def test_normalizing_constant(self): """check that normalizing_constant returns the correct value for a given bandwidth.""" train_data = np.array([[1,0],[2,0],[3,0]]) bandwidth = 0.25 kde = Kde(train_data, bandwidth) constant = kde.normalizing_constant() expected_constant = 2.54647908 self.assertAlmostEqual(expected_constant, constant, ACCURACY)
def test_log_likelihood(self): """check that log_likelihood returns correct values.""" train_data = np.array([[1,0],[2,0]]) bandwidth = 0.5 points = np.array([[3,0],[4,0]]) kde = Kde(train_data, bandwidth) log_lhood = kde.log_likelihood(points) expected_log_lhood = -12.286938687661852 self.assertAlmostEqual(expected_log_lhood, log_lhood)
def test_log_likelihood(self):
"""check that log_likelihood returns correct values."""
train_data = np.array([[1, 0], [2, 0]])
bandwidth = 0.5
points = np.array([[3, 0], [4, 0]])
kde = Kde(train_data, bandwidth)
log_lhood = kde.log_likelihood(points)
expected_log_lhood = -12.286938687661852
self.assertAlmostEqual(expected_log_lhood, log_lhood)
def test_normalizing_constant(self):
"""check that normalizing_constant returns the correct
value for a given bandwidth."""
train_data = np.array([[1, 0], [2, 0], [3, 0]])
bandwidth = 0.25
kde = Kde(train_data, bandwidth)
constant = kde.normalizing_constant()
expected_constant = 2.54647908
self.assertAlmostEqual(expected_constant, constant, ACCURACY)
def test_density(self): """check that density calculates probabilities correctly.""" train_data = np.array([[1,0],[2,0]]) bandwidth = 0.5 kde = Kde(train_data, bandwidth) test_point = np.array([[2,0]]) probability = kde.density(test_point) expected_probability = 0.36138844478748799 self.assertAlmostEqual(expected_probability, probability, ACCURACY)
def test_density(self):
"""check that density calculates probabilities
correctly."""
train_data = np.array([[1, 0], [2, 0]])
bandwidth = 0.5
kde = Kde(train_data, bandwidth)
test_point = np.array([[2, 0]])
probability = kde.density(test_point)
expected_probability = 0.36138844478748799
self.assertAlmostEqual(expected_probability, probability, ACCURACY)
def log_likelihood(pair, bandwidth): """returns the likelihood of the test data having arisen a kernel trained on the training data with the given bandwidth Parameters ---------- pair : list A list with two entries which contain the training and test data. bandwidth : float This bandwidth is a scalar which is multiplied by the identity matrix to form a bandwidth matrix. This matrix is then used to perform density estimation. """ kde = Kde(pair[0], bandwidth) log_lhood = kde.log_likelihood(pair[1]) return log_lhood