Project: Finding Donors for CharityML¶
This project is from Udacity Data Scientist course.
Overview¶
In this project, I employ several supervised algorithms of your choice to accurately model individuals' income using data collected from the 1994 U.S. Census. Then I choose the best candidate algorithm from preliminary results and further optimize this algorithm to best model the data.
The goal of this project 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 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
import matplotlib.pyplot as plt
import seaborn as sns
from IPython.display import display # Allows the use of display() for DataFrames
# Import supplementary visualization code visuals.py
import visuals as vs
import warnings
warnings.filterwarnings("ignore")
# Pretty display for notebooks
%matplotlib inline
# Load the Census dataset
data = pd.read_csv("census.csv")
# Success - Display the first record
data.head(n=5)
- 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'.
data.income.unique().tolist()
# Total number of records
n_records = len(data)
# Number of records where individual's income is more than $50,000
n_greater_50k = len(data.query('income == ">50K"'))
# Number of records where individual's income is at most $50,000
n_at_most_50k = len(data.query('income == "<=50K"'))
# 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: {0:.2f}%".format(greater_percent))
Variables Description
- age: continuous.
- workclass: Private, Self-emp-not-inc, Self-emp-inc, Federal-gov, Local-gov, State-gov, Without-pay, Never-worked.
- education: Bachelors, Some-college, 11th, HS-grad, Prof-school, Assoc-acdm, Assoc-voc, 9th, 7th-8th, 12th, Masters, 1st-4th, 10th, Doctorate, 5th-6th, Preschool.
- education-num: continuous.
- marital-status: Married-civ-spouse, Divorced, Never-married, Separated, Widowed, Married-spouse-absent, Married-AF-spouse.
- occupation: Tech-support, Craft-repair, Other-service, Sales, Exec-managerial, Prof-specialty, Handlers-cleaners, Machine-op-inspct, Adm-clerical, Farming-fishing, Transport-moving, Priv-house-serv, Protective-serv, Armed-Forces.
- relationship: Wife, Own-child, Husband, Not-in-family, Other-relative, Unmarried.
- race: Black, White, Asian-Pac-Islander, Amer-Indian-Eskimo, Other.
- sex: Female, Male.
- capital-gain: continuous.
- capital-loss: continuous.
- hours-per-week: continuous.
- native-country: United-States, Cambodia, England, Puerto-Rico, Canada, Germany, Outlying-US(Guam-USVI-etc), India, Japan, Greece, South, China, Cuba, Iran, Honduras, Philippines, Italy, Poland, Jamaica, Vietnam, Mexico, Portugal, Ireland, France, Dominican-Republic, Laos, Ecuador, Taiwan, Haiti, Columbia, Hungary, Guatemala, Nicaragua, Scotland, Thailand, Yugoslavia, El-Salvador, Trinadad&Tobago, Peru, Hong, Holand-Netherlands.
# descriptive statistics of continuous variables
data.describe()
# information of all variables
data.info()
# Histogram of all continuous variables
data.hist(figsize = (10,10), bins=30);
# Pair plot to wether income can be separated by other variables
sns.pairplot(data, hue="income", diag_kind="kde",plot_kws=dict(s=50, linewidth=1, alpha = 0.1),diag_kws=dict(shade=True));
Preprocess 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. 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))
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.
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
# 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
map_dict = {'>50K':1, '<=50K':0}
income = income_raw.map(map_dict)
# Print the number of features after one-hot encoding
encoded = list(features_final.columns)
print("{} total features after one-hot encoding.".format(len(encoded)))
# Uncomment the following line to see the encoded feature names
# print(encoded)
Shuffle and Split Data¶
Now all categorical variables have been converted into numerical features, and all numerical features have been normalized. 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.model_selection import train_test_split
# Split the 'features' and 'income' data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(features_final,
income,
test_size = 0.2,
random_state = 0)
# Show the results of the split
print("Training set has {} samples.".format(X_train.shape[0]))
print("Testing set has {} samples.".format(X_test.shape[0]))
Evaluating Model Performance¶
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.
Naive Predictor Performace¶
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.
# Calculate accuracy, precision and recall
accuracy = np.sum(income) / len(income)
recall = np.sum(income) / np.sum(income)
precision = np.sum(income) / len(income)
# Calculate F-score using the formula above for beta = 0.5 and correct values for precision and recall.
fscore = (1 + 0.25) * (precision * recall) / (0.25 * precision + recall)
# Print the results
print("Naive Predictor: [Accuracy score: {:.4f}, F-score: {:.4f}]".format(accuracy, fscore))
Supervised Learning Models¶
Logistic Regression¶
1. Real world application:¶
A few example applications include analysis of sheet metals, predicting safety issues in coal mines, and various medical applications. Machine Learning Algorithms for Business Applications – Complete Guide
2. Strengths:¶
Easy to interpret. Logistic regression outputs a number between 0 and 1, which can loosely be interpreted as a probability (0.312 could be interpreted as 31.2% chance of a credit card transaction being fraudulent). The feature weights easily indicate which features are more important in determining the classifications than others.
3. Weaknesses:¶
- It Is prone to overfit the model.
- Logistic regression may require a fairly large training set before it can make accurate predictions outside of the training set.
- Not an online technique. Incorporating new data requires running gradient descent again.
- Has tradeoffs with gradient descent. The faster gradient descent determines the final feature weights, the more likely it is to miss the optimal weights. It can sometimes be difficult to figure this out the optimal speed versus accuracy tradeoff, and trial-and-error can be time consuming.
4. What makes this model a good candidate¶
After normalizing, all numeric features are nearly normally distributted, so we can use logistic regression. And the boundary of the data is not very complex, so we can use logistic regression.
Ensemble Methods (Random Forest)¶
1. Real world application:¶
Object recognition Molecular Biology (Analyzing amino acid sequences) Remote sensing (Pattern recognition) Astronomy (Star Galaxy classification, etc) Introduction to Random forest
2. Strengths:¶
- One of the most accurate decision models.
- Works well on large datasets.
- Can be used to extract variable importance.
- Do not require feature engineering (scaling and normalization)
3. Weaknesses:¶
- Overfitting in case of noisy data.
- Unlike decision trees, results are difficult to interpret.
- Hyperparamters needs good tuning for high accuracy.
4. What makes this model a good candidate¶
Ensemble method makes a good model for the data considering the amount of features. After the one hot conversion there was 103 total features which is a lot. Ensemble method will automatically give more importance to relevant features. And it can prevent model from overfitting (compared to decision tree).
Support Vector Machines¶
1. Real world application:¶
Face detection / Text and hypertext categorization / Classification of images/ Bioinformatics (complex data)
2. Strengths:¶
It works really well with clear margin of separation It is effective in high dimensional spaces. It is effective in cases where number of dimensions is greater than the number of samples. It uses a subset of training points in the decision function (called support vectors), so it is also memory efficient.
3. Weaknesses:¶
It doesn’t perform well, when we have large data set because the required training time is higher It also doesn’t perform very well, when the data set has more noise i.e. target classes are overlapping SVM doesn’t directly provide probability estimates, these are calculated using an expensive five-fold cross-validation. Understanding Support Vector Machine algorithm from examples (along with code)
4. What makes this model a good candidate¶
After the one hot conversion there was 103 total features which is a lot. There are enough features for SVM to train. And from pair plots we can't see a clear linear boundry to separate the income. So maybe SVM with kernel is suitable for this question.
Creating a Training and Predicting Pipeline¶
- 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):
results = {}
# Fit the learner to the training data using slicing with 'sample_size' using .fit(training_features[:], training_labels[:])
start = time() # Get start time
learner = learner.fit(X_train[:sample_size], y_train[:sample_size])
end = time() # Get end time
# Calculate the training time
results['train_time'] = 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
Initial Model Evaluation¶
- Import the three supervised learning models
- Initialize the three models and store them in
'clf_A','clf_B', and'clf_C'. - Calculate the number of records equal to 1%, 10%, and 100% of the training data.
- Store those values in
'samples_1','samples_10', and'samples_100'respectively.
- Store those values in
# Import the three supervised learning models from sklearn
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier
from sklearn.svm import SVC
# Initialize the three models
clf_A = LogisticRegression(random_state=1)
clf_B = RandomForestClassifier(random_state=1)
clf_C = SVC(random_state=1)
# 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_100 = len(X_train)
samples_10 = round(0.1 * len(X_train))
samples_1 = round(0.01 * 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¶
- Choose from the three supervised learning models the best model to use on the student data.
- Perform a grid search optimization for the model over the entire training set (
X_trainandy_train) by tuning at least one parameter to improve upon the untuned model's F-score.
Choosing the Best Model
- metrics - F score on the testing when 100% of the training data is used,
- prediction/training time
- the algorithm's suitability for the data.
For this dataset, from the plots above we can know that logistic regression model is the best choice.
- From the F scores and accurancy scores, we can know that logistic regression have the highest scores both in accurancy and F score.
- SVM cost much more time than other two models
- Logistic regression model is easy to understand and easy to train, so it is suitable for this model. Random forest and SVM are hard to understand.
Describing the Model in Layman's Terms¶
The best model we choose for this dataset is logistic regression model. Logistic regression is useful in classification problem, like in problem that the outcome(y) we want to predict is 1 or 0, yes or no etc. This model is easy to understand. The logistic regression build a connection between input features and output outcomes. For one observation, it predicts the probability of getting one specific outcome based on the given features.
In this case, the input features are occupation, education level, age, sex etc. The output outcome is income <=50K or >50K. The feature weights in logistic regression easily indicate which features are more important in determining the classifications than others. For example, for the first obesrvation(Age:39, work class:State-gov education: Bachelor......), using the regression model we will get the probability of that his income is greater 50K.
This model is trained by using error function. Error function is calculated based on the probability we predict for each point. If we predict one point has a large probability of getting 1 and the true value is 1 (or a small probability of getting 1 and the true value is 0), it has a small error. Otherwise it has a large error. And we try to find a logistic regression to minimize this error function.
Logistic regression makes predictions using probability. It calculated the probability based on given features. If the probability is large than 0.5, it gives 1 as the predicted value. If the probability is smaller than 0.5, it gives 0 as the predicted value.
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.
# Import 'GridSearchCV', 'make_scorer', and any other necessary libraries
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import make_scorer, fbeta_score
# Initialize the classifier
clf = LogisticRegression()
C_list = [0.01 * 2**i for i in range(11)]
# Create the parameters list you wish to tune, using a dictionary if needed.
# HINT: parameters = {'parameter_1': [value1, value2], 'parameter_2': [value1, value2]}
parameters = {'penalty':['l1', 'l2'], 'C': C_list}
# 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)))
Final Model Evaluation¶
Results:¶
| Metric | Unoptimized Model | Optimized Model |
|---|---|---|
| Accuracy Score | 0.8419 | 0.8418 |
| F-score | 0.6832 | 0.6832 |
The unoptimized model and optimized model have the same score, but it is much better than the naive predictors.
Our optimized model’s performance scores are the same (F-Score) and lower (Accuracy Score) than the unoptimized model’s scores. The default hyper parameters of our Model are well-suited for this data, so they are giving a near optimum score without tuning.
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.
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.
- Import a supervised learning model from sklearn if it is different from the three used earlier.
- Train the supervised model on the entire training set.
- Extract the feature importances using
'.feature_importances_'.
# Import a supervised learning model that has 'feature_importances_'
from sklearn.ensemble import AdaBoostClassifier
# Train the supervised model on the training set using .fit(X_train, y_train)
model = AdaBoostClassifier().fit(X_train, y_train)
# Extract the feature importances using .feature_importances_
importances = model.feature_importances_
# Plot
vs.feature_plot(importances, X_train, y_train)
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)))
!!jupyter nbconvert *.ipynb