrix and ROC/AUC.\n",
"\n",
"In summary:\n",
"\n",
"The logistic regression model works by assigning a weight to each feature in the dataset. This weight explains how important, relatively, the feature is in determining which class (malignant or benign) samples fall into. It determines the probability based on these weights for each sample to be in one class or the other. The model performed very well, with a test score accuracy of 94% meaning that if we were to feed new samples into the model, it would correctly predict whether it was benign or malignant about 94% of the time. The random forest model achieved an even greater accuracy of 97%. It works by combining many tree-based models. These models essentially learn a hierarchy of if/else questions that leads to a decision of which class a sample belongs to, resulting in a recursive partitioning of the data. The factors that contributed to identification of samples as benign or malignant was different for each of the models, indicating that further work is necessary to carefully pre-process the data and select important features. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Part 2: Feedback"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Student sample 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"line 5: specify which module in sklearn to import model from\n",
"\n",
"line 9: good to use more descriptive names (i.e. 'data_df' instead of 'd')\n",
"\n",
"before setting up your data for prediction, you need to do some data exploration. check shape of data, any null values, any outliers, data types. are there any pre-processing steps you need to take? should you scale the data before modeling? what are your features? what is the target that you're predicting? are there any visualizations you can do to better understand your data?\n",
"\n",
"line 13 and 14: name your y or target rather than calling it 'x2'. check to see that your feature and target selection worked the way you expected.\n",
"\n",
"line 17: use a descriptive name when you instantiate the model, i.e. 'linear regression' instead of just 'model', since you may add other models later and will want to be able to distinguish between them.\n",
"\n",
"choice of model: we don't usually want to use a basic linear regression (ordinary least squares), want to use a model that has parameters that we can use to control model complexity and avoid overfitting to the training data, for example ridge regression. \n",
"\n",
"You imported train_test_split but didn't use it, so this step is unnecessary. Also line 20 is redundant because you already imported cross_val_score\n",
"\n",
"probably want to use a larger value for cv in the cross-validation, like 5, or set the cv to do a KFold or ShuffleSplit on the data to ensure the data is adequately shuffled.\n",
"\n",
"Make sure you review and understand the steps in the process of data exploration and cleaning, pre-processing, and especially implementing a model and fitting it to your data. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Student sample 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See above comments re. data exploration and pre-processing, naming model\n",
"\n",
"For model selection, if you were to choose a more complex model you could use GridSearchCV to tune the hyperparameters and do the cross validation. \n",
"\n",
"For scoring, you can also use R2 or MSE instead of or in addition to MAE. "
]
}
],
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