125. Feature selection 2 (model forward selection)

Here we use survival on the Titanic to demonstrate a model-based method to select the most important features.

Reducing the number of features we use can have three benefits:

• Simplifies model explanation
• Model fit may be improved by the removal of features that add no value
• Model will be faster to fit

In this notebook we will use a model-based approach whereby we incrementally add features that most increase model performance.

Two key advantages of this method are:

• It is relatively simple.
• It is tailored to the model in question.

Some key disadvantage of this method are:

• It may be slow if there are many parameters (though the loop to select features could be limited in the number of features to select).
• The selection of features may be dependent on model meta-parameters (such as level of regularisation).
• The selection of features may not transfer between models (e.g. a model that does not allow for feature interactions may not detect features which do not add much value independently).

We will go through the following steps:

• Download and save pre-processed data
• Split data into features (X) and label (y)
• Loop through features to select the feature that most increase ROC AUC
• Plot results

We will assess performance using k-fold stratification for better measurement of performance. If you are not familiar with k-fold stratification, have a look here.

And we will assess performance with a Receiver Operator Characteristic (ROC) curve. See here.

Load modules

A standard Anaconda install of Python (https://www.anaconda.com/distribution/) contains all the necessary modules.

import numpy as np
import pandas as pd

# Import machine learning methods
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import auc
from sklearn.metrics import roc_curve
from sklearn.model_selection import StratifiedKFold
from sklearn.preprocessing import StandardScaler

Load data

The section below downloads pre-processed data, and saves it to a subfolder (from where this code is run). If data has already been downloaded that cell may be skipped.

Code that was used to pre-process the data ready for machine learning may be found at: https://github.com/MichaelAllen1966/1804_python_healthcare/blob/master/titanic/01_preprocessing.ipynb:

download_required = True

if download_required:
    
    # Download processed data:
    address = 'https://raw.githubusercontent.com/MichaelAllen1966/' + \
                '1804_python_healthcare/master/titanic/data/processed_data.csv'
    
    data = pd.read_csv(address)

    # Create a data subfolder if one does not already exist
    import os
    data_directory ='./data/'
    if not os.path.exists(data_directory):
        os.makedirs(data_directory)

    # Save data
    data.to_csv(data_directory + 'processed_data.csv', index=False)

Load data:

data = pd.read_csv('data/processed_data.csv')

The first column is a passenger index number. We will remove this, as this is not part of the original Titanic passenger data.

# Drop Passengerid (axis=1 indicates we are removing a column rather than a row)
# We drop passenger ID as it is not original data

data.drop('PassengerId', inplace=True, axis=1)

Divide into X (features) and y (labels)

We will separate out our features (the data we use to make a prediction) from our label (what we are trying to predict). By convention our features are called X (usually upper case to denote multiple features), and the label (survive or not) y.

X = data.drop('Survived',axis=1) # X = all 'data' except the 'survived' column
y = data['Survived'] # y = 'survived' column from 'data'

Forward feature selection

Define data standardisation function.

def standardise_data(X_train, X_test):
    
    # Initialise a new scaling object for normalising input data
    sc = StandardScaler() 

    # Set up the scaler just on the training set
    sc.fit(X_train)

    # Apply the scaler to the training and test sets
    train_std=sc.transform(X_train)
    test_std=sc.transform(X_test)
    
    return train_std, test_std

The forward selection method:

• Keeps a list of selected features
• Keeps a list of features still available for selection
• Loops through available features:
  • Calculates added value for each feature (using stratified k-fold validation)
  • Selects feature that adds most value
  • Adds selected feature to selected features list and removes it from available features list

This method uses a while lop to keep exploring features until no more are available. An alternative would be to use a for loop with a maximum number of features to select.

# Create list to store accuracies and chosen features
roc_auc_by_feature_number = []
chosen_features = []

# Initialise chosen features list and run tracker
available_features = list(X)
run = 0
number_of_features = len(list(X))

# Loop through feature list to select next feature
while len(available_features)> 0:

    # Track and pront progress
    run += 1
    print ('Feature run {} of {}'.format(run, number_of_features))
    
    # Convert DataFrames to NumPy arrays
    y_np = y.values
    
    # Reset best feature and accuracy
    best_result = 0
    best_feature = ''

    # Loop through available features
    for feature in available_features:

        # Create copy of already chosen features to avoid orginal being changed
        features_to_use = chosen_features.copy()
        # Create a list of features from features already chosen + 1 new feature
        features_to_use.append(feature)
        # Get data for features, and convert to NumPy array
        X_np = X[features_to_use].values
        
        # Set up lists to hold results for each selected features
        test_auc_results = []
    
        # Set up k-fold training/test splits
        number_of_splits = 5
        skf = StratifiedKFold(n_splits = number_of_splits)
        skf.get_n_splits(X_np, y)
    
        # Loop through the k-fold splits
        for train_index, test_index in skf.split(X_np, y_np):
            
            # Get X and Y train/test
            X_train, X_test = X_np[train_index], X_np[test_index]
            y_train, y_test = y[train_index], y[test_index]
    
            # Get X and Y train/test
            X_train_std, X_test_std = standardise_data(X_train, X_test)
    
            # Set up and fit model
            model = LogisticRegression(solver='lbfgs')
            model.fit(X_train_std,y_train)
    
            # Predict test set labels
            y_pred_test = model.predict(X_test_std)
            
            # Calculate accuracy of test sets
            accuracy_test = np.mean(y_pred_test == y_test)
          
            # Get ROC AUC
            probabilities = model.predict_proba(X_test_std)
            probabilities = probabilities[:, 1] # Probability of 'survived'
            fpr, tpr, thresholds = roc_curve(y_test, probabilities)
            roc_auc = auc(fpr, tpr)
            test_auc_results.append(roc_auc)
        
        # Get average result from all k-fold splits
        feature_auc = np.mean(test_auc_results)
    
        # Update chosen feature and result if this feature is a new best
        if feature_auc > best_result:
            best_result = feature_auc
            best_feature = feature
    
    # k-fold splits are complete    
    # Add mean accuracy and AUC to record of accuracy by feature number
    roc_auc_by_feature_number.append(best_result)
    chosen_features.append(best_feature)
    available_features.remove(best_feature)

# Put results in DataFrame
results = pd.DataFrame()
results['feature to add'] = chosen_features
results['ROC AUC'] = roc_auc_by_feature_number

results

	feature to add	ROC AUC
0	male	0.766733
1	Pclass	0.833036
2	Age	0.843055
3	SibSp	0.848686
4	Embarked_S	0.853125
5	CabinLetter_E	0.855740
6	CabinNumberImputed	0.856158
7	CabinLetter_T	0.856160
8	CabinLetter_D	0.856167
9	CabinLetter_F	0.856307
10	EmbarkedImputed	0.856121
11	Embarked_missing	0.856094
12	CabinLetterImputed	0.855637
13	CabinLetter_missing	0.855744
14	Fare	0.855302
15	CabinLetter_A	0.854307
16	CabinLetter_B	0.853215
17	CabinNumber	0.852896
18	Embarked_C	0.851377
19	Embarked_Q	0.851324
20	CabinLetter_C	0.849972
21	AgeImputed	0.848673
22	CabinLetter_G	0.847432
23	Parch	0.845842

Plot results

import matplotlib.pyplot as plt
%matplotlib inline

chart_x = list(range(1, number_of_features+1))

plt.plot(chart_x, roc_auc_by_feature_number,
        label = 'ROC AUC')

plt.xlabel('Number of features')
plt.ylabel('Accuracy (ROC AUC)')
plt.legend()
plt.grid(True)

plt.show()

From the above results it looks like we could use just 5-7 features in this model. It may also be worth examining the same method using other performance scores (such as simple accuracy, or f1) in place of ROC AUC.

Note that accuracy of the model appears to decline with a greater number of features.