Logistic regression

Language used Python 3

Author: stormy-sandy

Logistic-Regression

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+# Logistic regression implemented from Scratch in Python
+import sys
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def sigmoid(scores):
+    return 1 / (1 + np.exp(-scores))
+
+
+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 range(1,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
+
+
+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)))
+
+plt.figure(figsize=(12, 8))
+plt.scatter(
+    simulated_separableish_features[:, 0],
+    simulated_separableish_features[:, 1],
+    c=simulated_labels,
+    alpha=.4)
+
+plt.show()
+
+# Running the model
+
+weights = logistic_regression(simulated_separableish_features,simulated_labels,num_steps=300000,
+    learning_rate=5e-5,
+    add_intercept=True)
+
+print(weights)