def average_pearsonr(mpdists, gpdists):
"""Computes the correlation factor on a per-node basis and then takes the
average.
"""
mpdists = squareform1(mpdists)
gpdists = squareform1(gpdists)
mpdists.sub_(mpdists.mean(axis=1))
gpdists.sub_(gpdists.mean(axis=1))
rs_num = (mpdists * gpdists).sum(axis=1)
rs_denom = (mpdists.norm(dim=1) * gpdists.norm(dim=1))
return (rs_num / rs_denom).mean()
def main():
torch.set_default_dtype(torch.float64)
save_dir = os.path.join(args.output_dir, args.manifold)
check_mkdir(save_dir, increment=False)
# generate the samples on the manifold, uniformly around "origin"
man = build_manifold(args.manifold)[0]
if args.use_rs:
samples = gen_samples_rs(man, args.num_nodes, args.radius)
elif args.use_gen2:
samples = gen_samples2(man, args.num_nodes, args.radius)
else:
samples = gen_samples(man, args.num_nodes, args.radius)
torch.save(samples, os.path.join(save_dir, 'xs.pt'))
dists = squareform1(man.pdist(samples))
plot_distances(dists, save_dir)
# create the graph
g = nx.Graph()
g.add_edges_from(np.argwhere(dists.numpy() < args.radius))
g.remove_edges_from(nx.selfloop_edges(g))
# plots
plot_degree_distribution(g, save_dir)
plot_points(man, samples, args.radius, save_dir)
def grid_fn(fn, man, radius, output_dir):
# sample
xs = fn(man, args.num_nodes, radius)
pdists = man.pdist(xs)
# save and plot the pdists
path = os.path.join(output_dir, 'pdists.npy')
np.save(path, pdists.numpy())
path = os.path.join(output_dir, 'pdists.pdf')
plot_distances(pdists, path, axvline=radius, xmax=2 * radius)
# save and plot the distances from zero too
zeros = man.zero(len(xs))
zero_dists = man.dist(zeros, xs)
path = os.path.join(output_dir, 'zero_dists.npy')
np.save(path, zero_dists)
path = os.path.join(output_dir, 'zero_dists.pdf')
plot_distances(zero_dists, path, xmax=radius)
pdists = squareform1(pdists).numpy()
thresholds = np.linspace(radius / 10, radius, args.num_thresholds)
for threshold in thresholds:
# create the graph
g = nx.Graph()
g.add_edges_from(np.argwhere(pdists < threshold))
g.remove_edges_from(nx.selfloop_edges(g))
# save it
save_dir = os.path.join(output_dir, f'{threshold:.2f}')
check_mkdir(save_dir, increment=False)
torch.save(xs, os.path.join(save_dir, 'xs.pt'))
nx.write_edgelist(g, os.path.join(save_dir, 'graph.edges.gz'))
def main():
torch.set_default_dtype(torch.float64)
save_dir = os.path.join(args.output_dir, args.manifold)
check_mkdir(save_dir, increment=False)
man = build_manifold(args.manifold)[0]
# generate the samples on the manifold, uniformly around "origin"
if args.use_rs:
samples = gen_samples_rs(man, args.num_nodes, args.radius,
np.sqrt(args.curvature_r_squared))
else:
samples = gen_samples_exp(man, args.num_nodes, args.radius)
plot_points(man, samples, args.radius, save_dir)
# the pairwise distances
torch.save(samples, os.path.join(save_dir, 'xs.pt'))
dists = squareform1(pdists(man, samples))
plot_distances(dists, save_dir)
# create the graph
g = nx.Graph()
g.add_edges_from(np.argwhere(dists.numpy() < args.radius))
g.remove_edges_from(nx.selfloop_edges(g))
# save it
filename = '{}_n{}_r{:.2f}'.format(args.manifold, args.num_nodes,
args.radius)
filename = filename.replace('.', 'p') + '.edges.gz'
nx.write_edgelist(g, os.path.join(save_dir, filename))
# plots
plot_degree_distribution(g, save_dir)
plot_graph_distances(g, save_dir)
def __call__(self, gdists, mdists, *, epoch=None, alpha=None):
dists = squareform1(mdists)
ms, bs, cs = self._sample_nodes(device=dists.device)
am = dists.gather(dim=1, index=ms)
ab = dists.gather(dim=1, index=bs)
ac = dists.gather(dim=1, index=cs)
bc = dists[bs, cs]
reg_terms = am + 0.25 * bc - 0.5 * (ab + ac)
return -self.lambda_reg * reg_terms.abs().sum()
def plot_distances(dists, output_dir):
plt.hist(squareform1(dists), bins=20)
plt.axvline(args.radius, color='red')
plt.xlabel('Distance')
plt.ylabel('Number of pairs')
xmax = 2 * args.radius if not args.dist_limit else args.dist_limit
plt.xlim(xmin=0, xmax=xmax)
plt.gca().get_yaxis().set_major_formatter(
plt.FuncFormatter(lambda x, loc: "{:,}".format(int(x))))
plt.title('manifold = {}, radius = {}'.format(args.manifold, args.radius))
plt.tight_layout()
plt.savefig(os.path.join(output_dir, 'dists.pdf'))
plt.close()
def __call__(self, theta, ret_margs=False):
n_nodes = nnm1d2_to_n(len(theta))
theta.requires_grad_() # Needed by `torch.grad` below!
# Construct the Laplacian.
L_off = squareform1(torch.exp(theta))
L_diag = torch.diag(L_off.sum(1))
L = L_diag - L_off
L = L[1:, 1:]
logz = tb.plogdet(L)
if not ret_margs:
return logz, None
margs, = torch.autograd.grad(logz, theta, create_graph=True)
with torch.no_grad():
assert abs(margs.sum() - (n_nodes - 1)) < 1e-4
return logz, margs
def main():
torch.set_default_dtype(torch.float64)
logging.getLogger().setLevel(logging.DEBUG)
save_dir = os.path.join(args.output_dir, args.manifold)
check_mkdir(save_dir, increment=False)
man = build_manifold(args.manifold)[0]
# generate the samples
xs = random_walk_graph(man, args.num_nodes, args.radius)
torch.save(xs, os.path.join(save_dir, 'xs.pt'))
plot_points(man, xs, args.radius, save_dir)
# the pairwise distances
pdists = man.pdist(xs)
xmax = 2 * args.radius if not args.dist_limit else args.dist_limit
plot_distances(pdists, os.path.join(save_dir, 'pdists.pdf'), xmax)
pdists = squareform1(pdists)
# the distances from 0
zeros = man.zero(len(xs))
zero_dists = man.dist(zeros, xs)
xmax = args.radius
plot_distances(zero_dists, os.path.join(save_dir, 'zero_dists.pdf'), xmax)
# create the graph
g = nx.Graph()
threshold = args.link_distance if args.link_distance else args.radius
g.add_edges_from(np.argwhere(pdists.numpy() < threshold))
g.remove_edges_from(nx.selfloop_edges(g))
# save it
filename = '{}_n{}_r{:.2f}_ld{:.2f}'.format(args.manifold, args.num_nodes,
args.radius, threshold)
filename = filename.replace('.', 'p') + '.edges.gz'
nx.write_edgelist(g, os.path.join(save_dir, filename))
# plots
plot_degree_distribution(g, save_dir)
plot_graph_distances(g, save_dir)
def __init__(self, pdists):
# We store the max-normalized squared distances.
pdists = pdists.pow(2)
pdists.div_(pdists.max())
self.pdists = squareform1(pdists)
