finetuned the parameters of numerical algorithms, used good asymptoti…

…c approximation in some regimes. now passing fdp to approxdp conversion test.

autodp/converter.py

@@ -637,15 +637,23 @@ def normal_equation(logx):
             else:
                 return min(abs(high),abs(low))
 
+        def normal_equation_loglogx(loglogx):
+            logx = np.exp(loglogx)
+            return normal_equation(logx)
+
         # find x such that y = 1-\delta
         tmp = fun1(np.log(1 - delta))
-        bound1 = np.log(-tmp - tmp**2 / 2 - tmp**3 / 6)
-        #bound1 = np.log(1-np.exp(fun1(np.log(1-delta))))
+        if abs(tmp) < 1e-5:
+            bound1 = np.log(-tmp - tmp**2 / 2 - tmp**3 / 6)
+        else:
+            bound1 = np.log(1-np.exp(fun1(np.log(1-delta))))
         #results = minimize_scalar(normal_equation, bounds=[-np.inf,0], bracket=[-1,-2])
         results = minimize_scalar(normal_equation, method="Bounded", bounds=[bound1,0],
-                                  options={'xatol': 1e-6, 'maxiter': 500, 'disp': 0})
+                                  options={'xatol': 1e-10, 'maxiter': 500, 'disp': 0})
         if results.success:
-            if abs(results.fun) > 1e-4:
+            if abs(results.fun) > 1e-4 and abs(results.x)>1e-10:
+                # This means that we hit xatol (x is close to 0, but
+                # the function value is not close to 0) In this case let's do an even larger search.
                 raise RuntimeError("'find_logx' fails to find the tangent line.")
             else:
                 return results.x

autodp/utils.py

@@ -94,7 +94,7 @@ def stable_norm_ppf_one_minus_x(logx):
     :param logx:
     :return: ppf(1-e^logx)
     """
-    if logx < -20:
+    if logx < -30:
         # asymptotic approximation
         norm_ppf_one_minus_x = np.sqrt(-2 * logx - np.log(-2*logx) - np.log(2*np.pi))
     # # if logx < -10:

test/unit_test_fdp_to_approxdp_conversion.py

@@ -6,7 +6,7 @@
 from absl.testing import absltest
 from absl.testing import parameterized
 
-params = [0.05, 0.1, 0.2, 0.5,1.0, 2.0, 5.0, 10.0]
+params = [0.05, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, 10.0]
 
 
 def _fdp_conversion(sigma):
@@ -32,7 +32,7 @@ def _fdp_conversion(sigma):
     return rel_diff
 
 
-_fdp_conversion(0.05)
+_fdp_conversion(1.0)
 
 class Test_approxDP2fDP_Conversion(parameterized.TestCase):