def test_additivity_with_weights(data, split_index):
"""
Test the additive propery of the KDE.
"""
x = np.linspace(-10, 15)
weights = np.arange(len(data)) + 1
weights = weights / np.sum(weights)
# Fit to add data
y = TreeKDE("epa").fit(data, weights).evaluate(x)
# Split up the data and the weights
data = list(data)
weights = list(weights)
data_first_split = data[:split_index]
data_second_split = data[split_index:]
weights_first_split = weights[:split_index]
weights_second_split = weights[split_index:]
# Fit to splits, and compensate for smaller data using weights
y_1 = TreeKDE("epa").fit(
data_first_split,
weights_first_split).evaluate(x) * sum(weights_first_split)
y_2 = TreeKDE("epa").fit(
data_second_split,
weights_second_split).evaluate(x) * sum(weights_second_split)
# Additive property of the functions
assert np.allclose(y, y_1 + y_2)
def test_additivity(data, split_index):
"""
Test the additive propery of the KDE.
"""
x = np.linspace(-10, 10)
# Fit to add data
y = TreeKDE("epa").fit(data).evaluate(x)
# Fit to splits, and compensate for smaller data using weights
weight_1 = split_index / len(data)
y_1 = TreeKDE("epa").fit(data[:split_index]).evaluate(x) * weight_1
weight_2 = (len(data) - split_index) / len(data)
y_2 = TreeKDE("epa").fit(data[split_index:]).evaluate(x) * weight_2
# Additive property of the functions
assert np.allclose(y, y_1 + y_2)
def test_against_R_density(kernel, bw, n, expected_result):
"""
Test against the following function call in R:
d <- density(c(0, 0.1, 1), kernel="{kernel}", bw={bw},
n={n}, from=-1, to=1);
d$y
"""
data = np.array([0, 0.1, 1])
x = np.linspace(-1, 1, num=n)
y = TreeKDE(kernel, bw=bw).fit(data).evaluate(x)
assert np.allclose(y, expected_result, atol=10**(-2.7))
def test_against_scipy_density(bw, n, expected_result):
"""
Test against the following function call in SciPy:
data = np.array([0, 0.1, 1])
x = np.linspace(-1, 1, {n})
bw = {bw}/np.asarray(data).std(ddof=1)
density_estimate = gaussian_kde(dataset = data, bw_method = bw)
y = density_estimate.evaluate(x)
# Note that scipy weights its bandwidth by the covariance of the
# input data. To make the results comparable to the other methods,
# we divide the bandwidth by the sample standard deviation here.
"""
data = np.array([0, 0.1, 1])
x = np.linspace(-1, 1, num=n)
y = TreeKDE(kernel="gaussian", bw=bw).fit(data).evaluate(x)
error = np.mean((y - expected_result)**2)
assert error < 1e-10