logistic regression

vanilla_logistic_regression.py

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+import numpy as np
+
+"""
+# Logistic Regression
+
+w^T · x = w0 + w1x1 + w2x2 + w3x3
+
+P(A|x) = σ(w^Tx)
+
+# Given data:
+
+D = ((x1, y1), ..., (xn, yn))
+x ∈ R
+y ∈ {0, 1}
+
+
+# Pro's:
+
+- interpretable
+- small # params (d + 1)
+- computationally efficient
+- extensible to multi-class
+
+# Cons
+
+- performance as good as other models
+
+# Maximum Likelihood Estimation MLE
+
+labels y
+input  x
+
+likelihood lw = P(y[i]| x[i], w) * P(y[j] | x[j], w) ... P(y[n] | x[n],w)
+
+in product notation
+
+lw = 
+"""
+
+
+def sigmoid(z):
+    """
+    :param z: w^Tx (scalar)
+    :return: σ(w^Tx) (scalar)
+    """
+    return 1 / (1 + np.exp(-z))