import numpy as np

np.random.seed(12)
num_observations = 5000

x1 = np.random.multivariate_normal([0, 0], [[1, .75],[.75, 1]], num_observations)
x2 = np.random.multivariate_normal([1, 4], [[1, .75],[.75, 1]], num_observations)

simulated_separableish_features = np.vstack((x1, x2)).astype(np.float32)
simulated_labels = np.hstack((np.zeros(num_observations),
                              np.ones(num_observations)))

def sigmoid(z):
    return 1 / (1 + np.exp(-z))

def log_likelihood(features, target, weights):
    scores = np.dot(features, weights)
    ll = np.sum( target*scores - np.log(1 + np.exp(scores)) )
    return ll

def logistic_regression(features, target, num_steps, learning_rate, add_intercept = False):
    if add_intercept:
        intercept = np.ones((features.shape[0], 1))
        features = np.hstack((intercept, features))
        
    weights = np.zeros(features.shape[1])
    
    for step in xrange(num_steps):
        scores = np.dot(features, weights)
        predictions = sigmoid(scores)

        # Update weights with gradient
        output_error_signal = target - predictions
        gradient = np.dot(features.T, output_error_signal)
        weights += learning_rate * gradient
        
        # Print log-likelihood every so often
        if step % 10000 == 0:
            print log_likelihood(features, target, weights)
        
    return weights

weights = logistic_regression(simulated_separableish_features, simulated_labels,
     num_steps = 300000, learning_rate = 5e-5, add_intercept=True)

data_with_intercept = np.hstack((np.ones((simulated_separableish_features.shape[0], 1)),
                                 simulated_separableish_features))
final_scores = np.dot(data_with_intercept, weights)
preds = np.round(sigmoid(final_scores))

print 'Accuracy from scratch: {0}'.format((preds == simulated_labels).sum().astype(float) / len(preds))
print 'Accuracy from sk-learn: {0}'.format(clf.score(simulated_separableish_features, simulated_labels))