Getting Started¶
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.
Exploring the Data¶
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.
# 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 five records
display(data.head(n=5))
Implementation: Data Exploration¶
A cursory investigation of the dataset will determine how many individuals fit into either group, and will tell us about the percentage of these individuals making more than \$50,000. In the code cell below, you will need to compute the following:
- The total number of records,
'n_records' - The number of individuals making more than \$50,000 annually,
'n_greater_50k'. - The number of individuals making at most \$50,000 annually,
'n_at_most_50k'. - The percentage of individuals making more than \$50,000 annually,
'greater_percent'.
HINT: You may need to look at the table above to understand how the 'income' entries are formatted.
# 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.query('income == ">50K"').shape[0]
# Number of records where individual's income is at most $50,000
n_at_most_50k = data.query('income == "<=50K"').shape[0]
# Percentage of individuals whose income is more than $50,000
greater_percent = (n_greater_50k / n_records) * 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))
Featureset 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¶
Before data can be used as input for machine learning algorithms, it often must be cleaned, formatted, and restructured — this is typically known as preprocessing. Fortunately, for this dataset, there are no invalid or missing entries we must deal with, however, there are some qualities about certain features that must be adjusted. This preprocessing can help tremendously with the outcome and predictive power of nearly all learning algorithms.
Transforming Skewed Continuous Features¶
A dataset may sometimes contain at least one feature whose values tend to lie near a single number, but will also have a non-trivial number of vastly larger or smaller values than that single number. Algorithms can be sensitive to such distributions of values and can underperform if the range is not properly normalized. With the census dataset two features fit this description: 'capital-gain' and 'capital-loss'.
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.
# 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.
# 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¶
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.
# 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))
Implementation: Data Preprocessing¶
From the table in Exploring the Data above, we can see there are several features for each record that are non-numeric. Typically, learning algorithms expect input to be numeric, which requires that non-numeric features (called categorical variables) be converted. One popular way to convert categorical variables is by using the one-hot encoding scheme. One-hot encoding creates a "dummy" variable for each possible category of each non-numeric feature. For example, assume someFeature has three possible entries: A, B, or C. We then encode this feature into someFeature_A, someFeature_B and someFeature_C.
| someFeature | someFeature_A | someFeature_B | someFeature_C | ||
|---|---|---|---|---|---|
| 0 | B | 0 | 1 | 0 | |
| 1 | C | ----> one-hot encode ----> | 0 | 0 | 1 |
| 2 | A | 1 | 0 | 0 |
Additionally, as with the non-numeric features, we need to convert the non-numeric target label, 'income' to numerical values for the learning algorithm to work. Since there are only two possible categories for this label ("<=50K" and ">50K"), we can avoid using one-hot encoding and simply encode these two categories as 0 and 1, respectively. In code cell below, you will need to implement the following:
- Use
pandas.get_dummies()to perform one-hot encoding on the'features_log_minmax_transform'data. - Convert the target label
'income_raw'to numerical entries.- Set records with "<=50K" to
0and records with ">50K" to1.
- Set records with "<=50K" to
# One-hot encode the 'features_log_minmax_transform' data using pandas.get_dummies()
features_final = pd.get_dummies(features_log_minmax_transform)
# Encode the 'income_raw' data to numerical values
income = np.where(income_raw == ">50K", 1, 0)
encoded = list(features_final.columns)
# Print the number of features after one-hot encoding
print("{} total features after one-hot encoding.".format(len(encoded)))
print(encoded)
Shuffle and Split Data¶
Now all categorical variables have been converted into numerical features, and all numerical features have been normalized. As always, we will now split the data (both features and their labels) into training and test sets. 80% of the data will be used for training and 20% for testing.
Run the code cell below to perform this split.
# 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]))
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).
Question 1 - 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? You must use the code cell below and assign your results to
'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:
- 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.
true_positive = float(0)
false_positive = float(0)
for x in income:
if x == 1:
# it is assumed everyone earned over 50k, so people who did are true-positives
true_positive = true_positive + 1
if x == 0:
# it is assumed everyone earned over 50k, so people who didn't are false-positives
false_positive = false_positive + 1
# it is assumed everyone earned over 50k, so therre are no false-negatives
false_negative = float(0)
accuracy = true_positive / (true_positive + false_positive)
recall = true_positive / (true_positive + false_negative)
precision = true_positive / (true_positive + false_positive)
beta = 0.5
# Calculate F-score using the formula above for beta = 0.5 and correct values for precision and recall.
fscore = float(1 + (beta) ** 2) * ((precision*recall) / (((beta**2) * precision) + 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 you may choose from:
- Gaussian Naive Bayes (GaussianNB)
- Decision Trees
- Ensemble Methods (Bagging, AdaBoost, Random Forest, Gradient Boosting)
- K-Nearest Neighbors (KNeighbors)
- Stochastic Gradient Descent Classifier (SGDC)
- Support Vector Machines (SVM)
- Logistic Regression
Question 2 - Model Application¶
List three of the supervised learning models above that are appropriate for this problem that you will test on the census data. For each model chosen
- Describe one real-world application in industry where the model can be applied.
- What are the strengths of the model; when does it perform well?
- What are the weaknesses of the model; when does it perform poorly?
- What makes this model a good candidate for the problem, given what you know about the data?
Answer:
Decision Tree :
Used in finance for option analysis.
Strengths :
- It is easy to understand compared to other algorithms for beginners.
- Feature selection is implicitly handled and best splits are at the top of the tree.
- Easy for anyone to code, visualize, manipulate, and explain
Weaknesses :
- Can easily overfit, since the number of samples isn't very high.
- Gets affected by outliers significantly compared to other ML algorithms.
Decision trees perform implicit feature selection, we want to know how to find donors given set of categorical and continuous (mostly categorical) features, decision tree would be a good choice to find the significant feature to decide about targetting/finding donors.
Gaussian Naive Bayes (GaussianNB) :
Credit scoring: features are selected to group users into credit score groups. Reference :- [http://ieeexplore.ieee.org/document/6282321/]
Strengths :
- Can make probabilistic predictions
- Not sensitive to irrelevant features.
- Need less training data.
- Very simple, easy to implement and fast.
Weaknesses :
- A subtle issue with Naive-Bayes is that if there are no occurrences of a class label and a certain attribute value together then the frequency-based probability estimate will be zero.
It is fast, reliable to train with small data. As we have small amount of train data and trying to achieve a good model we should try GaussianNB model.
Logistic Regression :
Credit Risk Analysis with logistic regression models.
Strengths :
- Outputs have a nice probabilistic interpretation and the algorithm can be regularized to avoid overfitting.
- Logistic models can be updated easily with new data using stochastic gradient descent.
Weaknesses :
- Logistic regression tends to underperform when there are multiple or non-linear decision boundaries.
- It is not flexible enough to naturally capture more complex relationships.
None of the data in the dataset is highly correlated, thus logistic regression should fit well for this data.
Implementation - Creating a Training and Predicting Pipeline¶
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:
- Import
fbeta_scoreandaccuracy_scorefromsklearn.metrics. - Fit the learner to the sampled training data and record the training time.
- Perform predictions on the test data
X_test, and also on the first 300 training pointsX_train[:300].- Record the total prediction time.
- Calculate the accuracy score for both the training subset and testing set.
- Calculate the F-score for both the training subset and testing set.
- Make sure that you set the
betaparameter!
- Make sure that you set the
# 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 = {}
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'] = 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'] = 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
Implementation: Initial Model Evaluation¶
In the code cell, you will need to implement the following:
- Import the three supervised learning models you've discussed in the previous section.
- Initialize the three models and store them in
'clf_A','clf_B', and'clf_C'.- Use a
'random_state'for each model you use, if provided. - Note: Use the default settings for each model — you will tune one specific model in a later section.
- Use a
- Calculate the number of records equal to 1%, 10%, and 100% of the training data.
- Store those values in
'samples_1','samples_10', and'samples_100'respectively.
- Store those values in
Note: Depending on which algorithms you chose, the following implementation may take some time to run!
# Import the three supervised learning models from sklearn
from sklearn.tree import DecisionTreeClassifier
from sklearn.naive_bayes import GaussianNB
from sklearn.linear_model import LogisticRegression
# Initialize the three models
clf_A = DecisionTreeClassifier(random_state=0)
clf_B = GaussianNB()
clf_C = LogisticRegression(random_state=0)
# Calculate the number of samples for 1%, 10%, and 100% of the training data
# samples_100 is the entire training set i.e. len(y_train)
# samples_10 is 10% of samples_100 (ensure to set the count of the values to be `int` and not `float`)
# samples_1 is 1% of samples_100 (ensure to set the count of the values to be `int` and not `float`)
samples_1 = len(X_train) // 100
samples_10 = len(X_train) // 10
samples_100 = len(X_train)
# Collect results on the learners
results = {}
for clf in [clf_A, clf_B, clf_C]:
clf_name = clf.__class__.__name__
results[clf_name] = {}
for i, samples in enumerate([samples_1, samples_10, samples_100]):
results[clf_name][i] = train_predict(clf, samples, X_train, y_train, X_test, y_test)
# Run metrics visualization for the three supervised learning models chosen
vs.evaluate(results, accuracy, fscore)
Improving Results¶
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.
Question 3 - Choosing the Best Model¶
- Based on the evaluation you performed earlier, in one to two paragraphs, explain to CharityML which of the three models you believe to be most appropriate for the task of identifying individuals that make more than \$50,000.
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:
- metrics - F score on the testing when 100% of the training data is used,
- prediction/training time
- the algorithm's suitability for the data.
Answer:
There are a number of factors which show that Logistic Regression is the best model in terms of performance for this data. First , it has the highest accuracy. Then, the f_score being the highest. The model performs well at 1%, better at 10%, and even better at 100%. This indicates that the more data we provide, the better this algorithm will perform. It is also incredibly fast to train and to test. It also has the benefit of providing a probabilistic output, which can provide a confidence level of the classification.
Question 4 - Describing the Model in Layman's Terms¶
- In one to two paragraphs, explain to CharityML, in layman's terms, how the final model chosen is supposed to work. Be sure that you are describing the major qualities of the model, such as how the model is trained and how the model makes a prediction. Avoid using advanced mathematical jargon, such as describing equations.
Answer:
Considering Logistic Regression to be the best fit for our problem, let us try to understand what Regression is and then let us try to explain what Logistic Regression is (In terms of Statistics/Machine Learning). Regression is, in the simplest terms understanding the relationship between the input and the output variables. Linear Regression is a very simple form of regression, linear regression establishes a linear relationship between the input and output variables. Logistic regression is basically a linear regression model which explains the relationship between one dependent binary variable and one or more nominal / ordinal / interval / ratio-level independent variables. The only difference is that the output for linear regression is a number which has a real meaning(a label) while, the output of a logistic regression is a number that represents the probability of the event / label happening (example, the probability of people clicking an ad online, the probability of death in titanic disaster, etc.). In our case predicting the probability of an individual making more money than $50,000. The intuition behind logistic regression is to transform the output of a linear regression to a range of (0,1) in which the probability lies. So, if for a person we are trying to find if he likes apple or mango, linear regression will produce an output like A or B (where, A: person likes Apple, B: person likes Mango) while logistic regression will output probabilities for both the A and B. So, if Probability(A) > Probability(B) then the person likes Apple, else Mango).
Now that we understood what Logistic regression is and what it tries to achieve / produce as output, let us try to understand how our logistic Regression Model works. Our objective is to classify a person as earning more than 50k or earning less than 50k. For our task, we have data which has certain features such as Age, Education Level, Hours per Week, Capital Loss, Capital Gain. With, basic intuition we could say that a person with higher education who works more hours per week would earn more. And someone with same education working same hours, but younger will earn less because he/she has less work experience. Our model also works the same way, but with huge no of features and huge population of data. It analyzes all the features and figures our relationship between the features. It finds out which features greatly impact a person’s earning and which don't. When the model is done with figuring out the training data, it defines a boundary. This process is called training the Model. After training we are ready to predict whether a person earns > 50 k or not. In this process, the model will input the data features to the already trained model and output probabilities belonging to each group. The model associates / allocates the person to belong to the class with higher probability (i.e. > 50 K or < 50 K in this case).
NOTE :- Probability of an event is the likelihood/chance of occurence of it and probability always lies in between 0 and 1.
Implementation: Model Tuning¶
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:
- Import
sklearn.grid_search.GridSearchCVandsklearn.metrics.make_scorer. - Initialize the classifier you've chosen and store it in
clf.- Set a
random_stateif one is available to the same state you set before.
- Set a
- Create a dictionary of parameters you wish to tune for the chosen model.
- Example:
parameters = {'parameter' : [list of values]}. - Note: Avoid tuning the
max_featuresparameter of your learner if that parameter is available!
- Example:
- Use
make_scorerto create anfbeta_scorescoring object (with $\beta = 0.5$). - Perform grid search on the classifier
clfusing the'scorer', and store it ingrid_obj. - Fit the grid search object to the training data (
X_train,y_train), and store it ingrid_fit.
Note: Depending on the algorithm chosen and the parameter list, the following implementation may take some time to run!
# Import 'GridSearchCV', 'make_scorer', and any other necessary libraries
from sklearn.grid_search import GridSearchCV
from sklearn.metrics import make_scorer
# Initialize the classifier
clf = LogisticRegression(random_state=0)
# Create the parameters list you wish to tune, using a dictionary if needed.
# parameters = {'parameter_1': [value1, value2], 'parameter_2': [value1, value2]}
parameters = {
'C': [0.001, 0.01, 0.1, 1, 10, 100, 1000],
'penalty': ['l1', 'l2']
}
# Make an fbeta_score scoring object using make_scorer()
scorer = make_scorer(fbeta_score, beta=0.5)
# Perform grid search on the classifier using 'scorer' as the scoring method using GridSearchCV()
grid_obj = GridSearchCV(clf, parameters, scoring=scorer)
# 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)))
Question 5 - Final Model Evaluation¶
- What is your optimized model's accuracy and F-score on the testing data?
- Are these scores better or worse than the unoptimized model?
- How do the results from your optimized model compare to the naive predictor benchmarks you found earlier in Question 1?_
Results:¶
| Metric | Naive / Benchmark Model | Unoptimized Model | Optimized Model |
|---|---|---|---|
| Accuracy Score | 0.2478 | 0.8419 | 0.8420 |
| F-score | 0.2917 | 0.6832 | 0.6842 |
Answer:
There doesn't seem to be any large improvement over the unoptimized model. This could be for a variety of reasons, including that the sparsity of the data doesn't matter all that much.
But, both the optimized and unoptimized models perform way better than the naive / benchmark model we created.
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.
Choose a scikit-learn classifier (e.g., adaboost, random forests) that has a feature_importance_ attribute, which is a function that ranks the importance of features according to the chosen classifier. In the next python cell fit this classifier to training set and use this attribute to determine the top 5 most important features for the census dataset.
Question 6 - Feature Relevance Observation¶
When Exploring the Data, it was shown there are thirteen available features for each individual on record in the census data. Of these thirteen records, which five features do you believe to be most important for prediction, and in what order would you rank them and why?
Answer:
I assume that the most important features that determine if a person makes more than $50,000 are the following :
Age - It seems likely that as someone gets older, they tend to earn / make more money (only upto a certain age say like 60 or 70 also which depends on a lot of other factors like country, type of job etc..).
Capital Gain - If someone has investments, they probably make a good salary.
Capital Loss - Just, similar to above but the difference being loss here.
Education - Higher education sort of correlates to higher wage and also it makes more sense in the usualy way as employers tend to pay high for employees with higher education.
Workclass - Certain types of jobs certainly pay higher than others, example people working in investment banking get paid more compared to IT services, etc...
Implementation - Extracting Feature Importance¶
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:
- 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_'.
We will be using a boosting classifier, usually the boosting models are used to boost the accuracy up if there is any possibilty (when put in laymans terms)
I chose AdaBoost.
# Import a supervised learning model that has 'feature_importances_'
from sklearn.feature_selection import SelectKBest
from sklearn.ensemble import AdaBoostClassifier
# Train the supervised model on the training set using .fit(X_train, y_train)
model = AdaBoostClassifier(random_state=0)
fit = model.fit(X_train,y_train)
# Extract the feature importances using .feature_importances_
importances = fit.feature_importances_
# Plot
vs.feature_plot(importances, X_train, y_train)
Question 7 - Extracting Feature Importance¶
Observe the visualization created above which displays the five most relevant features for predicting if an individual makes at most or above \$50,000.
- How do these five features compare to the five features you discussed in Question 6?
- If you were close to the same answer, how does this visualization confirm your thoughts?
- If you were not close, why do you think these features are more relevant?
Answer:
Well, most of my assumptions turned to be correct, but I am surprised to see hours-per-week instead of workclass. I am not very surprised to see that capital-loss contributed significantly to someone making more money.
I think hours-per-week makes more sense over workclass because irrespective of any workclass (maybe, atleast for this data), hardworkers are usually always paid with better benefits (hard work always pays off). Most importantly, hours-per-week showcase the amount of effort put in by a person / employee which end up increasing the productivity thereby generating better revenue to the firm as well as employee.
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)))
Question 8 - Effects of Feature Selection¶
- How does the final model's F-score and accuracy score on the reduced data using only five features compare to those same scores when all features are used?
- If training time was a factor, would you consider using the reduced data as your training set?
Answer:
In this case, I don't think it is a good idea to reduce the dimensions of training data.As, We had lost 4% accuracy, and 10% on the f_score after using the top five significant features. Since we're using logistic regression, I guess its not quite necessary to reduce the training or testing time, as the algorithm itself is pretty fast and efficient. But, this would greatly benefit algorithms like SVM and reduce the train and test time.