def compute(self):
# from prob_label, get p, rx, cs, n
ns, p, rx, cs = get_ns_model_source(self.prob_label)
r = self.rep
n = self.n
met_func = self.met_func
prob_label = self.prob_label
logger.info("computing. %s. prob=%s, r=%d,\
n=%d" % (met_func.__name__, prob_label, r, n))
with util.ContextTimer() as t:
job_result = met_func(p, rx, cs, n, r)
# create ScalarResult instance
result = SingleResult(job_result)
# submit the result to my own aggregator
self.aggregator.submit_result(result)
func_name = met_func.__name__
logger.info("done. ex1: %s, prob=%s, r=%d, n=%d. Took: %.3g s " %
(func_name, prob_label, r, n, t.secs))
# save result
fname = '%s-%s-n%d_r%d_a%.3f.p' \
%(prob_label, func_name, n, r, alpha )
glo.ex_save_result(ex, job_result, prob_label, fname)
def met_gkcsd_med(p, rx, cond_source, n, r):
"""
KCSD test with Gaussian kernels (for both kernels). Prefix g = Gaussian kernel.
med = Use median heuristic to choose the bandwidths for both kernels.
Compute the median heuristic on the data X and Y separate to get the two
bandwidths.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# median heuristic
sigx = util.pt_meddistance(X, subsample=600, seed=r + 3)
sigy = util.pt_meddistance(Y, subsample=600, seed=r + 38)
# kernels
# k = kernel on X
k = ker.PTKGauss(sigma2=sigx**2)
# l = kernel on Y
l = ker.PTKGauss(sigma2=sigy**2)
# Construct a KCSD test object
kcsdtest = cgof.KCSDTest(p,
k,
l,
alpha=alpha,
n_bootstrap=400,
seed=r + 88)
result = kcsdtest.perform_test(X, Y)
return {
# 'test': kcsdtest,
'test_result': result,
'time_secs': t.secs
}
def perform_test(self, X, Y):
import freqopttest.data as fdata
ds_p = self.ds_p
mmdtest = self.mmdtest
seed = self.seed
with util.ContextTimer() as t:
# split the data
X1, Y1, X2, Y2 = MMDSplitTest._split_half(X,
Y,
seed=self.seed + 330)
# Draw sample from p
Y2_ = ds_p.cond_pair_sample(X2, seed=seed + 13)
real_data = torch.cat([X1, Y1], dim=1).numpy()
model_data = torch.cat([X2, Y2_], dim=1).numpy()
# Run the two-sample test on p_sample and dat
# Make a two-sample test data
tst_data = fdata.TSTData(real_data, model_data)
# Test
results = mmdtest.perform_test(tst_data)
results['time_secs'] = t.secs
return results
def met_gmmd_med(p, rx, cond_source, n, r):
"""
A naive baseline which samples from the conditional density model p to
create a new joint sample. The test is performed with a two-sample MMD
test comparing the two joint samples. Use a Gaussian kernel for both X
and Y with median heuristic.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# median heuristic
sigx = util.pt_meddistance(X, subsample=600, seed=r + 3)
sigy = util.pt_meddistance(Y, subsample=600, seed=r + 38)
# kernels
# k = kernel on X. Need a kernel that can operator on numpy arrays
k = kgof.kernel.KGauss(sigma2=sigx**2)
# l = kernel on Y
l = kgof.kernel.KGauss(sigma2=sigy**2)
# Construct an MMD test object. Require freqopttest package.
mmdtest = cgof.MMDTest(p,
k,
l,
n_permute=400,
alpha=alpha,
seed=r + 37)
result = mmdtest.perform_test(X, Y)
return {
# 'test': mmdtest,
'test_result': result,
'time_secs': t.secs
}
def perform_test(self, X, Y):
with util.ContextTimer() as t:
alpha = self.alpha
n_bootstrap = self.n_bootstrap
n = X.shape[0]
ds = self.p.get_condsource()
test_stat = self.compute_stat(X, Y)
# bootstrapping
sim_stats = torch.zeros(n_bootstrap)
with torch.no_grad():
with util.TorchSeedContext(seed=self.seed):
for i in range(n_bootstrap):
idx = torch.randint(0, n, [n])
X_ = X[idx]
Y_ = ds.cond_pair_sample(X_, self.seed + i)
# Bootstrapped statistic
Hnb = CramerVonMisesTest.Hn(X_, Y_, X, Y)
Hn0b = self.Hn0(X_, Y_, X, Y)
boot_stat = torch.sum((Hnb - Hn0b)**2)
sim_stats[i] = boot_stat
# approximate p-value with the permutations
I = sim_stats > test_stat
pvalue = torch.mean(I.type(torch.float)).item()
results = {
'alpha': self.alpha,
'pvalue': pvalue,
'test_stat': test_stat.item(),
'h0_rejected': pvalue < alpha,
'n_simulate': n_bootstrap,
'time_secs': t.secs,
}
return results
def perform_test(self, X, Y):
"""
X: Torch tensor of size n x dx
Y: Torch tensor of size n x dy
perform the goodness-of-fit test and return values computed in a
dictionary:
{
alpha: 0.01,
pvalue: 0.0002,
test_stat: 2.3,
h0_rejected: True,
time_secs: ...
}
"""
with util.ContextTimer() as t:
alpha = self.alpha
stat = self.compute_stat(X, Y)
pvalue = (1 - dists.Normal(0, 1).cdf(stat)).item()
results = {
'alpha': self.alpha,
'pvalue': pvalue,
'test_stat': stat.item(),
'h0_rejected': pvalue < alpha,
'time_secs': t.secs,
}
return results
def met_gmmd_split_med(p, rx, cond_source, n, r):
"""
Same as met_gmmd_med but perform data splitting to guarantee that the
two sets of samples are independent. Effective sample size is then n/2.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# median heuristic
sigx = util.pt_meddistance(X, subsample=600, seed=r + 4)
sigy = util.pt_meddistance(Y, subsample=600, seed=r + 39)
# kernels
# k = kernel on X. Need a kernel that can operator on numpy arrays
k = kgof.kernel.KGauss(sigma2=sigx**2)
# l = kernel on Y
l = kgof.kernel.KGauss(sigma2=sigy**2)
# Construct an MMD test object. Require freqopttest package.
mmdtest = cgof.MMDSplitTest(p,
k,
l,
n_permute=400,
alpha=alpha,
seed=r + 47)
result = mmdtest.perform_test(X, Y)
return {
# 'test': mmdtest,
'test_result': result,
'time_secs': t.secs
}
def perform_test(self, X, Y):
with util.ContextTimer() as t:
alpha = self.alpha
stat = self.compute_stat(X, Y)
pvalue = (1 - dists.Normal(0, 1).cdf(stat)).item()
results = {
'alpha': self.alpha,
'pvalue': pvalue,
'test_stat': stat.item(),
'h0_rejected': pvalue < alpha,
'time_secs': t.secs,
}
return results
def met_zheng_cdf(p, rx, cond_source, n, r):
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# the test
zheng_cdf = cgof.ZhengCDFTest(p, alpha)
result = zheng_cdf.perform_test(X, Y)
return {
# 'test': zheng_test,
'test_result': result,
'time_secs': t.secs
}
def perform_test(self,
X,
Y,
return_simulated_stats=False,
return_ustat_gram=False):
"""
X,Y: torch tensors.
return_simulated_stats: If True, also include the boostrapped
statistics in the returned dictionary.
"""
with util.ContextTimer() as t:
alpha = self.alpha
n_bootstrap = self.n_bootstrap
n = X.shape[0]
test_stat, H = self.compute_stat(X, Y, return_ustat_gram=True)
# bootstrapping
sim_stats = torch.zeros(n_bootstrap)
mult_dist = dists.multinomial.Multinomial(total_count=n,
probs=torch.ones(n) / n)
with torch.no_grad():
with util.TorchSeedContext(seed=self.seed):
for i in range(n_bootstrap):
W = mult_dist.sample()
Wt = (W - 1.0) / n
# Bootstrapped statistic
boot_stat = n * (H.matmul(Wt).dot(Wt) -
torch.diag(H).dot(Wt**2))
sim_stats[i] = boot_stat
# approximate p-value with the permutations
I = sim_stats > test_stat
pvalue = torch.mean(I.type(torch.float)).item()
results = {
'alpha': self.alpha,
'pvalue': pvalue,
'test_stat': test_stat.item(),
'h0_rejected': pvalue < alpha,
'n_simulate': n_bootstrap,
'time_secs': t.secs,
}
if return_simulated_stats:
results['sim_stats'] = sim_stats.detach().numpy()
if return_ustat_gram:
results['H'] = H
return results
def met_zhengkl_gh(p, rx, cond_source, n, r):
"""
Zheng 2000 test implemented with Gauss Hermite quadrature.
"""
X, Y = sample_xy(rx, cond_source, n, r)
rate = (cond_source.dx() + cond_source.dy()) * 4. / 5
# start timing
with util.ContextTimer() as t:
# the test
zheng_gh = cgof.ZhengKLTestGaussHerm(p, alpha, rate=rate)
result = zheng_gh.perform_test(X, Y)
return {
# 'test': zheng_test,
'test_result': result,
'time_secs': t.secs
}
def met_zhengkl_mc(p, rx, cond_source, n, r):
"""
Zheng 2000 test implemented with Monte Carlo integration.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# number of Monte Carlo particles
n_mc = 10000
# the test
zheng_mc = cgof.ZhengKLTestMC(p, alpha, n_mc=n_mc)
result = zheng_mc.perform_test(X, Y)
return {
# 'test': zheng_test,
'test_result': result,
'time_secs': t.secs
}
def met_gfscd_J1_rand(p, rx, cond_source, n, r, J=1):
"""
FSCD test with Gaussian kernels on both X and Y.
* Use J=1 random test location by default.
* The test locations are drawn from a Gaussian fitted to the data drawn
from rx.
* Bandwithds of the Gaussian kernels are determined by the median
heuristic.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
tr, te = cdat.CondData(X, Y).split_tr_te(tr_proportion=0.3)
Xtr, Ytr = tr.xy()
# fit a Gaussian and draw J locations
npV = util.fit_gaussian_sample(Xtr.detach().numpy(), J, seed=r + 750)
V = torch.tensor(npV, dtype=torch.float)
# median heuristic
sigx = util.pt_meddistance(X, subsample=600, seed=2 + r)
sigy = util.pt_meddistance(Y, subsample=600, seed=93 + r)
# kernels
# k = kernel on X
k = ker.PTKGauss(sigma2=sigx**2)
# l = kernel on Y
l = ker.PTKGauss(sigma2=sigy**2)
# Construct a FSCD test object
fscdtest = cgof.FSCDTest(p,
k,
l,
V,
alpha=alpha,
n_bootstrap=400,
seed=r + 8)
# test on the full samples
result = fscdtest.perform_test(X, Y)
return {
# 'test': fscdtest,
'test_result': result,
'time_secs': t.secs
}
def met_cramer_vm(p, rx, cond_source, n, r):
"""
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# Construct a CramerVonMisesTest test object
cvm = cgof.CramerVonMisesTest(p,
alpha=alpha,
n_bootstrap=200,
seed=r + 88)
result = cvm.perform_test(X, Y)
return {
# 'test': kcsdtest,
'test_result': result,
'time_secs': t.secs
}
def met_zhengkl(p, rx, cond_source, n, r):
"""
"Zheng 2000, A CONSISTENT TEST OF CONDITIONAL PARAMETRIC DISTRIBUTIONS",
which uses the first order approximation of KL divergence as the decision
criterion.
Use cgoftest.ZhengKLTest.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# the test
zheng_test = cgof.ZhengKLTest(p, alpha)
result = zheng_test.perform_test(X, Y)
return {
# 'test': zheng_test,
'test_result': result,
'time_secs': t.secs
}
def met_gkcsd_opt_tr50(p, rx, cond_source, n, r, tr_proportion=0.5):
"""
KCSD test with Gaussian kernels (for both kernels).
Optimize the kernel bandwidths by maximizing the power criterin of the
KCSD test.
med = Use median heuristic to choose the bandwidths for both kernels.
Compute the median heuristic on the data X and Y separate to get the two
bandwidths.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# median heuristic
sigx = util.pt_meddistance(X, subsample=600, seed=r + 7)
sigy = util.pt_meddistance(Y, subsample=600, seed=r + 99)
# kernels
# k = kernel on X
k = ker.PTKGauss(sigma2=sigx**2)
# l = kernel on Y
l = ker.PTKGauss(sigma2=sigy**2)
# split the data
cd = cdat.CondData(X, Y)
tr, te = cd.split_tr_te(tr_proportion=tr_proportion)
# training data
Xtr, Ytr = tr.xy()
# abs_min, abs_max = torch.min(Xtr).item(), torch.max(Xtr).item()
# abs_stdx = torch.std(Xtr).item()
# abs_stdy = torch.std(Ytr).item()
kcsd_pc = cgof.KCSDPowerCriterion(p, k, l, Xtr, Ytr)
max_iter = 100
# learning rate
lr = 1e-3
# regularization in the power criterion
reg = 1e-3
# constraint satisfaction function
def con_f(params):
ksigma2 = params[0]
lsigma2 = params[1]
ksigma2.data.clamp_(min=1e-1, max=10 * sigx**2)
lsigma2.data.clamp_(min=1e-1, max=10 * sigy**2)
kcsd_pc.optimize_params([k.sigma2, l.sigma2],
constraint_f=con_f,
lr=lr,
reg=reg,
max_iter=max_iter)
# Construct a KCSD test object
kcsdtest = cgof.KCSDTest(p,
k,
l,
alpha=alpha,
n_bootstrap=400,
seed=r + 88)
Xte, Yte = te.xy()
# test on the test set
result = kcsdtest.perform_test(Xte, Yte)
return {
# 'test': kcsdtest,
'test_result': result,
'time_secs': t.secs
}
def met_gfscd_J1_opt_tr50(p, rx, cond_source, n, r, J=1, tr_proportion=0.5):
"""
FSCD test with Gaussian kernels on both X and Y.
Optimize both Gaussian bandwidhts and the test locations by maximizing
the test power.
The proportion of the training data used for the optimization is
controlled by tr_proportion.
"""
X, Y = sample_xy(rx, cond_source, n, r)
# start timing
with util.ContextTimer() as t:
# split the data
cd = cdat.CondData(X, Y)
tr, te = cd.split_tr_te(tr_proportion=tr_proportion)
# training data
Xtr, Ytr = tr.xy()
# fit a Gaussian and draw J locations as an initial point for V
npV = util.fit_gaussian_sample(Xtr.detach().numpy(), J, seed=r + 75)
V = torch.tensor(npV, dtype=torch.float)
# median heuristic
sigx = util.pt_meddistance(X, subsample=600, seed=30 + r)
sigy = util.pt_meddistance(Y, subsample=600, seed=40 + r)
# kernels
# k = kernel on X
k = ker.PTKGauss(sigma2=sigx**2)
# l = kernel on Y
l = ker.PTKGauss(sigma2=sigy**2)
abs_min, abs_max = torch.min(Xtr).item(), torch.max(Xtr).item()
abs_std = torch.std(Xtr).item()
# parameter tuning
fscd_pc = cgof.FSCDPowerCriterion(p, k, l, Xtr, Ytr)
max_iter = 200
# learning rate
lr = 1e-2
# regularization parameter when forming the power criterion
reg = 1e-4
# constraint satisfaction function
def con_f(params, V):
ksigma2 = params[0]
lsigma2 = params[1]
ksigma2.data.clamp_(min=1e-1, max=10 * sigx**2)
lsigma2.data.clamp_(min=1e-1, max=10 * sigy**2)
V.data.clamp_(min=abs_min - 2.0 * abs_std,
max=abs_max + 2.0 * abs_std)
# do the optimization. Parameters are optimized in-place
fscd_pc.optimize_params([k.sigma2, l.sigma2],
V,
constraint_f=con_f,
lr=lr,
reg=reg,
max_iter=max_iter)
# Now that k, l, and V are optimized. Construct a FSCD test object
fscdtest = cgof.FSCDTest(p,
k,
l,
V,
alpha=alpha,
n_bootstrap=400,
seed=r + 8)
Xte, Yte = te.xy()
# test only on the test samples
result = fscdtest.perform_test(Xte, Yte)
return {
# 'test': fscdtest,
'test_result': result,
'time_secs': t.secs
}