def test_from_samples(self):
"""
Example 1 (maxbel) and example 7 (ordered) from:
T. Denoeux (2006), "Constructing belief functions from sample data using multinomial confidence regions",
International Journal of Approximate Reasoning 42, 228-252.
Example 6 (mcd) from:
A. Aregui, T. Denoeux (2008), "Constructing consonant belief functions from sample data using confidence sets of pignistic probabilities",
International Journal of Approximate Reasoning 49, 575-594.
"""
precipitation_data = {1: 48, 2: 17, 3: 19, 4: 11, 5: 6, 6: 9}
failure_mode_data = {
1: 5,
2: 11,
3: 19,
4: 30,
5: 58,
6: 67,
7: 92,
8: 118,
9: 173,
10: 297
}
psych_data = {1: 91, 2: 49, 3: 37, 4: 43}
# maxbel
m = MassFunction.from_samples(psych_data, method='maxbel', alpha=0.05)
p_lower, p_upper = MassFunction._confidence_intervals(psych_data, 0.05)
def p_lower_set(hs):
l = u = 0
for h in psych_data.keys():
if h in hs:
l += p_lower[h]
else:
u += p_upper[h]
return max(l, 1 - u)
bel_sum = 0
for h in m.all():
bel = m.bel(h)
bel_sum += bel
self.assertLessEqual(bel - 0.00001,
p_lower_set(h)) # constraint (24)
self.assertTrue(
abs(1 - sum(m.values())) <
0.0001) #self.assertEqual(1, sum(m.values()) ) # constraint (25)
self.assertGreaterEqual(min(m.values()), 0) # constraint (26)
self.assertGreaterEqual(bel_sum, 6.23) # optimization criterion
# maxbel-ordered
m = MassFunction.from_samples(precipitation_data,
method='maxbel-ordered',
alpha=0.05)
self.assertAlmostEqual(0.32, m[(1, )], 2)
self.assertAlmostEqual(0.085, m[(2, )], 3)
self.assertAlmostEqual(0.098, m[(3, )], 3)
self.assertAlmostEqual(0.047, m[(4, )], 3)
self.assertAlmostEqual(0.020, m[(5, )], 3)
self.assertAlmostEqual(0.035, m[(6, )], 3)
self.assertAlmostEqual(0.13, m[range(1, 5)], 2)
self.assertAlmostEqual(0.11, m[range(1, 6)], 2)
self.assertAlmostEqual(0.012, m[range(2, 6)], 2)
self.assertAlmostEqual(0.14, m[range(2, 7)], 2)
# mcd
poss = {
1: 0.171,
2: 0.258,
3: 0.353,
4: 0.462,
5: 0.688,
6: 0.735,
7: 0.804,
8: 0.867,
9: 0.935,
10: 1.0
} # 8: 0.873
m = MassFunction.from_samples(failure_mode_data,
method='mcd',
alpha=0.1)
self._assert_equal_belief(MassFunction.from_possibility(poss), m, 1)
# mcd-approximate
m = MassFunction.from_samples(failure_mode_data,
method='mcd-approximate',
alpha=0.1)
poss = {
1: 0.171,
2: 0.258,
3: 0.353,
4: 0.462,
5: 0.688,
6: 0.747,
7: 0.875,
8: 0.973,
9: 1.0,
10: 1.0
}
self._assert_equal_belief(MassFunction.from_possibility(poss), m, 2)
# bayesian
m = MassFunction.from_samples(precipitation_data,
method='bayesian',
s=0)
for e, n in precipitation_data.items():
self.assertEqual(n / float(sum(precipitation_data.values())),
m[(e, )])
# idm
m = MassFunction.from_samples(precipitation_data, method='idm', s=1)
self.assertAlmostEqual(
1. / float(sum(precipitation_data.values()) + 1),
m[MassFunction._convert(precipitation_data.keys())])
for e, n in precipitation_data.items():
self.assertAlmostEqual(
n / float(sum(precipitation_data.values()) + 1), m[(e, )])
def test_from_samples(self):
"""
Example 1 (maxbel) and example 7 (ordered) from:
T. Denoeux (2006), "Constructing belief functions from sample data using multinomial confidence regions",
International Journal of Approximate Reasoning 42, 228-252.
Example 6 (mcd) from:
A. Aregui, T. Denoeux (2008), "Constructing consonant belief functions from sample data using confidence sets of pignistic probabilities",
International Journal of Approximate Reasoning 49, 575-594.
"""
precipitation_data = {1:48, 2:17, 3:19, 4:11, 5:6, 6:9}
failure_mode_data = {1:5, 2:11, 3:19, 4:30, 5:58, 6:67, 7:92, 8:118, 9:173, 10:297}
psych_data = {1:91, 2:49, 3:37, 4:43}
# maxbel
m = MassFunction.from_samples(psych_data, method='maxbel', alpha=0.05)
p_lower, p_upper = MassFunction._confidence_intervals(psych_data, 0.05)
def p_lower_set(hs):
l = u = 0
for h in psych_data.keys():
if h in hs:
l += p_lower[h]
else:
u += p_upper[h]
return max(l, 1 - u)
bel_sum = 0
for h in m.all():
bel = m.bel(h)
bel_sum += bel
self.assertLessEqual(bel, p_lower_set(h)) # constraint (24)
self.assertEqual(1, sum(m.values())) # constraint (25)
self.assertGreaterEqual(min(m.values()), 0) # constraint (26)
self.assertGreaterEqual(bel_sum, 6.23) # optimization criterion
# maxbel-ordered
m = MassFunction.from_samples(precipitation_data, method='maxbel-ordered', alpha=0.05)
self.assertAlmostEqual(0.32, m[(1,)], 2)
self.assertAlmostEqual(0.085, m[(2,)], 3)
self.assertAlmostEqual(0.098, m[(3,)], 3)
self.assertAlmostEqual(0.047, m[(4,)], 3)
self.assertAlmostEqual(0.020, m[(5,)], 3)
self.assertAlmostEqual(0.035, m[(6,)], 3)
self.assertAlmostEqual(0.13, m[range(1, 5)], 2)
self.assertAlmostEqual(0.11, m[range(1, 6)], 2)
self.assertAlmostEqual(0.012, m[range(2, 6)], 2)
self.assertAlmostEqual(0.14, m[range(2, 7)], 2)
# mcd
poss = {1: 0.171, 2: 0.258, 3: 0.353, 4: 0.462, 5: 0.688, 6: 0.735, 7: 0.804, 8: 0.867, 9: 0.935, 10: 1.0} # 8: 0.873
m = MassFunction.from_samples(failure_mode_data, method='mcd', alpha=0.1)
self._assert_equal_belief(MassFunction.from_possibility(poss), m, 1)
# mcd-approximate
m = MassFunction.from_samples(failure_mode_data, method='mcd-approximate', alpha=0.1)
poss = {1: 0.171, 2: 0.258, 3: 0.353, 4: 0.462, 5: 0.688, 6: 0.747, 7: 0.875, 8: 0.973, 9: 1.0, 10: 1.0}
self._assert_equal_belief(MassFunction.from_possibility(poss), m, 2)
# bayesian
m = MassFunction.from_samples(precipitation_data, method='bayesian', s=0)
for e, n in precipitation_data.items():
self.assertEqual(n / float(sum(precipitation_data.values())), m[(e,)])
# idm
m = MassFunction.from_samples(precipitation_data, method='idm', s=1)
self.assertAlmostEqual(1. / float(sum(precipitation_data.values()) + 1), m[MassFunction._convert(precipitation_data.keys())])
for e, n in precipitation_data.items():
self.assertAlmostEqual(n / float(sum(precipitation_data.values()) + 1), m[(e,)])
