In this notebook, some template code has already been provided for you, and it will be your job to implement the additional functionality necessary to successfully complete this project. Sections that begin with 'Implementation' in the header indicate that the following block of code will require additional functionality which you must provide. Instructions will be provided for each section and the specifics of the implementation are marked in the code block with a 'TODO' statement. Please be sure to read the instructions carefully!
In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a 'Question X' header. Carefully read each question and provide thorough answers in the following text boxes that begin with 'Answer:'. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.
Note: Please specify WHICH VERSION OF PYTHON you are using when submitting this notebook. Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.
In this project, you will employ several supervised algorithms of your choice to accurately model individuals' income using data collected from the 1994 U.S. Census. You will then choose the best candidate algorithm from preliminary results and further optimize this algorithm to best model the data. Your 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.
Run the code cell below to load necessary Python libraries and 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.
In [1]:
# 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
import sklearn as sk
# 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=1))
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. In the code cell below, you will need to compute the following:
'n_records''n_greater_50k'.'n_at_most_50k'.'greater_percent'. HINT: You may need to look at the table above to understand how the 'income' entries are formatted.
In [2]:
# Total number of records
n_records = data.shape[0]
# Number of records where individual's income is more than $50,000
n_greater_50k = data[data.income=='>50K'].shape[0]
# Number of records where individual's income is at most $50,000
n_at_most_50k = data[data.income=='<=50K'].shape[0]
# 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: {}%".format(greater_percent))
Featureset Exploration
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.
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'.
Run the code cell below to plot a histogram of these two features. Note the range of the values present and how they are distributed.
In [3]:
# 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 '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 the logarithm successfully.
Run the code cell below to perform a transformation on the data and visualize the results. Again, note the range of values and how they are distributed.
In [4]:
# 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)
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, as exampled below.
Run the code cell below to normalize each numerical feature. We will use sklearn.preprocessing.MinMaxScaler for this.
In [5]:
# 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))
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, you will need to implement the following:
pandas.get_dummies() to perform one-hot encoding on the 'features_log_minmax_transform' data.'income_raw' to numerical entries.0 and records with ">50K" to 1.
In [6]:
# TODO: 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_raw.map({"<=50K" : 0, ">50K": 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
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.
Run the code cell below to perform this split.
In [7]:
# Import train_test_split
from sklearn.cross_validation 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]))
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.
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).
'accuracy' and 'fscore' to be used later.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.
HINT:
In [8]:
'''
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)
FP = income.count() - TP
TN = 0.0
FN = 0.0
# TODO: Calculate accuracy, precision and recall
accuracy = (TP + TN)/income.count()
recall = float(TP) / (TP + FN)
precision = float(TP) / (TP + FP)
# TODO: Calculate F-score using the formula above for beta = 0.5 and correct values for precision and recall.
fscore = (1+0.5*0.5)*(precision * recall)/(0.5 * 0.5 * precision + recall)
# Print the results
print("Naive Predictor: [Accuracy score: {:.4f}, F-score: {:.4f}]".format(accuracy, fscore))
The following are some of the supervised learning models that are currently available in scikit-learn that you may choose from:
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
HINT:
Structure your answer in the same format as above^, with 4 parts for each of the three models you pick. Please include references with your answer.
Answer: For this binary classification task, I suggest the use of the following three models.
SVM
SVMs are widely used in classification of images, facial detection and hand writing recognition. SVMs are well suited for domains with non-linear and disjointed sets of descision boundaries.
The model is particularly good at handling multi-modal data, adapts well to non-linearity in decision boundary.
The model takes longer to train and is not a suitable choice for larger datasets. The model is inherently non-explainable.
The model is good candidate for the data as it is able to deal with categorical and continous variables and the hunch is that the decision boundary for this given data may be non-linear.
Logistic Regression
Logistic regression belongs to a class of linear models that are good at modeling binary classification problems. They are widely used in all sorts of systems, including recommendation systems, search ranking, spam classification amongst many others.
The model is simple and intutive to train and is explainable. It is also able to deal with categorical and continious domain data.
This model does not take into account interaction features on it own, although it could be engineered to support interaction features.
The model is a good candidate as it has one of the shortest training time and is good at handling sparse features.
Gradient Boosted Decision Trees
Gradient Boosted Decision Trees are widely used in industry for solving classification problems in bio medicine, industrial manufaturing amongst many others. Common example of its application in the two domains involves identifying diseased v/s healthy tissue in bio medicence and separating deffective goods from correctly manufactured ones in manufacturing.
The model is particularly good at combining a number of weak learners, can handle categorical variables, are good at generating non-linear decision boundaries and incorporating interaction features.
The model performs poorly if the feature space is restricted and there are very few features to sample from at each stage. This could potentially restrict the number of trees being generated.
This model is a good candidate as it could easily handle categorical data.
To properly evaluate the performance of each model you've chosen, it's important that you create a training and predicting pipeline that allows you to quickly and effectively train models using various sizes of training data and perform predictions on the testing data. Your implementation here will be used in the following section. In the code block below, you will need to implement the following:
fbeta_score and accuracy_score from sklearn.metrics.X_test, and also on the first 300 training points X_train[:300].beta parameter!
In [9]:
# Import two metrics from sklearn - fbeta_score and accuracy_score
from sklearn.metrics import fbeta_score, 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' using .fit(training_features[:], training_labels[:])
start = time() # Get start time
model = learner.fit(X_train[:int(sample_size)], y_train[:int(sample_size)])
end = time() # Get end time
# Calculate the training time
results['train_time'] = 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 = model.predict(X_test)
predictions_train = model.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 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
In the code cell, you will need to implement the following:
'clf_A', 'clf_B', and 'clf_C'.'random_state' for each model you use, if provided.'samples_1', 'samples_10', and 'samples_100' respectively.Note: Depending on which algorithms you chose, the following implementation may take some time to run!
In [10]:
#Import the three supervised learning models from sklearn
import sklearn.linear_model as lm
import sklearn.svm as svm
import sklearn.ensemble as en
#Initialize the three models
clf_A = lm.LogisticRegression(random_state=1741)
clf_B = svm.SVC(random_state=1741)
clf_C = en.GradientBoostingClassifier(random_state=1741)
# 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(np.round(0.1 * samples_100))
samples_1 = int(np.round(0.01 * samples_100))
# 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)
In this final section, you will choose from the three supervised learning models the best model to use on the student data. You 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.
HINT:
Look at the graph at the bottom left from the cell above(the visualization created by vs.evaluate(results, accuracy, fscore)) and check the F score for the testing set when 100% of the training set is used. Which model has the highest score? Your answer should include discussion of the:
Answer:
Gradient Boosted Descision Trees perform better than SVM and logistic regression. As observed accuracy of all the models increases as the data size increases for both training and test sets. It is noteworthy to see that the GBDT performance continues to improve both in terms of its accuracy and fscore. The training time for the model is the second best at 20ms for the entire training set. Although the training time is larger than logistic regression, it is still 5x faster than the SVM. In addition, GBDT is able to incorporate one hot encoded features and provides the best in class performance.
HINT:
When explaining your model, if using external resources please include all citations.
Answer:
CharityML could help target potential donors based on their likely contribution. The classification score generated by the machine learned model could help classify a person into a potential high/low value donor based on a number of features such as age, education, occupation, gender and type of income. The model is able to identify donors that potentially donate >=50K the 80% accuracy. We use information of past donors to learn relationship between their personal attributes and the type of donation that they made. By using the model to predict for some of the past donors, we are able to test our model for accuracy. Although simple analysis of the data would suggest that people of a certain age and gender are more likely to make a donation of a certain type the relationship between donation type and a persons attributes is more nuanced. The machine learned model captures such subtle information and looks at how other personal attributes like level of education and/or disposable income may impact the donation. In doing so, the model learns patterns incomprehensible to a human eye.
Additional Description A machine learned model like a decision tree could be used to learn rules from the charity data. A decision tree identifies patterns such as people of a certain age group, sex, race, income are more likely to make charitable contributions. It encodes the pattern as a series of hierachical conditions on the features. These patterns could be potentially very verbose where by each row in the data has a deticated rule associated with it, which would result in decision trees that could predict well on the current data, but fail to generalize over an unseen dataset. A decision tree which is restricted in depth and also has some minimum number of data points in the leaf node may result in a learner, which may not be highly accurate but generalizes well over unseen data and thus represents a weak learner.
The above mentioned model based on Gradient Boosted Decision Trees is created by combining a number of weak learners. Each of the weak learner is a decision tree and a number of trees are generated iteratively. In each iteration the points that were misclassified are weighted heavily and have a higher likelihood of being included in the training set for the next iteration. Let f_i be the function captured by tree at the ith iteration and (y_i - yhat_i) represent the error generated by the tree generated in ith iteration. In the (i+1)^th iteration, the decision tree is trained to predict the misclassified points. By repititively applying the algorithm to data for training subsequent generation of trees, the algorithm is maximizing that the subsequent trees are trained on data where the current algorithm has worst performance.
Fine tune the chosen model. Use grid search (GridSearchCV) with at least one important parameter tuned with at least 3 different values. You will need to use the entire training set for this. In the code cell below, you will need to implement the following:
sklearn.grid_search.GridSearchCV and sklearn.metrics.make_scorer.clf.random_state if one is available to the same state you set before.parameters = {'parameter' : [list of values]}.max_features parameter of your learner if that parameter is available!make_scorer to create an fbeta_score scoring object (with $\beta = 0.5$).clf using the 'scorer', and store it in grid_obj.X_train, y_train), and store it in grid_fit.Note: Depending on the algorithm chosen and the parameter list, the following implementation may take some time to run!
In [11]:
# Import 'GridSearchCV', 'make_scorer', and any other necessary libraries
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import make_scorer
# Initialize the classifier
clf = en.GradientBoostingClassifier(random_state=1741)
# Create the parameters list you wish to tune, using a dictionary if needed.
# HINT: parameters = {'parameter_1': [value1, value2], 'parameter_2': [value1, value2]}
parameters = {'max_depth':[5,8,10], 'learning_rate':[0.1, 1.0, 10.0], 'min_samples_leaf':[20,50,100]}
# TODO: Make an fbeta_score scoring object using make_scorer()
scorer = make_scorer(fbeta_score, beta=0.5)
# TODO: Perform grid search on the classifier using 'scorer' as the scoring method using GridSearchCV()
grid_obj = GridSearchCV(clf, param_grid=parameters, scoring=scorer)
# TODO: 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_
# 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)))
Note: Fill in the table below with your results, and then provide discussion in the Answer box.
Answer: These scores for optimized model are better than the scores for un-optimized model.
The naive estimator discussed in Question 1, has an Accuracy score: 0.2478, F-score: 0.2917, which indicates that the model had low accuracy, with an accuracy of 0.87 and f-score of 0.75, the optimized model shows substantial improvent over the naive estimator.
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.
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.
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:
Based on the data exploration, I would consider that:
would be most important features, as the amount of disposable income, earning potential and geo-location may determine the amount of income people have and are able to contribute. As what we are trying to predict is an indicated net amount >=50K, it does not indicate the percentage of absolute income that one is donating and hence, earning potential would be a key feature
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 cell below, you will need to implement the following:
'.feature_importances_'.
In [12]:
import sklearn.linear_model as lm
import sklearn.svm as svm
import sklearn.ensemble as en
# TODO: Train the supervised model on the training set using .fit(X_train, y_train)
model = en.GradientBoostingClassifier(random_state=0).fit(X_train, y_train)
# TODO: Extract the feature importances using .feature_importances_
importances = model.feature_importances_
# Plot
vs.feature_plot(importances, X_train, y_train)
Observe the visualization created above which displays the five most relevant features for predicting if an individual makes at most or above \$50,000.
Answer:
The set of features is similar to that mentioned in answer to question 6, the rank order is different than what I had mentioned. The visualization confirms that although marital_status is an important indicator, a sub category of Married_civ_spouse is more indicative within the category
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.
In [13]:
# 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)))
Answer:
There is a detoriation when using a reduced feature set of important features only. The deteoriated model still performs at 95% of the fully trained model. If training time was a factor then this reduced model may be an acceptable solution.
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