expt_lmdk_sel: Testing the Pareto principle

code/lib/exp_mech.py

@@ -62,6 +62,47 @@ def exponential(x, R, u, delta, epsilon):
     return np.array([]), pr
 
 
+'''
+  The exponential mechanism.
+
+  Parameters:
+    x - The data.
+    R - The possible outputs.
+    u - The scoring function.
+    delta - The sensitivity of the scoring function.
+    epsilon - The privacy budget.
+  Returns:
+    res - A randomly sampled output.
+    pr - The PDF of all possible outputs.
+'''
+def exponential_pareto(x, R, u, delta, epsilon):
+  # Calculate the score for each element of R
+  scores = [u(x, r) for r in R]
+  # Keep the top 20%
+  n = int(len(scores)*.2)
+  scores = np.sort(scores)[-n : ]
+  # Normalize the scores between 0 and 1
+  # (the higher, the better the utility)
+  scores = 1 - (scores - np.min(scores))/(np.max(scores) - np.min(scores))
+
+  # Calculate the probability for each element, based on its score
+  pr = [np.exp(epsilon*score/(2*delta)) for score in scores]
+
+  # Normalize the probabilities so that they sum to 1
+  pr = pr/np.linalg.norm(pr, ord = 1)
+
+  # Debugging
+  # print(R[np.argmax(pr)], pr.max(), scores[np.argmax(pr)])
+  # print(R[np.argmin(pr)], pr.min(), scores[np.argmin(pr)])
+  # print(abs(pr.max() - pr.min()), abs(scores[np.argmax(pr)] - scores[np.argmin(pr)]))
+
+  # Choose an element from R based on the probabilities
+  if len(pr) > 0:
+    return R[np.random.choice(range(n), 1, p = pr)[0]], pr
+  else:
+    return np.array([]), pr
+
+
 def main():
   start, end = 1.0, 10.0
   scale = 1.0