Assignment #3 (demo). Decision trees with a toy task and the UCI Adult dataset#

../../_images/ods_stickers.jpg

mlcourse.ai – Open Machine Learning Course

Authors: Maria Kuna (Sumarokova), and Yury Kashnitsky. Translated and edited by Gleb Filatov, Aleksey Kiselev, Anastasia Manokhina, Egor Polusmak, and Yuanyuan Pao. All content is distributed under the Creative Commons CC BY-NC-SA 4.0 license.

Same assignment as a Kaggle Kernel + solution. Fill in the answers in the web-form.

Let’s start by loading all necessary libraries:

import collections
from io import StringIO

import numpy as np
import pandas as pd
import pydotplus  # pip install pydotplus
import seaborn as sns
from ipywidgets import Image
from sklearn import preprocessing
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score
from sklearn.model_selection import GridSearchCV
from sklearn.preprocessing import LabelEncoder
from sklearn.tree import DecisionTreeClassifier, export_graphviz

from matplotlib import pyplot as plt
plt.rcParams["figure.figsize"] = (10, 8)

Part 1. Toy dataset “Will They? Won’t They?”#

Your goal is to figure out how decision trees work by walking through a toy problem. While a single decision tree does not yield outstanding results, other performant algorithms like gradient boosting and random forests are based on the same idea. That is why knowing how decision trees work might be useful.

We’ll go through a toy example of binary classification - Person A is deciding whether they will go on a second date with Person B. It will depend on their looks, eloquence, alcohol consumption (only for example), and how much money was spent on the first date.

Creating the dataset#

# Create dataframe with dummy variables
def create_df(dic, feature_list):
    out = pd.DataFrame(dic)
    out = pd.concat([out, pd.get_dummies(out[feature_list])], axis=1)
    out.drop(feature_list, axis=1, inplace=True)
    return out


# Some feature values are present in train and absent in test and vice-versa.
def intersect_features(train, test):
    common_feat = list(set(train.keys()) & set(test.keys()))
    return train[common_feat], test[common_feat]

features = ["Looks", "Alcoholic_beverage", "Eloquence", "Money_spent"]

Training data#

df_train = {}
df_train["Looks"] = [
    "handsome",
    "handsome",
    "handsome",
    "repulsive",
    "repulsive",
    "repulsive",
    "handsome",
]
df_train["Alcoholic_beverage"] = ["yes", "yes", "no", "no", "yes", "yes", "yes"]
df_train["Eloquence"] = ["high", "low", "average", "average", "low", "high", "average"]
df_train["Money_spent"] = ["lots", "little", "lots", "little", "lots", "lots", "lots"]
df_train["Will_go"] = LabelEncoder().fit_transform(["+", "-", "+", "-", "-", "+", "+"])

df_train = create_df(df_train, features)
df_train
Will_go Looks_handsome Looks_repulsive Alcoholic_beverage_no Alcoholic_beverage_yes Eloquence_average Eloquence_high Eloquence_low Money_spent_little Money_spent_lots
0 0 1 0 0 1 0 1 0 0 1
1 1 1 0 0 1 0 0 1 1 0
2 0 1 0 1 0 1 0 0 0 1
3 1 0 1 1 0 1 0 0 1 0
4 1 0 1 0 1 0 0 1 0 1
5 0 0 1 0 1 0 1 0 0 1
6 0 1 0 0 1 1 0 0 0 1

Test data#

df_test = {}
df_test["Looks"] = ["handsome", "handsome", "repulsive"]
df_test["Alcoholic_beverage"] = ["no", "yes", "yes"]
df_test["Eloquence"] = ["average", "high", "average"]
df_test["Money_spent"] = ["lots", "little", "lots"]
df_test = create_df(df_test, features)
df_test
Looks_handsome Looks_repulsive Alcoholic_beverage_no Alcoholic_beverage_yes Eloquence_average Eloquence_high Money_spent_little Money_spent_lots
0 1 0 1 0 1 0 0 1
1 1 0 0 1 0 1 1 0
2 0 1 0 1 1 0 0 1 
# Some feature values are present in train and absent in test and vice-versa.
y = df_train["Will_go"]
df_train, df_test = intersect_features(train=df_train, test=df_test)
df_train
Alcoholic_beverage_yes Looks_repulsive Money_spent_lots Alcoholic_beverage_no Eloquence_average Money_spent_little Eloquence_high Looks_handsome
0 1 0 1 0 0 0 1 1
1 1 0 0 0 0 1 0 1
2 0 0 1 1 1 0 0 1
3 0 1 0 1 1 1 0 0
4 1 1 1 0 0 0 0 0
5 1 1 1 0 0 0 1 0
6 1 0 1 0 1 0 0 1 
df_test
Alcoholic_beverage_yes Looks_repulsive Money_spent_lots Alcoholic_beverage_no Eloquence_average Money_spent_little Eloquence_high Looks_handsome
0 0 0 1 1 1 0 0 1
1 1 0 0 0 0 1 1 1
2 1 1 1 0 1 0 0 0

Draw a decision tree (by hand or in any graphics editor) for this dataset. Optionally you can also implement tree construction and draw it here.#

1. What is the entropy \(S_0\) of the initial system? By system states, we mean values of the binary feature “Will_go” - 0 or 1 - two states in total.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

2. Let’s split the data by the feature “Looks_handsome”. What is the entropy \(S_1\) of the left group - the one with “Looks_handsome”. What is the entropy \(S_2\) in the opposite group? What is the information gain (IG) if we consider such a split?

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Train a decision tree using sklearn on the training data. You may choose any depth for the tree.#

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Additional: display the resulting tree using graphviz. You can use pydot or a web-service, e.g. this one.#

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Part 2. Functions for calculating entropy and information gain.#

Consider the following warm-up example: we have 9 blue balls and 11 yellow balls. Let ball have label 1 if it is blue, 0 otherwise.

balls = [1 for i in range(9)] + [0 for i in range(11)]

Next split the balls into two groups:

# two groups
balls_left = [1 for i in range(8)] + [0 for i in range(5)]  # 8 blue and 5 yellow
balls_right = [1 for i in range(1)] + [0 for i in range(6)]  # 1 blue and 6 yellow

Implement a function to calculate the Shannon Entropy#

def entropy(a_list):
    # You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
    pass

Tests

print(entropy(balls))  # 9 blue и 11 yellow
print(entropy(balls_left))  # 8 blue и 5 yellow
print(entropy(balls_right))  # 1 blue и 6 yellow
print(entropy([1, 2, 3, 4, 5, 6]))  # entropy of a fair 6-sided die

None
None
None
None

3. What is the entropy of the state given by the list balls_left?

4. What is the entropy of a fair dice? (where we look at a dice as a system with 6 equally probable states)?

# information gain calculation
def information_gain(root, left, right):
    """ root - initial data, left and right - two partitions of initial data"""

    # You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
    pass

5. What is the information gain from splitting the initial dataset into balls_left and balls_right ?

def information_gains(X, y):
    """Outputs information gain when splitting with each feature"""

    # You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
    pass

Optional:#

  • Implement a decision tree building algorithm by calling information_gains recursively

  • Plot the resulting tree

Part 3. The “Adult” dataset#

Dataset description:

Dataset UCI Adult (no need to download it, we have a copy in the course repository): classify people using demographic data - whether they earn more than $50,000 per year or not.

Feature descriptions:

  • Age – continuous feature

  • Workclass – continuous feature

  • fnlwgt – final weight of object, continuous feature

  • Education – categorical feature

  • Education_Num – number of years of education, continuous feature

  • Martial_Status – categorical feature

  • Occupation – categorical feature

  • Relationship – categorical feature

  • Race – categorical feature

  • Sex – categorical feature

  • Capital_Gain – continuous feature

  • Capital_Loss – continuous feature

  • Hours_per_week – continuous feature

  • Country – categorical feature

Target – earnings level, categorical (binary) feature.

Reading train and test data

# for Jupyter-book, we copy data from GitHub, locally, to save Internet traffic,
# you can specify the data/ folder from the root of your cloned
# https://github.com/Yorko/mlcourse.ai repo, to save Internet traffic
DATA_PATH = "https://raw.githubusercontent.com/Yorko/mlcourse.ai/main/data/"

data_train = pd.read_csv(DATA_PATH + "adult_train.csv", sep=";")

data_train.tail()
Age Workclass fnlwgt Education Education_Num Martial_Status Occupation Relationship Race Sex Capital_Gain Capital_Loss Hours_per_week Country Target
32556 27 Private 257302 Assoc-acdm 12 Married-civ-spouse Tech-support Wife White Female 0 0 38 United-States <=50K
32557 40 Private 154374 HS-grad 9 Married-civ-spouse Machine-op-inspct Husband White Male 0 0 40 United-States >50K
32558 58 Private 151910 HS-grad 9 Widowed Adm-clerical Unmarried White Female 0 0 40 United-States <=50K
32559 22 Private 201490 HS-grad 9 Never-married Adm-clerical Own-child White Male 0 0 20 United-States <=50K
32560 52 Self-emp-inc 287927 HS-grad 9 Married-civ-spouse Exec-managerial Wife White Female 15024 0 40 United-States >50K 
data_test = pd.read_csv(DATA_PATH + "adult_test.csv", sep=";")

data_test.tail()
Age Workclass fnlwgt Education Education_Num Martial_Status Occupation Relationship Race Sex Capital_Gain Capital_Loss Hours_per_week Country Target
16277 39 Private 215419.0 Bachelors 13.0 Divorced Prof-specialty Not-in-family White Female 0.0 0.0 36.0 United-States <=50K.
16278 64 NaN 321403.0 HS-grad 9.0 Widowed NaN Other-relative Black Male 0.0 0.0 40.0 United-States <=50K.
16279 38 Private 374983.0 Bachelors 13.0 Married-civ-spouse Prof-specialty Husband White Male 0.0 0.0 50.0 United-States <=50K.
16280 44 Private 83891.0 Bachelors 13.0 Divorced Adm-clerical Own-child Asian-Pac-Islander Male 5455.0 0.0 40.0 United-States <=50K.
16281 35 Self-emp-inc 182148.0 Bachelors 13.0 Married-civ-spouse Exec-managerial Husband White Male 0.0 0.0 60.0 United-States >50K. 
# necessary to remove rows with incorrect labels in test dataset
data_test = data_test[
    (data_test["Target"] == " >50K.") | (data_test["Target"] == " <=50K.")
]

# encode target variable as integer
data_train.loc[data_train["Target"] == " <=50K", "Target"] = 0
data_train.loc[data_train["Target"] == " >50K", "Target"] = 1

data_test.loc[data_test["Target"] == " <=50K.", "Target"] = 0
data_test.loc[data_test["Target"] == " >50K.", "Target"] = 1

Primary data analysis

data_test.describe(include="all").T
count unique top freq mean std min 25% 50% 75% max
Age 16281 73 35 461 NaN NaN NaN NaN NaN NaN NaN
Workclass 15318 8 Private 11210 NaN NaN NaN NaN NaN NaN NaN
fnlwgt 16281.0 NaN NaN NaN 189435.677784 105714.907671 13492.0 116736.0 177831.0 238384.0 1490400.0
Education 16281 16 HS-grad 5283 NaN NaN NaN NaN NaN NaN NaN
Education_Num 16281.0 NaN NaN NaN 10.072907 2.567545 1.0 9.0 10.0 12.0 16.0
Martial_Status 16281 7 Married-civ-spouse 7403 NaN NaN NaN NaN NaN NaN NaN
Occupation 15315 14 Prof-specialty 2032 NaN NaN NaN NaN NaN NaN NaN
Relationship 16281 6 Husband 6523 NaN NaN NaN NaN NaN NaN NaN
Race 16281 5 White 13946 NaN NaN NaN NaN NaN NaN NaN
Sex 16281 2 Male 10860 NaN NaN NaN NaN NaN NaN NaN
Capital_Gain 16281.0 NaN NaN NaN 1081.905104 7583.935968 0.0 0.0 0.0 0.0 99999.0
Capital_Loss 16281.0 NaN NaN NaN 87.899269 403.105286 0.0 0.0 0.0 0.0 3770.0
Hours_per_week 16281.0 NaN NaN NaN 40.392236 12.479332 1.0 40.0 40.0 45.0 99.0
Country 16007 40 United-States 14662 NaN NaN NaN NaN NaN NaN NaN
Target 16281.0 2.0 0.0 12435.0 NaN NaN NaN NaN NaN NaN NaN 
data_train["Target"].value_counts()

0    24720
1     7841
Name: Target, dtype: int64

fig = plt.figure(figsize=(25, 15))
cols = 5
rows = int(data_train.shape[1] / cols)
for i, column in enumerate(data_train.columns):
    ax = fig.add_subplot(rows, cols, i + 1)
    ax.set_title(column)
    if data_train.dtypes[column] == object:
        data_train[column].value_counts().plot(kind="bar", axes=ax)
    else:
        data_train[column].hist(axes=ax)
        plt.xticks(rotation="vertical")
plt.subplots_adjust(hspace=0.7, wspace=0.2);
../../_images/d42332786e0fcb8b6468c2f14943926414ecc1e517aaccbdc6c822f6eaa140d1.png

Checking data types

data_train.dtypes

Age                int64
Workclass         object
fnlwgt             int64
Education         object
Education_Num      int64
Martial_Status    object
Occupation        object
Relationship      object
Race              object
Sex               object
Capital_Gain       int64
Capital_Loss       int64
Hours_per_week     int64
Country           object
Target            object
dtype: object

data_test.dtypes

Age                object
Workclass          object
fnlwgt            float64
Education          object
Education_Num     float64
Martial_Status     object
Occupation         object
Relationship       object
Race               object
Sex                object
Capital_Gain      float64
Capital_Loss      float64
Hours_per_week    float64
Country            object
Target             object
dtype: object

As we see, in the test data, age is treated as type object. We need to fix this.

data_test["Age"] = data_test["Age"].astype(int)

Also we’ll cast all float features to int type to keep types consistent between our train and test data.

data_test["fnlwgt"] = data_test["fnlwgt"].astype(int)
data_test["Education_Num"] = data_test["Education_Num"].astype(int)
data_test["Capital_Gain"] = data_test["Capital_Gain"].astype(int)
data_test["Capital_Loss"] = data_test["Capital_Loss"].astype(int)
data_test["Hours_per_week"] = data_test["Hours_per_week"].astype(int)

Save targets separately.

y_train = data_train.pop('Target')
y_test = data_test.pop('Target')

Fill in missing data for continuous features with their median values, for categorical features with their mode.

# choose categorical and continuous features from data

categorical_columns = [
    c for c in data_train.columns if data_train[c].dtype.name == "object"
]
numerical_columns = [
    c for c in data_train.columns if data_train[c].dtype.name != "object"
]

print("categorical_columns:", categorical_columns)
print("numerical_columns:", numerical_columns)

categorical_columns: ['Workclass', 'Education', 'Martial_Status', 'Occupation', 'Relationship', 'Race', 'Sex', 'Country']
numerical_columns: ['Age', 'fnlwgt', 'Education_Num', 'Capital_Gain', 'Capital_Loss', 'Hours_per_week']

# we see some missing values
data_train.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 32561 entries, 0 to 32560
Data columns (total 14 columns):
 #   Column          Non-Null Count  Dtype 
---  ------          --------------  ----- 
 0   Age             32561 non-null  int64 
 1   Workclass       30725 non-null  object
 2   fnlwgt          32561 non-null  int64 
 3   Education       32561 non-null  object
 4   Education_Num   32561 non-null  int64 
 5   Martial_Status  32561 non-null  object
 6   Occupation      30718 non-null  object
 7   Relationship    32561 non-null  object
 8   Race            32561 non-null  object
 9   Sex             32561 non-null  object
 10  Capital_Gain    32561 non-null  int64 
 11  Capital_Loss    32561 non-null  int64 
 12  Hours_per_week  32561 non-null  int64 
 13  Country         31978 non-null  object
dtypes: int64(6), object(8)
memory usage: 3.5+ MB

# fill missing data

for c in categorical_columns:
    data_train[c].fillna(data_train[c].mode()[0], inplace=True)
    data_test[c].fillna(data_train[c].mode()[0], inplace=True)

for c in numerical_columns:
    data_train[c].fillna(data_train[c].median(), inplace=True)
    data_test[c].fillna(data_train[c].median(), inplace=True)

# no more missing values
data_train.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 32561 entries, 0 to 32560
Data columns (total 14 columns):
 #   Column          Non-Null Count  Dtype 
---  ------          --------------  ----- 
 0   Age             32561 non-null  int64 
 1   Workclass       32561 non-null  object
 2   fnlwgt          32561 non-null  int64 
 3   Education       32561 non-null  object
 4   Education_Num   32561 non-null  int64 
 5   Martial_Status  32561 non-null  object
 6   Occupation      32561 non-null  object
 7   Relationship    32561 non-null  object
 8   Race            32561 non-null  object
 9   Sex             32561 non-null  object
 10  Capital_Gain    32561 non-null  int64 
 11  Capital_Loss    32561 non-null  int64 
 12  Hours_per_week  32561 non-null  int64 
 13  Country         32561 non-null  object
dtypes: int64(6), object(8)
memory usage: 3.5+ MB

We’ll dummy code some categorical features: Workclass, Education, Martial_Status, Occupation, Relationship, Race, Sex, Country. It can be done via pandas method get_dummies

data_train = pd.concat(
    [data_train[numerical_columns], pd.get_dummies(data_train[categorical_columns])],
    axis=1,
)

data_test = pd.concat(
    [data_test[numerical_columns], pd.get_dummies(data_test[categorical_columns])],
    axis=1,
)

set(data_train.columns) - set(data_test.columns)

{'Country_ Holand-Netherlands'}

data_train.shape, data_test.shape

((32561, 105), (16281, 104))

There is no Holland in the test data. Create new zero-valued feature.

data_test["Country_ Holand-Netherlands"] = 0

set(data_train.columns) - set(data_test.columns)

set()

data_train.head(2)
Age fnlwgt Education_Num Capital_Gain Capital_Loss Hours_per_week Workclass_ Federal-gov Workclass_ Local-gov Workclass_ Never-worked Workclass_ Private ... Country_ Portugal Country_ Puerto-Rico Country_ Scotland Country_ South Country_ Taiwan Country_ Thailand Country_ Trinadad&Tobago Country_ United-States Country_ Vietnam Country_ Yugoslavia
0 39 77516 13 2174 0 40 0 0 0 0 ... 0 0 0 0 0 0 0 1 0 0
1 50 83311 13 0 0 13 0 0 0 0 ... 0 0 0 0 0 0 0 1 0 0

2 rows × 105 columns

data_test.head(2)
Age fnlwgt Education_Num Capital_Gain Capital_Loss Hours_per_week Workclass_ Federal-gov Workclass_ Local-gov Workclass_ Never-worked Workclass_ Private ... Country_ Puerto-Rico Country_ Scotland Country_ South Country_ Taiwan Country_ Thailand Country_ Trinadad&Tobago Country_ United-States Country_ Vietnam Country_ Yugoslavia Country_ Holand-Netherlands
1 25 226802 7 0 0 40 0 0 0 1 ... 0 0 0 0 0 0 1 0 0 0
2 38 89814 9 0 0 50 0 0 0 1 ... 0 0 0 0 0 0 1 0 0 0

2 rows × 105 columns

X_train = data_train
X_test = data_test

3.1 Decision tree without parameter tuning#

Train a decision tree (DecisionTreeClassifier) with a maximum depth of 3, and evaluate the accuracy metric on the test data. Use parameter random_state = 17 for results reproducibility.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit) (read-only in a JupyterBook, pls run jupyter-notebook to edit)
# tree =
# tree.fit

Make a prediction with the trained model on the test data.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
# tree_predictions = tree.predict

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
# accuracy_score

6. What is the test set accuracy of a decision tree with maximum tree depth of 3 and random_state = 17?

3.2 Decision tree with parameter tuning#

Train a decision tree (DecisionTreeClassifier, random_state = 17). Find the optimal maximum depth using 5-fold cross-validation (GridSearchCV).

tree_params = {"max_depth": range(2, 11)}

locally_best_tree = GridSearchCV  # You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

locally_best_tree.fit
# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

<function sklearn.model_selection._search.BaseSearchCV.fit(self, X, y=None, *, groups=None, **fit_params)>

Train a decision tree with maximum depth of 9 (it is the best max_depth in my case), and compute the test set accuracy. Use parameter random_state = 17 for reproducibility.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
# tuned_tree =
# tuned_tree.fit
# tuned_tree_predictions = tuned_tree.predict
# accuracy_score

7. What is the test set accuracy of a decision tree with maximum depth of 9 and random_state = 17?

3.3 (Optional) Random forest without parameter tuning#

Let’s take a sneak peek of upcoming lectures and try to use a random forest for our task. For now, you can imagine a random forest as a bunch of decision trees, trained on slightly different subsets of the training data.

Train a random forest (RandomForestClassifier). Set the number of trees to 100 and use random_state = 17.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)
# rf =
# rf.fit # You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Make predictions for the test data and assess accuracy.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

3.4 (Optional) Random forest with parameter tuning#

Train a random forest (RandomForestClassifier). Tune the maximum depth and maximum number of features for each tree using GridSearchCV.

# forest_params = {'max_depth': range(10, 21),
#                 'max_features': range(5, 105, 20)}

# locally_best_forest = GridSearchCV # You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

# locally_best_forest.fit # You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)

Make predictions for the test data and assess accuracy.

# You code here (read-only in a JupyterBook, pls run jupyter-notebook to edit)