73. Machine learning: neural networks

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The last of our machine learning methods that we will look at in this introduction is neural networks.

Neural networks power much of modern image and voice recongition. They can cope with highly complex data, but often take large amounts of data to train well. There are many parameters that can be changes, so fine-tuning a neural net can require extensive work. We will not go into all the ways they may be fine-tuned here, but just look at a simple example.

Once again we will re-use our logistic regression model, and replace the model training function with one based on neural networks. Hopefully you now have got the idea that once you set up your machine learning model it is easy to try different machine learning methods in scikitlearn.

# import required modules

from sklearn import datasets
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import numpy as np

def calculate_diagnostic_performance (actual_predicted):
    """ Calculate diagnostic performance.
    Takes a Numpy array of 1 and zero, two columns: actual and predicted
    Note that some statistics are repeats with different names
    (precision = positive_predictive_value and recall = sensitivity).
    Both names are returned
    Returns a dictionary of results:
    1) accuracy: proportion of test results that are correct    
    2) sensitivity: proportion of true +ve identified
    3) specificity: proportion of true -ve identified
    4) positive likelihood: increased probability of true +ve if test +ve
    5) negative likelihood: reduced probability of true +ve if test -ve
    6) false positive rate: proportion of false +ves in true -ve patients
    7) false negative rate:  proportion of false -ves in true +ve patients
    8) positive predictive value: chance of true +ve if test +ve
    9) negative predictive value: chance of true -ve if test -ve
    10) precision = positive predictive value 
    11) recall = sensitivity
    12) f1 = (2 * precision * recall) / (precision + recall)
    13) positive rate = rate of true +ve (not strictly a performance measure)
    # Calculate results
    actual_positives = actual_predicted[:, 0] == 1
    actual_negatives = actual_predicted[:, 0] == 0
    test_positives = actual_predicted[:, 1] == 1
    test_negatives = actual_predicted[:, 1] == 0
    test_correct = actual_predicted[:, 0] == actual_predicted[:, 1]
    accuracy = np.average(test_correct)
    true_positives = actual_positives & test_positives
    true_negatives = actual_negatives & test_negatives
    sensitivity = np.sum(true_positives) / np.sum(actual_positives)
    specificity = np.sum(true_negatives) / np.sum(actual_negatives)
    positive_likelihood = sensitivity / (1 - specificity)
    negative_likelihood = (1 - sensitivity) / specificity
    false_positive_rate = 1 - specificity
    false_negative_rate = 1 - sensitivity
    positive_predictive_value = np.sum(true_positives) / np.sum(test_positives)
    negative_predictive_value = np.sum(true_negatives) / np.sum(test_negatives)
    precision = positive_predictive_value
    recall = sensitivity
    f1 = (2 * precision * recall) / (precision + recall)
    positive_rate = np.mean(actual_predicted[:,1])
    # Add results to dictionary
    performance = {}
    performance['accuracy'] = accuracy
    performance['sensitivity'] = sensitivity
    performance['specificity'] = specificity
    performance['positive_likelihood'] = positive_likelihood
    performance['negative_likelihood'] = negative_likelihood
    performance['false_positive_rate'] = false_positive_rate
    performance['false_negative_rate'] = false_negative_rate
    performance['positive_predictive_value'] = positive_predictive_value
    performance['negative_predictive_value'] = negative_predictive_value
    performance['precision'] = precision
    performance['recall'] = recall
    performance['f1'] = f1
    performance['positive_rate'] = positive_rate

    return performance

def load_data ():
    """Load the data set. Here we load the Breast Cancer Wisconsin (Diagnostic)
    Data Set. Data could be loaded from other sources though the structure
    should be compatible with thi sdata set, that is an object with the 
    following attribtes:
        .data (holds feature data)
        .feature_names (holds feature titles)
        .target_names (holds outcome classification names)
        .target (holds classification as zero-based number)
        .DESCR (holds text-based description of data set)"""
    data_set = datasets.load_breast_cancer()
    return data_set

def normalise (X_train,X_test):
    """Normalise X data, so that training set has mean of zero and standard
    deviation of one"""
    # Initialise a new scaling object for normalising input data
    # Set up the scaler just on the training set
    # Apply the scaler to the training and test sets
    return X_train_std, X_test_std

def print_diagnostic_results (performance):
    """Iterate through, and print, the performance metrics dictionary"""
    print('\nMachine learning diagnostic performance measures:')
    for key, value in performance.items():
        print (key,'= %0.3f' %value) # print 3 decimal places

def split_data (data_set, split=0.25):
    """Extract X and y data from data_set object, and split into tarining and
    test data. Split defaults to 75% training, 25% test if not other value 
    passed to function"""
        X,y,test_size=split, random_state=0)
    return X_train,X_test,y_train,y_test

def test_model(model, X, y):
    """Return predicted y given X (attributes)"""
    y_pred = model.predict(X)
    test_results = np.vstack((y, y_pred)).T
    return test_results

def train_model (X, y):
    """Train the model """
    from sklearn.neural_network import MLPClassifier
    model = MLPClassifier(solver='lbfgs', alpha=1e-8, hidden_layer_sizes=(50, 5),
                        max_iter=100000, shuffle=True, learning_rate_init=0.001,
                        activation='relu', learning_rate='constant', tol=1e-7,
    model.fit(X_train_std, y_train)   
    return model

###### Main code #######

# Load data
data_set = load_data()

# Split data into trainign and test sets
X_train,X_test,y_train,y_test = split_data(data_set, 0.25)

# Normalise data
X_train_std, X_test_std = normalise(X_train,X_test)

# Train model
model = train_model(X_train_std,y_train)

# Produce results for test set
test_results = test_model(model, X_test_std, y_test)

# Measure performance of test set predictions
performance = calculate_diagnostic_performance(test_results)

# Print performance metrics


Machine learning diagnostic performance measures:
accuracy = 0.958
sensitivity = 0.967
specificity = 0.943
positive_likelihood = 17.078
negative_likelihood = 0.035
false_positive_rate = 0.057
false_negative_rate = 0.033
positive_predictive_value = 0.967
negative_predictive_value = 0.943
precision = 0.967
recall = 0.967
f1 = 0.967
positive_rate = 0.629


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