Added customer churn analysis notebook forked from aprial/growth-workshop.

analyses/churn_measurements.py

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+from __future__ import division
+import numpy as np
+
+__author__ = "Eric Chiang"
+__email__  = "eric[at]yhathq.com"
+
+"""
+
+Measurements inspired by Philip Tetlock's "Expert Political Judgment"
+
+Equations take from Yaniv, Yates, & Smith (1991):
+  "Measures of Descrimination Skill in Probabilistic Judgement"
+
+"""
+
+
+def calibration(prob,outcome,n_bins=10):
+    """Calibration measurement for a set of predictions.
+
+    When predicting events at a given probability, how far is frequency
+    of positive outcomes from that probability?
+    NOTE: Lower scores are better
+
+    prob: array_like, float
+        Probability estimates for a set of events
+
+    outcome: array_like, bool
+        If event predicted occurred
+
+    n_bins: int
+        Number of judgement categories to prefrom calculation over.
+        Prediction are binned based on probability, since "descrete" 
+        probabilities aren't required. 
+
+    """
+    prob = np.array(prob)
+    outcome = np.array(outcome)
+
+    c = 0.0
+    # Construct bins
+    judgement_bins = np.arange(n_bins + 1) / n_bins
+    # Which bin is each prediction in?
+    bin_num = np.digitize(prob,judgement_bins)
+    for j_bin in np.unique(bin_num):
+        # Is event in bin
+        in_bin = bin_num == j_bin
+        # Predicted probability taken as average of preds in bin
+        predicted_prob = np.mean(prob[in_bin])
+        # How often did events in this bin actually happen?
+        true_bin_prob = np.mean(outcome[in_bin])
+        # Squared distance between predicted and true times num of obs
+        c += np.sum(in_bin) * ((predicted_prob - true_bin_prob) ** 2)
+    return c / len(prob)
+
+def discrimination(prob,outcome,n_bins=10):
+    """Discrimination measurement for a set of predictions.
+
+    For each judgement category, how far from the base probability
+    is the true frequency of that bin?
+    NOTE: High scores are better
+
+    prob: array_like, float
+        Probability estimates for a set of events
+
+    outcome: array_like, bool
+        If event predicted occurred
+
+    n_bins: int
+        Number of judgement categories to prefrom calculation over.
+        Prediction are binned based on probability, since "descrete" 
+        probabilities aren't required. 
+
+    """
+    prob = np.array(prob)
+    outcome = np.array(outcome)
+
+    d = 0.0
+    # Base frequency of outcomes
+    base_prob = np.mean(outcome)
+    # Construct bins
+    judgement_bins = np.arange(n_bins + 1) / n_bins
+    # Which bin is each prediction in?
+    bin_num = np.digitize(prob,judgement_bins)
+    for j_bin in np.unique(bin_num):
+        in_bin = bin_num == j_bin
+        true_bin_prob = np.mean(outcome[in_bin])
+        # Squared distance between true and base times num of obs
+        d += np.sum(in_bin) * ((true_bin_prob - base_prob) ** 2)
+    return d / len(prob)