def test_ksd():
"""Test quadratic time KSD
Following the example in:
https://github.com/wittawatj/kernel-gof/blob/master/ipynb/gof_kernel_stein.ipynb
"""
seed = 42
d = 2 # dimensionality
n = 800 # samples
# Density
mean = np.zeros(d)
variance = 1.0
p = density.IsotropicNormal(mean, variance)
# Samples from same density
ds = data.DSIsotropicNormal(mean, variance)
samples = ds.sample(n, seed=seed + 1)
# Gaussian kernel with median heuristic
sig2 = util.meddistance(samples.data(), subsample=1000)**2
k = kernel.KGauss(sig2)
print(f"Kernel bandwidth: {sig2}")
# KSD
bootstrapper = gof.bootstrapper_rademacher
kstein = gof.KernelSteinTest(p,
k,
bootstrapper=bootstrapper,
alpha=0.01,
n_simulate=500,
seed=seed + 1)
test_result = kstein.perform_test(samples,
return_simulated_stats=False,
return_ustat_gram=False)
print(test_result)
assert test_result["h0_rejected"] == False
# KSD with samples from different density
ds = data.DSLaplace(d=d, loc=0, scale=1.0 / np.sqrt(2))
samples = ds.sample(n, seed=seed + 1)
sig2 = util.meddistance(samples.data(), subsample=1000)**2
print(f"Kernel bandwidth: {sig2}")
k = kernel.KGauss(sig2)
bootstrapper = gof.bootstrapper_rademacher
kstein = gof.KernelSteinTest(p,
k,
bootstrapper=bootstrapper,
alpha=0.01,
n_simulate=500,
seed=seed + 1)
test_result = kstein.perform_test(samples,
return_simulated_stats=False,
return_ustat_gram=False)
print(test_result)
assert test_result["h0_rejected"] == True
def job_kstein_med(p, data_source, tr, te, r):
"""
Kernel Stein discrepancy test of Liu et al., 2016 and Chwialkowski et al.,
2016. Use full sample. Use Gaussian kernel.
"""
# full data
data = tr + te
X = data.data()
with util.ContextTimer() as t:
# median heuristic
med = util.meddistance(X, subsample=1000)
k = kernel.KGauss(med**2)
kstein = gof.KernelSteinTest(p,
k,
alpha=alpha,
n_simulate=1000,
seed=r)
kstein_result = kstein.perform_test(data)
return {"test_result": kstein_result, "time_secs": t.secs}
def job_kstein_imq(p, data_source, tr, te, r):
"""
Kernel Stein discrepancy test of Liu et al., 2016 and Chwialkowski et al.,
2016. Use full sample. Use the inverse multiquadric kernel (IMQ) studied
in
Measuring Sample Quality with Kernels
Gorham and Mackey 2017.
Parameters are fixed to the recommented values: beta = b = -0.5, c = 1.
"""
# full data
data = tr + te
X = data.data()
with util.ContextTimer() as t:
k = kernel.KIMQ(b=-0.5, c=1.0)
kstein = gof.KernelSteinTest(p,
k,
alpha=alpha,
n_simulate=1000,
seed=r)
kstein_result = kstein.perform_test(data)
return {"test_result": kstein_result, "time_secs": t.secs}