def _configure_thresholds(self):
# Each bootstrap sample splits the reference samples into a sub-reference sample (x)
# and an extended test window (y). The extended test window will be treated as W overlapping
# test windows of size W (so 2W-1 test samples in total)
w_size = self.window_size
etw_size = 2 * w_size - 1 # etw = extended test window
nkc_size = self.n - self.n_kernel_centers # nkc = non-kernel-centers
rw_size = nkc_size - etw_size # rw = ref-window
perms = [torch.randperm(nkc_size) for _ in range(self.n_bootstraps)]
x_inds_all = [perm[:rw_size] for perm in perms]
y_inds_all = [perm[rw_size:] for perm in perms]
# For stability in high dimensions we don't divide H by (pi*sigma^2)^(d/2)
# Results in an alternative test-stat of LSDD*(pi*sigma^2)^(d/2). Same p-vals etc.
H = GaussianRBF(np.sqrt(2.) * self.kernel.sigma)(self.kernel_centers,
self.kernel_centers)
# Compute lsdds for first test-window. We infer regularisation constant lambda here.
y_inds_all_0 = [y_inds[:w_size] for y_inds in y_inds_all]
lsdds_0, H_lam_inv = permed_lsdds(
self.k_xc,
x_inds_all,
y_inds_all_0,
H,
lam_rd_max=self.lambda_rd_max,
)
# Can compute threshold for first window
thresholds = [quantile(lsdds_0, 1 - self.fpr)]
# And now to iterate through the other W-1 overlapping windows
p_bar = tqdm(range(1, w_size),
"Computing thresholds") if self.verbose else range(
1, w_size)
for w in p_bar:
y_inds_all_w = [y_inds[w:(w + w_size)] for y_inds in y_inds_all]
lsdds_w, _ = permed_lsdds(self.k_xc,
x_inds_all,
y_inds_all_w,
H,
H_lam_inv=H_lam_inv)
thresholds.append(quantile(lsdds_w, 1 - self.fpr))
x_inds_all = [
x_inds_all[i] for i in range(len(x_inds_all))
if lsdds_w[i] < thresholds[-1]
]
y_inds_all = [
y_inds_all[i] for i in range(len(y_inds_all))
if lsdds_w[i] < thresholds[-1]
]
self.thresholds = thresholds
self.H_lam_inv = H_lam_inv
def test_quantile(quantile_params):
type, sorted = quantile_params
sample = (0.5 + torch.arange(1e6)) / 1e6
if not sorted:
sample = sample[torch.randperm(len(sample))]
np.testing.assert_almost_equal(quantile(sample,
0.001,
type=type,
sorted=sorted),
0.001,
decimal=6)
np.testing.assert_almost_equal(quantile(sample,
0.999,
type=type,
sorted=sorted),
0.999,
decimal=6)
assert quantile(torch.ones(100), 0.42, type=type, sorted=sorted) == 1
with pytest.raises(ValueError):
quantile(torch.ones(10), 0.999, type=type, sorted=sorted)
with pytest.raises(ValueError):
quantile(torch.ones(100, 100), 0.5, type=type, sorted=sorted)
def _configure_thresholds(self):
# Each bootstrap sample splits the reference samples into a sub-reference sample (x)
# and an extended test window (y). The extended test window will be treated as W overlapping
# test windows of size W (so 2W-1 test samples in total)
w_size = self.window_size
etw_size = 2*w_size-1 # etw = extended test window
rw_size = self.n - etw_size # rw = sub-ref window
perms = [torch.randperm(self.n) for _ in range(self.n_bootstraps)]
x_inds_all = [perm[:-etw_size] for perm in perms]
y_inds_all = [perm[-etw_size:] for perm in perms]
if self.verbose:
print("Generating permutations of kernel matrix..")
# Need to compute mmd for each bs for each of W overlapping windows
# Most of the computation can be done once however
# We avoid summing the rw_size^2 submatrix for each bootstrap sample by instead computing the full
# sum once and then subtracting the relavent parts (k_xx_sum = k_full_sum - 2*k_xy_sum - k_yy_sum).
# We also reduce computation of k_xy_sum from O(nW) to O(W) by caching column sums
k_full_sum = zero_diag(self.k_xx).sum()
k_xy_col_sums_all = [
self.k_xx[x_inds][:, y_inds].sum(0) for x_inds, y_inds in
(tqdm(zip(x_inds_all, y_inds_all), total=self.n_bootstraps) if self.verbose else
zip(x_inds_all, y_inds_all))
]
k_xx_sums_all = [(
k_full_sum - zero_diag(self.k_xx[y_inds][:, y_inds]).sum() - 2*k_xy_col_sums.sum()
)/(rw_size*(rw_size-1)) for y_inds, k_xy_col_sums in zip(y_inds_all, k_xy_col_sums_all)]
k_xy_col_sums_all = [k_xy_col_sums/(rw_size*w_size) for k_xy_col_sums in k_xy_col_sums_all]
# Now to iterate through the W overlapping windows
thresholds = []
p_bar = tqdm(range(w_size), "Computing thresholds") if self.verbose else range(w_size)
for w in p_bar:
y_inds_all_w = [y_inds[w:w+w_size] for y_inds in y_inds_all] # test windows of size w_size
mmds = [(
k_xx_sum +
zero_diag(self.k_xx[y_inds_w][:, y_inds_w]).sum()/(w_size*(w_size-1)) -
2*k_xy_col_sums[w:w+w_size].sum()
) for k_xx_sum, y_inds_w, k_xy_col_sums in zip(k_xx_sums_all, y_inds_all_w, k_xy_col_sums_all)
]
mmds = torch.tensor(mmds) # an mmd for each bootstrap sample
# Now we discard all bootstrap samples for which mmd is in top (1/ert)% and record the thresholds
thresholds.append(quantile(mmds, 1-self.fpr))
y_inds_all = [y_inds_all[i] for i in range(len(y_inds_all)) if mmds[i] < thresholds[-1]]
k_xx_sums_all = [
k_xx_sums_all[i] for i in range(len(k_xx_sums_all)) if mmds[i] < thresholds[-1]
]
k_xy_col_sums_all = [
k_xy_col_sums_all[i] for i in range(len(k_xy_col_sums_all)) if mmds[i] < thresholds[-1]
]
self.thresholds = thresholds