Welcome to the second project of the Machine Learning Engineer Nanodegree! 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 [72]:
# 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=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 [73]:
len(data[data['income']==">50K"])
Out[73]:
In [74]:
# TODO: Total number of records
n_records = len(data['income'].index)
# TODO: Number of records where individual's income is more than $50,000
n_greater_50k = len(data[data['income']==">50K"])
# TODO: Number of records where individual's income is at most $50,000
n_at_most_50k = len(data[data['income']=="<=50K"])
# TODO: Percentage of individuals whose income is more than $50,000
greater_percent = float(n_greater_50k*100.00/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)
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 [75]:
# 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 [76]:
# 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 [77]:
# 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 [78]:
# 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 [79]:
# 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.HINT:
In [80]:
'''
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
FN = 0
# TODO: Calculate accuracy, precision and recall
accuracy = float((TP+TN))/len(income)
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.
# HINT: The formula above can be written as (1 + beta**2) * (precision * recall) / ((beta**2 * precision) + recall)
beta = 0.5
fscore = (1 + beta**2) * (precision * recall) / ((beta**2 * 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:
Model 1 : K-Nearest Neighbors:
-> KNN model can be used by shopping site to recomend items to the user which are similar to the products bought earlier.
-> Model trainig is not required and it is ready to apply. It performs well on large data.
-> Usage of features while calculating distances is unclear and confusing.
-> As we have large dataset and this model easy to implement which makes it a candidate for this problem.
Model 2 : Decision Trees:
-> Decision Tree model is used for classification of images in the image search techniques and image optimization.
-> Decision trees have fast training speed and easy to visualize when the model has smaller decision trees compared to bigger trees.
-> Performace of the Decision trees are low when the tree size increases very often and can result in overfitting of the model.
-> Easy visualization and implementation of huge data is possible in Decision tree, hence makes it a candidate for this problem.
Model 3 : Ensemble Methods - GradientBoostingClassifier:
-> This model is used for applications like being learned with respect to different loss functions.
->Most of the time ensembling models perform well when we consider the feature specific models
-> The predictive power, roboustness to the outliers are the considerable strenghts of this model .
-> We require more hyper parameters to tune the model and attimes results in overfitting of the model.It is sequential in natures which results in hard scaling .
-> As we have miture of numerical and categorical features in the data it's better to use this model an we can run all the individual methods parallely, hence makes it a candidate for this problem.
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 [81]:
# TODO: Import two metrics from sklearn - fbeta_score and accuracy_score
from sklearn.metrics import fbeta_score
from sklearn.metrics import 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 = {}
# TODO: Fit the learner to the training data using slicing with 'sample_size' using .fit(training_features[:], training_labels[:])
start = time() # Get start time
learner.fit(features_final[:sample_size], income[:sample_size])
end = time() # Get end time
# TODO: Calculate the training time
results['train_time'] = end - start
# TODO: 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
# TODO: Calculate the total prediction time
results['pred_time'] = end - start
# TODO: Compute accuracy on the first 300 training samples which is y_train[:300]
results['acc_train'] = accuracy_score(y_train[:300],predictions_train)
# TODO: Compute accuracy on test set using accuracy_score()
results['acc_test'] = accuracy_score(y_test,predictions_test)
# TODO: 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)
# TODO: 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 [82]:
# TODO: Import the three supervised learning models from sklearn
from sklearn.neighbors import KNeighborsClassifier
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import GradientBoostingClassifier
# TODO: Initialize the three models
# n_neighbors=int(math.log(len(X_train),2))
clf_A = KNeighborsClassifier()
clf_B = DecisionTreeClassifier(random_state=13)
clf_C = GradientBoostingClassifier(random_state=13)
# TODO: 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
# HINT: samples_1 is 1% of samples_100
samples_100 = len(X_train)
samples_10 = int (len(X_train) * 0.1)
samples_1 = int (len(X_train) * 0.01)
# 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)
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:
The most appropriate model would be Decision Trees as we can see from the graph the accuracy and F-score of this model is comparatively greater to other. Model training time for this learning model is low compared to other and even while predicting the time is very little. Hence the Decision Tree learning model can be applied to get higher accuracy and performance.
HINT:
When explaining your model, if using external resources please include all citations.
Answer:
The Decision Tree Learning Model works more effecietly as it takes less time to excute. The model training and predicting requires very less time to work on. Its very simple and any one can easyly understand the classification and the tree description.
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 [83]:
# TODO: Import 'GridSearchCV', 'make_scorer', and any other necessary libraries
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import make_scorer
# TODO: Initialize the classifier
clf = DecisionTreeClassifier(random_state=13)
# TODO: 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':[3, 4, 5]}
# 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,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:
-> The optimized model's accuracy and F-score are improved when compared to unoptimized model.
-> These are comparatively better and the tuning the model resuted in improved performance.
-> The results of the optimized model are far better than the naive predictors benchmarks, we can see that there is a hude change in the values from the above table.
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:
The most important features would be:
-> Occupation: Salary differs with the job.
-> Education: Persons who have higher education qualification posses higher paid jobs.
-> Hours-per-week: By working for more hours people earn more money.
-> Capital-Gain: Higher the Capital_Gain higher is the salary of the person.
-> Age : Persons of higher age have more money when compared to low aged person.
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 [84]:
# TODO: Import a supervised learning model that has 'feature_importances_'
from sklearn.ensemble import AdaBoostClassifier
# TODO: Train the supervised model on the training set using .fit(X_train, y_train)
model = AdaBoostClassifier(random_state=13)
model.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:
-> Most of the features mentioned earlier matched with above five features except one which is 'Occupation'. The added feature was the Capital_loss, however this feature as higher importance compared to the mentioned one.
-> The visualization helps to better understand the mentioned features.
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 [85]:
# 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:
-> Both the Accuracy and F-score are reduced, where we have 2% decrease in the accuracy and 5% decrease in the F-score.
-> Eventhough its better when we compare it with our unoptimized model. As we consider few features its obvious to get reduced result.
-> If we consider the training time, the reduced data comes in handy as it is the most important when we deal with huge data sets.