Getting Started¶
Data¶
In this project, we will employ several supervised algorithms of your choice to accurately model individuals' income using data collected from the 1994 U.S. Census. We will then choose the best candidate algorithm from preliminary results and further optimize this algorithm to best model the data. The goal with this implementation is to construct a model that accurately predicts whether an individual makes more than $50,000. This sort of task can arise in a non-profit setting, where organizations survive on donations. Understanding an individual's income can help a non-profit better understand how large of a donation to request, or whether or not they should reach out to begin with. While it can be difficult to determine an individual's general income bracket directly from public sources, we can (as we will see) infer this value from other publically available features.
The dataset for this project originates from the UCI Machine Learning Repository. The datset was donated by Ron Kohavi and Barry Becker, after being published in the article "Scaling Up the Accuracy of Naive-Bayes Classifiers: A Decision-Tree Hybrid". You can find the article by Ron Kohavi online. The data we investigate here consists of small changes to the original dataset, such as removing the 'fnlwgt' feature and records with missing or ill-formatted entries.
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# Import libraries necessary for this project
import numpy as np
import pandas as pd
from time import time
import warnings
warnings.filterwarnings("ignore", category = UserWarning, module = "matplotlib")
from IPython.display import display
import seaborn as sns
import matplotlib.pyplot as pl
import matplotlib.patches as mpatches
%matplotlib inline
################################
### ADD EXTRA LIBRARIES HERE ###
################################
# Import sklearn.preprocessing.StandardScaler
from sklearn.preprocessing import MinMaxScaler
# Import train_test_split
from sklearn.model_selection import train_test_split
# Import metrics
from sklearn.metrics import f1_score, accuracy_score, fbeta_score
from sklearn.metrics import confusion_matrix, make_scorer
# Import the three supervised learning models from sklearn
from sklearn.ensemble import AdaBoostClassifier, GradientBoostingClassifier, RandomForestClassifier
from sklearn.svm import LinearSVC
from sklearn.linear_model import SGDClassifier
# Import the model selector
from sklearn import grid_search
from sklearn.model_selection import GridSearchCV
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# https://github.com/udacity/machine-learning/blob/master/projects/finding_donors/visuals.py
pl.style.use('seaborn-whitegrid')
def distribution(data, transformed = False):
"""
Visualization code for displaying skewed distributions of features
"""
# Create figure
fig = pl.figure(figsize = (18, 6));
# Skewed feature plotting
for i, feature in enumerate(['capital-gain','capital-loss']):
ax = fig.add_subplot(1, 2, i+1)
ax.hist(data[feature], bins = 25, color = '#00A0A0')
ax.set_title("'%s' Feature Distribution"%(feature), fontsize = 14)
ax.set_xlabel("Value")
ax.set_ylabel("Number of Records")
ax.set_ylim((0, 2000))
ax.set_yticks([0, 500, 1000, 1500, 2000])
ax.set_yticklabels([0, 500, 1000, 1500, ">2000"])
# Plot aesthetics
if transformed:
fig.suptitle("Log-transformed Distributions of Continuous Census Data Features", \
fontsize = 16, y = 1.03)
else:
fig.suptitle("Skewed Distributions of Continuous Census Data Features", \
fontsize = 16, y = 1.03)
fig.tight_layout()
fig.show()
def evaluate(results, accuracy, f1):
"""
Visualization code to display results of various learners.
inputs:
- learners: a list of supervised learners
- stats: a list of dictionaries of the statistic results from 'train_predict()'
- accuracy: The score for the naive predictor
- f1: The score for the naive predictor
"""
# Create figure
fig, ax = pl.subplots(2, 3, figsize = (18, 9))
# Constants
bar_width = 0.3
colors = ['#A00000','#00A0A0','#00A000']
# Super loop to plot four panels of data
for k, learner in enumerate(results.keys()):
for j, metric in enumerate(['train_time', 'acc_train', 'f_train', 'pred_time', 'acc_test', 'f_test']):
for i in np.arange(3):
# Creative plot code
ax[int(j/3), j%3].bar(i+k*bar_width, results[learner][i][metric],
width = bar_width, color = colors[k])
ax[int(j/3), j%3].set_xticks([0.45, 1.45, 2.45])
ax[int(j/3), j%3].set_xticklabels(["1%", "10%", "100%"])
ax[int(j/3), j%3].set_xlabel("Training Set Size")
ax[int(j/3), j%3].set_xlim((-0.1, 3.0))
# Add unique y-labels
ax[0, 0].set_ylabel("Time (in seconds)")
ax[0, 1].set_ylabel("Accuracy Score")
ax[0, 2].set_ylabel("F-score")
ax[1, 0].set_ylabel("Time (in seconds)")
ax[1, 1].set_ylabel("Accuracy Score")
ax[1, 2].set_ylabel("F-score")
# Add titles
ax[0, 0].set_title("Model Training")
ax[0, 1].set_title("Accuracy Score on Training Subset")
ax[0, 2].set_title("F-score on Training Subset")
ax[1, 0].set_title("Model Predicting")
ax[1, 1].set_title("Accuracy Score on Testing Set")
ax[1, 2].set_title("F-score on Testing Set")
# Add horizontal lines for naive predictors
ax[0, 1].axhline(y = accuracy, xmin = -0.1, xmax = 3.0, linewidth = 1, color = 'k', linestyle = 'dashed')
ax[1, 1].axhline(y = accuracy, xmin = -0.1, xmax = 3.0, linewidth = 1, color = 'k', linestyle = 'dashed')
ax[0, 2].axhline(y = f1, xmin = -0.1, xmax = 3.0, linewidth = 1, color = 'k', linestyle = 'dashed')
ax[1, 2].axhline(y = f1, xmin = -0.1, xmax = 3.0, linewidth = 1, color = 'k', linestyle = 'dashed')
# Set y-limits for score panels
ax[0, 1].set_ylim((0, 1))
ax[0, 2].set_ylim((0, 1))
ax[1, 1].set_ylim((0, 1))
ax[1, 2].set_ylim((0, 1))
# Create patches for the legend
patches = []
for i, learner in enumerate(results.keys()):
patches.append(mpatches.Patch(color = colors[i], label = learner))
pl.legend(handles = patches, bbox_to_anchor = (-0.8, 2.53), \
loc = 'upper center', borderaxespad = 0., ncol = 3, fontsize = 'x-large')
# Aesthetics
pl.suptitle("Performance Metrics for Three Supervised Learning Models", fontsize = 16, y = 1.15)
pl.tight_layout()
pl.show()
def feature_plot(importances, X_train, y_train):
# Display the five most important features
indices = np.argsort(importances)[::-1]
columns = X_train.columns.values[indices[:5]]
values = importances[indices][:5]
# Creat the plot
fig = pl.figure(figsize = (18, 8))
pl.title("Normalized Weights for First Five Most Predictive Features", fontsize = 16)
pl.bar(np.arange(5), values, width = 0.6, align="center", color = '#00A000', \
label = "Feature Weight")
pl.bar(np.arange(5) - 0.3, np.cumsum(values), width = 0.2, align = "center", color = '#00A0A0', \
label = "Cumulative Feature Weight")
pl.xticks(np.arange(5), columns)
pl.xlim((-0.5, 4.5))
pl.ylabel("Weight", fontsize = 12)
pl.xlabel("Feature", fontsize = 12)
pl.legend(loc = 'upper center')
pl.tight_layout()
pl.show()
Exploring the Data¶
Let's load the census data. Note that the last column from this dataset, 'income', will be our target label (whether an individual makes more than, or at most, $50,000 annually). All other columns are features about each individual in the census database.
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# Load the Census dataset
data = pd.read_csv("census.csv")
# Success - Display the first record
display(data.head(7).T)
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data.describe()
Implementation: Data Exploration¶
A cursory investigation of the dataset will determine how many individuals fit into either group, and will tell us about the percentage of these individuals making more than 50,000 USD. We need to compute the following:
- The total number of records,
'n_records'. - The number of individuals making more than 50,000 USD annually,
'n_greater_50k'. - The number of individuals making at most 50,000 USD annually,
'n_at_most_50k'. - The percentage of individuals making more than 50,000 USD annually,
'greater_percent'.
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# Total number of records
n_records = len(data)
# Number of records where individual's income is more than $50,000
n_greater_50k = len(data[data['income'] == '>50K'])
# Number of records where individual's income is at most $50,000
n_at_most_50k = len(data[data['income'] == '<=50K'])
# Percentage of individuals whose income is more than $50,000
greater_percent = n_greater_50k * 100.0 / n_records
# Print the results
print ("Total number of records: {}".format(n_records))
print ("Individuals making more than $50,000: {}".format(n_greater_50k))
print ("Individuals making at most $50,000: {}".format(n_at_most_50k))
print ("Percentage of individuals making more than $50,000: {:.2f}%".format(greater_percent))
Features' Description¶
- age: continuous.
- workclass: Private, Self-emp-not-inc, Self-emp-inc, Federal-gov, Local-gov, State-gov, Without-pay, Never-worked.
- education: Bachelors, Some-college, 11th, HS-grad, Prof-school, Assoc-acdm, Assoc-voc, 9th, 7th-8th, 12th, Masters, 1st-4th, 10th, Doctorate, 5th-6th, Preschool.
- education-num: continuous.
- marital-status: Married-civ-spouse, Divorced, Never-married, Separated, Widowed, Married-spouse-absent, Married-AF-spouse.
- occupation: Tech-support, Craft-repair, Other-service, Sales, Exec-managerial, Prof-specialty, Handlers-cleaners, Machine-op-inspct, Adm-clerical, Farming-fishing, Transport-moving, Priv-house-serv, Protective-serv, Armed-Forces.
- relationship: Wife, Own-child, Husband, Not-in-family, Other-relative, Unmarried.
- race: Black, White, Asian-Pac-Islander, Amer-Indian-Eskimo, Other.
- sex: Female, Male.
- capital-gain: continuous.
- capital-loss: continuous.
- hours-per-week: continuous.
- native-country: United-States, Cambodia, England, Puerto-Rico, Canada, Germany, Outlying-US(Guam-USVI-etc), India, Japan, Greece, South, China, Cuba, Iran, Honduras, Philippines, Italy, Poland, Jamaica, Vietnam, Mexico, Portugal, Ireland, France, Dominican-Republic, Laos, Ecuador, Taiwan, Haiti, Columbia, Hungary, Guatemala, Nicaragua, Scotland, Thailand, Yugoslavia, El-Salvador, Trinadad&Tobago, Peru, Hong, Holand-Netherlands.
Preparing the Data¶
Before data can be used as input for machine learning algorithms, it often must be cleaned, formatted, and restructured — this is typically known as preprocessing. Fortunately, for this dataset, there are no invalid or missing entries we must deal with, however, there are some qualities about certain features that must be adjusted. This preprocessing can help tremendously with the outcome and predictive power of nearly all learning algorithms.
Transforming Skewed Continuous Features¶
A dataset may sometimes contain at least one feature whose values tend to lie near a single number, but will also have a non-trivial number of vastly larger or smaller values than that single number. Algorithms can be sensitive to such distributions of values and can underperform if the range is not properly normalized. With the census dataset two features fit this description: 'capital-gain' and 'capital-loss'.
Let's plot a histogram of these two features and have a look on the range of the values present and how they are distributed.
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# Split the data into features and target label
income_raw = data['income']
features_raw = data.drop('income', axis = 1)
# Visualize skewed continuous features of original data
distribution(data)
For highly-skewed feature distributions such as 'capital-gain' and 'capital-loss', it is common practice to apply a logarithmic transformation on the data so that the very large and very small values do not negatively affect the performance of a learning algorithm. Using a logarithmic transformation significantly reduces the range of values caused by outliers. Care must be taken when applying this transformation, however: the logarithm of 0 is undefined, so we must translate the values by a small amount above 0 to apply the logarithm successfully.
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# Log-transform the skewed features
skewed = ['capital-gain', 'capital-loss']
features_raw[skewed] = data[skewed].apply(lambda x: np.log(x + 1))
# Visualize the new log distributions
distribution(features_raw, transformed = True)
Normalizing Numerical Features¶
In addition to performing transformations on features that are highly skewed, it is often good practice to perform some type of scaling on numerical features. Applying a scaling to the data does not change the shape of each feature's distribution (such as 'capital-gain' or 'capital-loss' above); however, normalization ensures that each feature is treated equally when applying supervised learners. Note that once scaling is applied, observing the data in its raw form will no longer have the same original meaning.
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# Initialize a scaler, then apply it to the features
scaler = MinMaxScaler()
numerical = ['age', 'education-num', 'capital-gain', 'capital-loss', 'hours-per-week']
features_raw[numerical] = scaler.fit_transform(data[numerical])
# Show an example of a record with scaling applied
display(features_raw.head(n = 7).T)
Implementation: Data Preprocessing¶
From the table in Exploring the Data above, we can see there are several features for each record that are non-numeric. Typically, learning algorithms expect input to be numeric, which requires that non-numeric features (called categorical variables) be converted. One popular way to convert categorical variables is by using the one-hot encoding scheme. One-hot encoding creates a "dummy" variable for each possible category of each non-numeric feature. For example, assume someFeature has three possible entries: A, B, or C. We then encode this feature into someFeature_A, someFeature_B and someFeature_C.
| someFeature | someFeature_A | someFeature_B | someFeature_C | ||
|---|---|---|---|---|---|
| 0 | B | 0 | 1 | 0 | |
| 1 | C | ----> one-hot encode ----> | 0 | 0 | 1 |
| 2 | A | 1 | 0 | 0 |
Additionally, as with the non-numeric features, we need to convert the non-numeric target label, 'income' to numerical values for the learning algorithm to work. Since there are only two possible categories for this label ("<=50K" and ">50K"), we can avoid using one-hot encoding and simply encode these two categories as 0 and 1, respectively.
In code cell below, we will need to implement the following:
- Use
pandas.get_dummies()to perform one-hot encoding on the'features_raw'data. - Convert the target label
'income_raw'to numerical entries.- Set records with "<=50K" to
0and records with ">50K" to1.
- Set records with "<=50K" to
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# One-hot encode the 'features_raw' data using pandas.get_dummies()
categorical = ['workclass', 'education_level', 'marital-status', 'occupation',
'relationship', 'race', 'sex', 'native-country']
features = pd.DataFrame(features_raw)
for element in categorical:
features[element] = pd.get_dummies(features_raw[element])
# Encode the 'income_raw' data to numerical values
income = income_raw.replace(['<=50K', '>50K'], [0,1])
# Print the number of features after one-hot encoding
encoded = list(features[categorical].columns)
print ("{} total features after one-hot encoding.".format(len(encoded)))
# Uncomment the following line to see the encoded feature names
print (encoded)
Shuffle and Split Data¶
Now all categorical variables have been converted into numerical features, and all numerical features have been normalized. As always, we will now split the data (both features and their labels) into training and test sets. 80% of the data will be used for training and 20% for testing.
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# Split the 'features' and 'income' data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(features, income, test_size = 0.2, random_state = 0)
# Show the results of the split
print ("Training set has {} samples.".format(X_train.shape[0]))
print ("Testing set has {} samples.".format(X_test.shape[0]))
Evaluating Model Performance¶
In this section, we will investigate four different algorithms, and determine which is best at modeling the data. Three of these algorithms will be supervised learners of your choice, and the fourth algorithm is known as a naive predictor.
Metrics and the Naive Predictor¶
CharityML, equipped with their research, knows individuals that make more than 50,000 USD are most likely to donate to their charity. Because of this, CharityML is particularly interested in predicting who makes more than 50,000 USD accurately. It would seem that using accuracy as a metric for evaluating a particular model's performace would be appropriate. Additionally, identifying someone that does not make more than 50,000 USD as someone who does would be detrimental to CharityML, since they are looking to find individuals willing to donate. Therefore, a model's ability to precisely predict those that make more than 50,000 USD is more important than the model's ability to recall those individuals. We can use F-beta score as a metric that considers both precision and recall:
$$ \color{#00A0A0} {F_{\beta} = (1 + \beta^2) \cdot \frac{precision \cdot recall}{\left( \beta^2 \cdot precision \right) + recall}} $$In particular, when $\boldsymbol {\beta = 0.5}$, more emphasis is placed on precision. This is called the F$_{0.5}$ score (or F-score for simplicity).
Looking at the distribution of classes (those who make at most 50,000 USD, and those who make more), it's clear most individuals do not make more than 50,000 USD. This can greatly affect accuracy, since we could simply say "this person does not make more than 50,000 USD" and generally be right, without ever looking at the data! Making such a statement would be called naive, since we have not considered any information to substantiate the claim. It is always important to consider the naive prediction for your data, to help establish a benchmark for whether a model is performing well. That been said, using that prediction would be pointless: If we predicted all people made less than 50,000 USD, CharityML would identify no one as donors.
$Note: \ Recap \ of \ accuracy, \ precision, \ recall$¶
Accuracy measures how often the classifier makes the correct prediction. It’s the ratio of the number of correct predictions to the total number of predictions (the number of test data points).
$accuracy = \dfrac{ number \ of \ correct\ predictions }{ total\ number \ of \ predictions}$¶
Precision tells us what proportion of data points we classified as individuals making more than 50,000 USD, actually made more than 50,000 USD. It is a ratio of true positives to all positives (all points classified as individuals making more than 50,000 USD, irrespective of whether that was the correct classification), in other words it is the ratio of
$precision = \dfrac{ true \ positives } { true \ positives \ + \ false \ positives }$¶
Recall (sensitivity) tells us what proportion of individuals that actually made more than 50,000 USD were classified by us as individuals making more than 50,000 USD. It is a ratio of true positives to all individuals that actually made more than 50,000 USD, in other words it is the ratio of
$recall = \dfrac{ true \ positives } { true \ positives \ + \ false \ negatives }$¶
For classification problems that are skewed in their classification distributions like in our case, accuracy by itself is not a very good metric. Precision and recall help a lot and can be combined to get the F1 score, which is the weighted average (harmonic mean) of the precision and recall scores. This score can range from 0 to 1, with 1 being the best possible F1 score (we take the harmonic mean as we are dealing with ratios).
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'''
TP = np.sum(income) # Counting the ones as this is the naive case. Note that 'income' is the 'income_raw' data
encoded to numerical values done in the data preprocessing step.
FP = income.count() - TP # Specific to the naive case
TN = 0 # No predicted negatives in the naive case
FN = 0 # No predicted negatives in the naive case
'''
# TODO: Calculate accuracy, precision and recall
accuracy = accuracy_score(income, np.array([1]*len(income)))
recall = 1 # == np.sum(income) /(np.sum(income)+0)
precision = np.sum(income)/len(income)
beta = 0.5
# TODO: Calculate F-score using the formula above for beta = 0.5 and correct values for precision and recall.
fscore = (1 + beta**2) * (precision * recall) / ((beta**2 * precision) + recall)
# Alternative method
# fscore = fbeta_score(income, np.array([1]*len(income)), beta=0.5)
# Print the results
print ("Naive Predictor: [Accuracy score: {:.4f}, F-score: {:.4f}]".format(accuracy, fscore))
Supervised Learning Models¶
The following supervised learning models are currently available in scikit-learn that you may choose from:
- Gaussian Naive Bayes (GaussianNB)
- Decision Trees
- Ensemble Methods (Bagging, AdaBoost, Random Forest, Gradient Boosting)
- K-Nearest Neighbors (KNeighbors)
- Stochastic Gradient Descent Classifier (SGDC)
- Support Vector Machines (SVM)
- Logistic Regression
Question 2 - Model Application¶
List three of the supervised learning models above that are appropriate for this problem that you will test on the census data. For each model chosen
- Describe one real-world application in industry where the model can be applied. (You may need to do research for this — give references!)
- What are the strengths of the model; when does it perform well?
- What are the weaknesses of the model; when does it perform poorly?
- What makes this model a good candidate for the problem, given what you know about the data?
Answer 2¶
I have chosen the following models: GradientBoostingClassifier(); RandomForestClassifier(); AdaBoostClassifier(). All of them are ensemble methods and combine the predictions of several base estimators to improve generalizability / robustness over a single estimator.
Useful Links:
- A Gentle Introduction to the Gradient Boosting Algorithm for Machine Learning
- Gradient Boosting Method and Random Forest - Mark Landry
- Data Mining: Ensemble Learning
Let's have a look at their applications and characteristics:
1) GradientBoostingClassifier.
- Applications: in the field of learning to rank (for example, web-seach), in ecology, etc.
- The advantages and the disadvantages
(Gradient Tree Boosting):- Strengths: natural handling of data of mixed type (= heterogeneous features), predictive power, robustness to outliers in output space (via robust loss functions).
- Weaknesses: scalability, due to the sequential nature of boosting it can hardly be parallelized.
2) RandomForestClassifier.
- Applications: in ecology, bioinformatics, etc.
- The advantages and the disadvantages
(Random Forests)- Strengths: runs efficiently on large data bases; gives estimates of what variables are important in the classification; maintains accuracy when a large proportion of the data are missing; high prediction accuracy.
- Weaknesses: difficult to interpret, can be slow to evaluate.
3) AdaBoostClassifier.
- Applications: the problem of face detection, text classification, etc.
- The advantages and the disadvantages
(The AdaBoost algorithm)- Strengths: can be used with data that is textual, numeric, discrete, etc.; can be combined with any other learning algorithm, not prone to overfitting; simple to implement.
- Weaknesses: can be sensitive to noisy data and outliers; the performance depends on data and weak learner (can fail if weak classifiers too complex).
The outputs in our case are the variant of social ranking and it's a well-known fact that ensemble classifiers tend to be a better choice for this ranking.
All these algorithms will produce enough good predictions because of some reasons:
- they usually demonstrate a high performance in practical tasks;
- they not so prone to overfitting;
- they work well with mixed types of features (categorical and numeric).
Implementation: Creating a Training and Predicting Pipeline¶
To properly evaluate the performance of each model we've chosen, it's important that we create a training and predicting pipeline that allows us to quickly and effectively train models using various sizes of training data and perform predictions on the testing data. The implementation here will be used in the following section.
We will do the following points:
- Import
fbeta_scoreandaccuracy_scorefromsklearn.metrics. - Fit the learner to the sampled training data and record the training time.
- Perform predictions on the test data
X_test, and also on the first 300 training pointsX_train[:300].- Record the total prediction time.
- Calculate the accuracy score for both the training subset and testing set.
- Calculate the F-score for both the training subset and testing set.
- Make sure that you set the
betaparameter!
- Make sure that you set the
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# Import two metrics from sklearn - fbeta_score and accuracy_score
def train_predict(learner, sample_size, X_train, y_train, X_test, y_test):
'''
inputs:
- learner: the learning algorithm to be trained and predicted on
- sample_size: the size of samples (number) to be drawn from training set
- X_train: features training set
- y_train: income training set
- X_test: features testing set
- y_test: income testing set
'''
results = {}
# Fit the learner to the training data using slicing with 'sample_size'
start = time() # Get start time
learner = learner
learner.fit(X_train[:sample_size], y_train[:sample_size])
end = time() # Get end time
# Calculate the training time
results['train_time'] = end - start
# Get the predictions on the test set,
# then get predictions on the first 300 training samples
start = time() # Get start time
predictions_test = learner.predict(X_test)
predictions_train = learner.predict(X_train[:300])
end = time() # Get end time
# Calculate the total prediction time
results['pred_time'] = end - start
# Compute accuracy on the first 300 training samples
results['acc_train'] = accuracy_score(y_train[:300], predictions_train)
# Compute accuracy on test set
results['acc_test'] = accuracy_score(y_test, predictions_test)
# Compute F-score on the the first 300 training samples
results['f_train'] = fbeta_score(y_train[:300], predictions_train, average='macro', beta=0.5)
# Compute F-score on the test set
results['f_test'] = fbeta_score(y_test, predictions_test, average='macro', beta=0.5)
# Success
print ("{} trained on {} samples.".format(learner.__class__.__name__, sample_size))
# Return the results
return results
Implementation: Initial Model Evaluation¶
Next steps are the following:
- Import the three supervised learning models you've discussed in the previous section.
Initialize the three models and store them in
'clf_A','clf_B', and'clf_C'.- Use a
'random_state'for each model you use, if provided. - Note: Use the default settings for each model — you will tune one specific model in a later section.
- Use a
Calculate the number of records equal to 1%, 10%, and 100% of the training data.
- Store those values in
'samples_1','samples_10', and'samples_100'respectively.
- Store those values in
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# Import the three supervised learning models from sklearn
# Initialize the three models
clf_A = GradientBoostingClassifier(random_state=10)
clf_B = RandomForestClassifier()
clf_C = AdaBoostClassifier()
# Calculate the number of samples for 1%, 10%, and 100% of the training data
samples_1 = int(len(X_train)/100)
samples_10 = int(len(X_train)/10)
samples_100 = len(X_train)
# Collect results on the learners
results = {}
for clf in [clf_A, clf_B, clf_C]:
clf_name = clf.__class__.__name__
results[clf_name] = {}
for i, samples in enumerate([samples_1, samples_10, samples_100]):
results[clf_name][i] = \
train_predict(clf, samples, X_train, y_train, X_test, y_test)
# Run metrics visualization for the three supervised learning models chosen
evaluate(results, accuracy, fscore)
Improving Results¶
In this final section, we will choose from the three supervised learning models the best model to use on the student data. We will then perform a grid search optimization for the model over the entire training set (X_train and y_train) by tuning at least one parameter to improve upon the untuned model's F-score.
Question 3 - Choosing the Best Model¶
Based on the evaluation you performed earlier, in one to two paragraphs, explain to CharityML which of the three models you believe to be most appropriate for the task of identifying individuals that make more than 50,000 USD.
Answer 3¶
I think that for this case, we need to choose the GradientBoostingClassifier algorithm as it showed the highest accuracy and F-score for the testing set and escaped overfitting. The algorithm is proved to be very time-consuming in the training process, but it can be ignored since the amount of data is not very big.
The confusion matrix can be used to evaluate the quality of the output for the chosen classifier.
hide_code
# Compute confusion matrix for a model
model = clf_A
cm = confusion_matrix(y_test.values, model.predict(X_test))
sns.heatmap(cm, annot=True, cmap='BuGn',
xticklabels=['no', 'yes'], yticklabels=['no', 'yes'])
pl.ylabel('True label')
pl.xlabel('Predicted label')
pl.title('Confusion matrix for:\n{}'.format(model.__class__.__name__));
Question 4 - Describing the Model in Layman's Terms¶
In one to two paragraphs, explain to CharityML, in layman's terms, how the final model chosen is supposed to work. Be sure that you are describing the major qualities of the model, such as how the model is trained and how the model makes a prediction. Avoid using advanced mathematical or technical jargon, such as describing equations or discussing the algorithm implementation.
Answer 4¶
Let's describe the mechanism of the model with three important component: the measurement for checking how well our model predicts the outputs based on input values, the algorithm from the certain group (for examples, decision trees) for making predictions, the additive mechanism for algorithms for minimizing the measure function.
At first, we set up the most important component (a measurement) that maps every event onto a real number intuitively representing some "cost" associated with this event. The goal of estimation for supervised learning is to find the measure function that models all inputs (events) well: if it were applied to the training set, it should predict the output values enough well. Then we check the model effectiveness applied it to the testing set. The measurement quantifies the amount by which the predictions deviate from the actual output values. Naturally, our task is to reach the minimum "cost".
At each particular Gradient Boosting iteration, a new algorithm (in practice, it is almost always from a tree-based group) is trained with respect to the error that was learned so far. This procedure has the following steps:
- add one algorithm that can reduce the loss based on the current estimates (existing algorithms in the model are not changed);
- use an effective procedure called gradient descent to minimize the loss:
- fit a new model to the data;
- choose the directions for changing the measure function by finding the negative moving rates of this function, it helps to get a lower cost on the next iteration;
- find the best step-size in the chosen directions, the step magnitude is multiplied by a factor between 0 and 1 called a learning rate;
- update the measure function;
- repeat till the fixed number of algorithms are added or the loss reaches an acceptable level or the loss no longer improves on an external validation dataset.
The result of the model training should be that predictions slowly converge toward observed values.
The model for the CharityML is trained to produce the best predictions for the 'income' categorical variable, and the loss function evaluates how these predictions deviate from the actual values.
Implementation: Model Tuning¶
We will tune the chosen model and use grid search (GridSearchCV) with at least one important parameter tuned with at least 3 different values. We will need to use the entire training set for this.
Our steps:
- Import
sklearn.grid_search.GridSearchCVandsklearn.metrics.make_scorer. - Initialize the classifier you've chosen and store it in
clf.- Set a
random_stateif one is available to the same state you set before.
- Set a
- Create a dictionary of parameters you wish to tune for the chosen model.
- Example:
parameters = {'parameter' : [list of values]}. - Note: Avoid tuning the
max_featuresparameter of your learner if that parameter is available!
- Example:
- Use
make_scorerto create anfbeta_scorescoring object (with $\beta = 0.5$). - Perform grid search on the classifier
clfusing the'scorer', and store it ingrid_obj. - Fit the grid search object to the training data (
X_train,y_train), and store it ingrid_fit.
hide_code
# Import 'GridSearchCV', 'make_scorer', and any other necessary libraries
# Initialize the classifier
clf = GradientBoostingClassifier(random_state=10)
# Create the parameters list you wish to tune
parameters = {'n_estimators': [104, 208, 416],
'learning_rate':[0.1, 0.2, 0.3],
'max_depth': [2, 3, 4]}
# Make an fbeta_score scoring object
scorer = make_scorer(fbeta_score, beta=0.5)
# Perform grid search on the classifier using 'scorer' as the scoring method
grid_obj = GridSearchCV(estimator=clf, param_grid=parameters, scoring=scorer)
# Fit the grid search object to the training data and find the optimal parameters
grid_fit = grid_obj.fit(X_train, y_train)
# Get the estimator
best_clf = grid_fit.best_estimator_
# Make predictions using the unoptimized and model
predictions = (clf.fit(X_train, y_train)).predict(X_test)
best_predictions = best_clf.predict(X_test)
# Report the before-and-afterscores
print ("Unoptimized model\n------")
print ("Accuracy score on testing data: {:.4f}".format(accuracy_score(y_test, predictions)))
print ("F-score on testing data: {:.4f}".format(fbeta_score(y_test, predictions, beta = 0.5)))
print ("\nOptimized Model\n------")
print ("Final accuracy score on the testing data: {:.4f}".format(accuracy_score(y_test, best_predictions)))
print ("Final F-score on the testing data: {:.4f}".format(fbeta_score(y_test, best_predictions, beta = 0.5)))
print ("\nOptimized Model Parameters\n------")
print (best_clf.get_params())
Question 5 - Final Model Evaluation¶
What is your optimized model's accuracy and F-score on the testing data? Are these scores better or worse than the unoptimized model? How do the results from your optimized model compare to the naive predictor benchmarks you found earlier in Question 1?
Results:¶
| Metric | Benchmark Predictor | Unoptimized Model | Optimized Model |
|---|---|---|---|
| Accuracy Score | 0.2478 | 0.8541 | 0.8570 |
| F-score | 0.2917 | 0.7235 | 0.7312 |
Answer 5¶
Final accuracy score and F-score on the testing data are 0.8570 and 0.7312 respectively. These indicators are better than for the non-optimized model and they are 4-5 times greater than the initial prediction indicators for the naive predictor benchmarks.
Feature Importance¶
An important task when performing supervised learning on a dataset like the census data we study here is determining which features provide the most predictive power. By focusing on the relationship between only a few crucial features and the target label we simplify our understanding of the phenomenon, which is most always a useful thing to do. In the case of this project, that means we wish to identify a small number of features that most strongly predict whether an individual makes at most or more than 50,000 USD.
We will choose a scikit-learn classifier (e.g., adaboost, random forests) that has a feature_importance_ attribute, which is a function that ranks the importance of features according to the chosen classifier, in the next python cell fit this classifier to training set and use this attribute to determine the top 5 most important features for the census dataset.
Question 6 - Feature Relevance Observation¶
When Exploring the Data, it was shown there are thirteen available features for each individual on record in the census data.
Of these thirteen records, which five features do you believe to be most important for prediction, and in what order would you rank them and why?
Answer 6¶
For me, the variables “age”, “education-num”, “occupation”, “relationship”, “hours-per-week” look like the most influential. Of course, it is expected to receive a higher pay if the person has studied longer, has a high paying occupation, is older and more experienced, has a longtime relationship and works more hours per week.
I would rank them in the following order:
1) education-num; 2) age; 3) hours-per-week; 4) occupation; 5) relationship.
Implementation: Extracting Feature Importance¶
We will choose a scikit-learn supervised learning algorithm that has a feature_importance_ attribute availble for it. This attribute is a function that ranks the importance of each feature when making predictions based on the chosen algorithm.
We will need to implement the following:
- Import a supervised learning model from sklearn if it is different from the three used earlier.
- Train the supervised model on the entire training set.
- Extract the feature importances using
'.feature_importances_'.
hide_code
# Import a supervised learning model that has 'feature_importances_'
# Train the supervised model on the training set
model = GradientBoostingClassifier(n_estimators=208, learning_rate=0.3, \
max_depth=2, random_state=10).fit(X_train, y_train)
# Extract the feature importances
importances = model.feature_importances_
# Plot
feature_plot(importances, X_train, y_train)
Question 7 - Extracting Feature Importance¶
Observe the visualization created above which displays the five most relevant features for predicting if an individual makes at most or above 50,000 USD.
How do these five features compare to the five features you discussed in Question 6? If you were close to the same answer, how does this visualization confirm your thoughts? If you were not close, why do you think these features are more relevant?
Answer 7¶
This visualization confirms my thoughts about the most influential features but, in many cases, does not confirm the order which I predicted and include the features capital-gain and capital-loss. I think it happens because the age in practice has more meaning than I expected. And the capital gain and capital loss variables show a high correlation to income levels so these variables can be used for prediction.
Feature Selection¶
How does a model perform if we only use a subset of all the available features in the data? With less features required to train, the expectation is that training and prediction time is much lower — at the cost of performance metrics. From the visualization above, we see that the top five most important features contribute more than half of the importance of all features present in the data. This hints that we can attempt to reduce the feature space and simplify the information required for the model to learn.
The code cell below will use the same optimized model we found earlier, and train it on the same training set with only the top five important features.
hide_code
# Import functionality for cloning a model
from sklearn.base import clone
# Reduce the feature space
X_train_reduced = X_train[X_train.columns.values[(np.argsort(importances)[::-1])[:5]]]
X_test_reduced = X_test[X_test.columns.values[(np.argsort(importances)[::-1])[:5]]]
# Train on the "best" model found from grid search earlier
clf = (clone(best_clf)).fit(X_train_reduced, y_train)
# Make new predictions
reduced_predictions = clf.predict(X_test_reduced)
# Report scores from the final model using both versions of data
print ("Final Model trained on full data\n------")
print ("Accuracy on testing data: {:.4f}".format(accuracy_score(y_test, best_predictions)))
print ("F-score on testing data: {:.4f}".format(fbeta_score(y_test, best_predictions, beta = 0.5)))
print ("\nFinal Model trained on reduced data\n------")
print ("Accuracy on testing data: {:.4f}".format(accuracy_score(y_test, reduced_predictions)))
print ("F-score on testing data: {:.4f}".format(fbeta_score(y_test, reduced_predictions, beta = 0.5)))
Question 8 - Effects of Feature Selection¶
How does the final model's F-score and accuracy score on the reduced data using only five features compare to those same scores when all features are used?
If training time was a factor, would you consider using the reduced data as your training set?
Answer 8¶
The final model's F-score and accuracy score on the reduced data does not decrease a lot. It becomes (0.6969, 0.8418) instead of (0.7312, 0.8570). It means we can confirm the use of the reduced data with a high level of confidence if training time is an important factor.
Conclusion¶
In this project, models of classifiers and their application to predict categorical variables were discussed in detail. We studied the methods of data preparing and model optimizing as well.