In this project, I employed several supervised machine learning algorithms to model individuals' income using U.S. census data from 1994.
Our client, a non-profit, wanted to accurately predict whether certain individuals made more than $50,000 to be able to solicit them for donations to support their cause.
This cut-off at $50K as very important for them because this will influence the effectiveness and efficiency of their fundraising goals.
Our model will help them determine those who make more than $50,000 and this in turn will help the non-profit reach out to them.
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. However, the data we investigate here consists of small changes to the original dataset, such as removing records with missing or ill-formatted entries.
NOTE This project is the project that I submitted through the udacity course on Data Science This post has been modified for my own personal learning purposes, and it includes certain passages from the original document due to clarity of explanations.
Exploring the Data¶
- Load necesary Python Libraries
- Load Data
- Column
'income'is our target label - All other columns are features
# Import libraries necessary for this project
import numpy as np
import pandas as pd
from time import time
from IPython.display import display # Allows the use of display() for DataFrames
# Import supplementary visualization code visuals.py
import visuals as vs
# Pretty display for notebooks
%matplotlib inline
# Load the Census dataset
data = pd.read_csv("census.csv")
# Success - Display the first record
display(data.head(n=5))
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.
# Total number of records
n_records = len(data['income'])
n_records1 = data['income'].value_counts()
# Number of records where individual's income is more than $50,000
n_greater_50k = n_records1[1]
# Number of records where individual's income is at most $50,000
n_at_most_50k = n_records1[0]
# Percentage of individuals whose income is more than $50,000
greater_percent = (n_records1[1].sum()/n_records1.sum())*100
# 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: {}%".format(greater_percent))
Feature set Exploration ¶
- 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 : Prepocessing¶
Data Cleaning, Reformatting and Restricting is sometimes necessary to be able to employ our machine learning algorithms. Luckily, this data is clean and has no missing values. However, there are some qualities that must be adjusted such as highly skewed values.
Transforming Skewed Continuous Features¶
Algorithms can be sensitive to skewed distributions of values and can underperform if the range is not properly normalized. Here, we have two features that must be normalized: 'capital-gain' and 'capital-loss'.
The code cell below plots a histogram of these two features. Note the range of the values and how they are distributed.
# 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
vs.distribution(data)
For highly-skewed feature distributions such as we see above, 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.
This is usually a good idea because using a logarithmic transformation significantly reduces the range of values caused by outliers. However, We must be taken when applying this transformation because the logarithm of 0 is undefined, so we must translate the values by a small amount above 0 to apply the the logarithm successfully.
The code cell below performs a transformation on the data and visualizes the results. Again, note the range of values and how they are distributed.
# Log-transform the skewed features
skewed = ['capital-gain', 'capital-loss']
features_log_transformed = pd.DataFrame(data = features_raw)
features_log_transformed[skewed] = features_raw[skewed].apply(lambda x: np.log(x + 1))
# Visualize the new log distributions
vs.distribution(features_log_transformed, transformed = True)
Normalizing Numerical Features¶
Just like we transformed our highly skewed features, we also want to scale our numerical features. Note that this scaling does not cage the shape of any feature's distribution like above. But, normalization makes sure that our features are treated equally when applying our supervised learner algorithms. Note that when we normalize the data, we would not be able to read it in its raw form anymore, this data will have new meaning.
# Import sklearn.preprocessing.StandardScaler
from sklearn.preprocessing import MinMaxScaler
# Initialize a scaler, then apply it to the features
scaler = MinMaxScaler() # default=(0, 1)
numerical = ['age', 'education-num', 'capital-gain', 'capital-loss', 'hours-per-week']
features_log_minmax_transform = pd.DataFrame(data = features_log_transformed)
features_log_minmax_transform[numerical] = scaler.fit_transform(features_log_transformed[numerical])
# Show an example of a record with scaling applied
display(features_log_minmax_transform.head(n = 5))
Data Preprocessing¶
We can see that there are several non-numeic features for each record. Given that typically, learning algorithms expect input to be numeric, we must convert non-numeric features (called categorical variables) using the one-hot encoding scheme. One-hot encoding creates a "dummy" variable for each possible category of each non-numeric feature.
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.
# One-hot encode the 'features_log_minmax_transform' data using pandas.get_dummies()
features_final = pd.get_dummies(features_log_minmax_transform)
# TODO: Encode the 'income_raw' data to numerical values
income = income = pd.get_dummies(income_raw, prefix='income').iloc[:,1:]
# Print the number of features after one-hot encoding
encoded = list(features_final.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. 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.
# Import train_test_split
from sklearn.model_selection import train_test_split
# Split the 'features' and 'income' data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(features_final,
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 are most likely to donate to their charity. Because of this, *CharityML* is particularly interested in predicting who makes more than \$50,000 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 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 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:
$$ F_{\beta} = (1 + \beta^2) \cdot \frac{precision \cdot recall}{\left( \beta^2 \cdot precision \right) + recall} $$
In particular, when $\beta = 0.5$, 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, and those who make more), it's clear most individuals do not make more than \$50,000. This can greatly affect accuracy, since we could simply say "this person does not make more than \$50,000" 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, 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).
Precision tells us what proportion of messages we classified as spam, actually were spam. It is a ratio of true positives(words classified as spam, and which are actually spam) to all positives(all words classified as spam, irrespective of whether that was the correct classificatio), in other words it is the ratio of
[True Positives/(True Positives + False Positives)]
Recall(sensitivity) tells us what proportion of messages that actually were spam were classified by us as spam. It is a ratio of true positives(words classified as spam, and which are actually spam) to all the words that were actually spam, in other words it is the ratio of
[True Positives/(True Positives + False Negatives)]
For classification problems that are skewed in their classification distributions like in our case, for example if we had a 100 text messages and only 2 were spam and the rest 98 weren't, accuracy by itself is not a very good metric. We could classify 90 messages as not spam(including the 2 that were spam but we classify them as not spam, hence they would be false negatives) and 10 as spam(all 10 false positives) and still get a reasonably good accuracy score. For such cases, precision and recall come in very handy. These two metrics can be combined to get the F1 score, which is 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).
Naive Predictor Performace¶
- If we chose a model that always predicted an individual made more than $50,000, what would that model's accuracy and F-score be on this dataset?
Please note that the the purpose of generating a naive predictor is simply to show what a base model without any intelligence would look like. In the real world, ideally your base model would be either the results of a previous model or could be based on a research paper upon which you are looking to improve. When there is no benchmark model set, getting a result better than random choice is a place you could start from.
Note:
- When we have a model that always predicts '1' (i.e. the individual makes more than 50k) then our model will have no True Negatives(TN) or False Negatives(FN) as we are not making any negative('0' value) predictions. Therefore our Accuracy in this case becomes the same as our Precision(True Positives/(True Positives + False Positives)) as every prediction that we have made with value '1' that should have '0' becomes a False Positive; therefore our denominator in this case is the total number of records we have in total.
- Our Recall score(True Positives/(True Positives + False Negatives)) in this setting becomes 1 as we have no False Negatives.
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score
'''
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
'''
TP = np.sum(income)
TP = 34014
FP = income.count()
FP - 45222
TN = 0
FN = 0
# Calculate accuracy, precision and recall
accuracy = greater_percent/100.0
recall = 1
precision = 0.4292
beta=0.5
# Calculate F-score using the formula above for beta = 0.5 and correct values for precision and recall.
fscore = (1 + beta**2)*(accuracy*recall)/((beta**2*accuracy) + recall)
# Print the results
print("Naive Predictor: [Accuracy score: {:.4f}, F-score: {:.4f}]".format(accuracy, fscore))
Supervised Learning Models¶
The following are some of the supervised learning models that are currently available in scikit-learn that I could 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
Here are the Three that I chose:¶
Ensemble Method: Random Forest¶
- Describe one real-world application in industry where the model can be applied. Random Forest can be used in marketing research to understand customer purchasing behavior or customer interest.
- What are the strengths of the model; when does it perform well?
The pooling mechanism of combining many decision trees and their outputs provides a stronger and more robust prediction based on a collection of data. Additionally, random forests allow us to measure the importance of each feature which can be very helpful in further understanding the model.
source
- What are the weaknesses of the model; when does it perform poorly? Random forests have high variance which means that the model can be too flexible and will attempt to fit every data point, i.e. overfitting.
- What makes this model a good candidate for the problem, given what you know about the data? Given the data that we have especially given that we have information on education level, work classes and capital gains, we can base on previous research comfortable predict who would make more or less than $50K
K Nearest Neighbor¶
- Describe one real-world application in industry where the model can be applied.
A recommender system can be one of the application of KNN
source
- What are the strengths of the model; when does it perform well? one of its strengths is that it is one of the simplest machine learning algorithms and that it can be used for both classification AND regression. It is also very helpful in finding patterns and similar items.
- What are the weaknesses of the model; when does it perform poorly?
if the class distribution within the data set is skewed then the classification is most likely not a good outcome. A way to get around it is to weight the classification and account for the distance between test points and their k nearest neighbors.
source
- What makes this model a good candidate for the problem, given what you know about the data? The KNN output is class membership, this output is obtained through a process in which the objects are classified through 'a majority vote' from its neighbors. This method of classification can help us see different categories of people with varying characteristics, helping us make better prediction about who earns more than $50K
Logistic Regression¶
- Describe one real-world application in industry where the model can be applied. Logistic regression can be used to estimate the probability of an airport being turned into a cargo hub!
- What are the strengths of the model; when does it perform well? Logistic regression strengths lie in that it is highly efficient, and does not require many computational resources. it doesn't require features to be scales nor any tuning. it's a simple one!
- What are the weaknesses of the model; when does it perform poorly? Logistic regression performs better when certain characteristics are unrelated, i.e. preferable no correlation between the data. this can be hard depending on the data.
- What makes this model a good candidate for the problem, given what you know about the data? Logistic regression is incredible for binary classification, it can be the base of many deep learning and neural network tasks. However, for this project, logistic regression is good for telling us a quick yes or no on whether a particular person make more than %50K.
Creating a Training and Predicting Pipeline¶
To properly evaluate the performance of each model, it's important to 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. In the code below, Here's what we needed to implement :
- 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.
# Import two metrics from sklearn - fbeta_score and accuracy_score
from sklearn.metrics import accuracy_score, fbeta_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' using .fit(training_features[:], training_labels[:])
start = time() # Get start time
learner = learner.fit(X_train[:sample_size], y_train[:sample_size])
end = time() # Get end time
# Calculate the training time
results['train_time'] = "Train time in {:.3f} seconds".format(end-start)
# Get the predictions on the test set(X_test),
# then get predictions on the first 300 training samples(X_train) using .predict()
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'] = "Train time in {:.3f} seconds".format(end-start)
# Compute accuracy on the first 300 training samples which is y_train[:300]
results['acc_train'] = accuracy_score(y_train[:300], predictions_train)
# Compute accuracy on test set using accuracy_score()
results['acc_test'] = accuracy_score(y_test, predictions_test)
# Compute F-score on the the first 300 training samples using fbeta_score()
results['f_train'] = fbeta_score(y_train[:300], predictions_train, beta=0.5)
# Compute F-score on the test set which is y_test
results['f_test'] = fbeta_score(y_test,predictions_test,beta=0.5)
# Success
print("{} trained on {} samples.".format(learner.__class__.__name__, sample_size))
# Return the results
return results
Initial Model Evaluation¶
In the code cell, Here's what we needed to implement:
- 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'.Calculate the number of records equal to 1%, 10%, and 100% of the training data.
# Import the three supervised learning models from sklearn
from sklearn.ensemble import RandomForestClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.linear_model import LogisticRegression
# Initialize the three models
clf_A = RandomForestClassifier(random_state=0)
clf_B = KNeighborsClassifier()
clf_C = LogisticRegression(random_state=0)
# Calculate the number of samples for 1%, 10%, and 100% of the training data
# HINT: samples_100 is the entire training set i.e. len(y_train)
# HINT: samples_10 is 10% of samples_100 (ensure to set the count of the values to be `int` and not `float`)
# HINT: samples_1 is 1% of samples_100 (ensure to set the count of the values to be `int` and not `float`)
samples_100 = len(y_train)
samples_10 = int(round(len(y_train*.1)))
samples_1 = int(round(len(y_train)*.01))
# 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
vs.evaluate(results, accuracy, fscore)
Improving Results and Choosing the Best Model¶
Now is when we choose from the three supervised learning models the best model to use on the data. We needed to 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.
Best Model Choice¶
From the graph above, we can see that during the training phase that the Random Forest and KNN algorithms outperform their Logistic Regression counterpart in both accuracy and fscore on all sample sizes. However, in the test data output, we can see that Logistic Regression and Random forest are relatively tied in how well they analyzed the data and produced good results in both accuracy and fscore values.
If we had to choose a model, I would suggest Logistic regression, because it takes the least amount of time, is not as flexible ( does not have too high a variance) like Random Forest, does not like strong correlations in the data and because it performed consistently better on the accuracy and fscore measures.
Best Model Choice in Layman's Terms¶
The model that we came up with is logistic regression, this model can look at some data and tell us the probability that any person we input into our model would either make more or less than 50K, with a relatively high accuracy level. The reason I mention accuracy is because you brought up that misclassifying people who make less than 50k as someone who does make more than 50K would be detrimental, so we took that seriously and focused more on the accuracy of our predictions. the way that it works behind the scenes, very simply, is that it looks at each characteristic like schooling and tries to account for how that would influence the overall probabilities of our person making more than $50K. overall, this is a very strong prediction algorithm that can answer your question in a pinch!
Model Tuning¶
To fine tune the chosen model, we used grid search (GridSearchCV) with at least one important parameter tuned with at least 3 different values. We needed the entire training set for this. In the code cell below, Here's what we needed to implement:
- Import
sklearn.grid_search.GridSearchCVandsklearn.metrics.make_scorer. - Initialize the chosen classifier 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 we wish to tune for the chosen model.
- Example:
parameters = {'parameter' : [list of values]}.
- 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.
# Import 'GridSearchCV', 'make_scorer', and any other necessary libraries
from sklearn.linear_model import LogisticRegression
from sklearn import grid_search
from sklearn.model_selection import GridSearchCV
from sklearn.cross_validation import StratifiedShuffleSplit
from sklearn.metrics import make_scorer
from sklearn.metrics import fbeta_score
from sklearn.metrics import accuracy_score
# Initialize the classifier
clf = LogisticRegression()
# Create the parameters list you wish to tune, using a dictionary if needed.
# HINT: parameters = {'parameter_1': [value1, value2], 'parameter_2': [value1, value2]}
#parameters = {'n_estimators':[100,150,200]}
parameters = {'solver': ['newton-cg', 'lbfgs'],
'C': [0.01, 0.1, 1.0, 10.0, 100.0, 1000.0]}
# Make an fbeta_score scoring object using make_scorer()
scorer = make_scorer(fbeta_score, beta=0.5)
cv = StratifiedShuffleSplit(y_train, test_size=0.5, random_state=2)
# Perform grid search on the classifier using 'scorer' as the scoring method using GridSearchCV()
grid_obj = GridSearchCV(clf, parameters, scoring=scorer, cv=cv)
# Fit the grid search object to the training data and find the optimal parameters using fit()
grid_fit = grid_obj.fit(X_train, y_train)
# Get the estimator
best_clf = grid_fit.best_estimator_
best_clf.fit(X_train, y_train)
# 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)))
Final Model Evaluation¶
- What is the 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 our optimized model compare to the naive predictor benchmarks we found earlier?
Results:¶
| Metric | Benchmark Predictor | Unoptimized Model | Optimized Model |
|---|---|---|---|
| Accuracy Score | 0.2478 | 0.8419 | 0.8423 |
| F-score | 0.2917 | 0.6832 | 0.6849 |
In the table above, we can see clearly that the tuned model did significantly better on both accuracy and f-score that the benchmark predictor. We can also see that the optimized model also did better than the unoptimized model.
the results show a start difference and confirm that the benchmark initial assumption that all individuals made more than ($50k) was not the correct approach as evident through the accuracy score and the fscore's vast improvement in the optimized model.
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.
To do this, we must 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 code below, we fit this classifier to training set and use this attribute to determine the top 5 most important features for the census dataset.
Feature Relevance Observation¶
First: Intuition Which five original features do we believe to be most important for prediction, and in what order would we rank them and why?
Answer: Subjectively speaking and given that we are estimating income, I would say that age, education level, sex, race, and capital gain would make the best indicators, again subjectively speaking. Those indicators are all associated with more wealth at least in the minds of the general public. Older people and those with graduate levels of education are usually in leadership and management position who, on average, earn more. Additionally, historical precedence and corporate cultures have disproportionately awarded men and specifically white men bigger salaries than women and people of color. capital gain indicates a different stream of income that not many have.
#display column
data.columns
Extracting Feature Importance¶
To do this, we must 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.
In the code below, Here's what we needed to implement:
- 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_'.
# Import a supervised learning model that has 'feature_importances_'
from sklearn.ensemble import GradientBoostingClassifier
# Train the supervised model on the training set using .fit(X_train, y_train)
model = GradientBoostingClassifier(random_state=0, n_estimators=370).fit(X_train, y_train)
# Extract the feature importances using .feature_importances_
importances = best_clf.feature_importances_
# Plot
vs.feature_plot(importances, X_train, y_train)
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.
- How do these five features compare to the five features we intuitively extracted?
- How does this visualization affect your thoughts?
Answer:
The model's selected features chose three of the five that I've mentioned, namely; education, age, and capital gain. what's interesting is that the model also placed emphasis on the marital status as those who are married are more likely to make more than 50K. However, similar to my prediction, sex does play a role as it highlighted the important feature or being a husband. This visualization is very indicative of the structure of society at the time and the social and economic strata at that time.
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 you found earlier, and train it on the same training set with only the top five important features.
# 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)))
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 we consider using the reduced data as our training set?
Answer:
Although both the accuracy score and the Fscores decreased, it is still pretty close and I would say that the emphasis placed on a decrease in value is highly dependent of the work environment and the requirement of any particular project.
And again, depending on the needs of the project and the client, if they were ok with this score, I would absolutely reduce the time to run it if possible at all!