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Gradient_experiment.py
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Gradient_experiment.py
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import matplotlib.pyplot as plt
import HDA
import ot
import numpy as np
import gromov
import time
import argparse
import pickle
import sklearn.neighbors
import itertools
import tikzplotlib
def find_T(nb_iter, dataset_path="./gradient_experiment/dataset/", nb_samples=200):
param = {"alpha": [1], "nb_iter": nb_iter, "nb_samples": [nb_samples], "epsilon": 1}
with open(dataset_path, "rb") as handle:
dict_dataset = pickle.load(handle)
C1, C2, p, q = dict_dataset["C1"], dict_dataset["C2"], dict_dataset["p"], dict_dataset["q"]
# print(np.allclose(C1, C1.T, rtol=1e-10, atol=1e-10) and np.allclose(C2, C2.T, rtol=1e-10, atol=1e-10))
param["p"], param["q"] = [p], [q]
def f(C1, C2):
return (C1 - C2) ** 2
loss_fun = [f]
param["loss_fun"] = loss_fun
def make_f(sx):
def f(*x):
return sx[x]
return f
Sx_ = [make_f(C1)]
Tx_ = [make_f(C2)]
T_ = [p[:, np.newaxis] * q[np.newaxis, :]]
T_pos = [[0] * len(C1.shape)]
T, log = gromov.CO_Generalisation_OT(p=[p], q=[q],
loss_fun=loss_fun,
X1=Sx_, X2=Tx_,
T=T_,
M=[None],
T_pos=T_pos,
alpha=param["alpha"],
nb_iter=param["nb_iter"],
nb_samples=param["nb_samples"],
epsilon=param["epsilon"],
KL=1,
threshold=1e-15,
log=True,
sparse_T=False)
return T, param, T_pos, Sx_, Tx_
def diff_grad(T, param, T_pos, X1, X2, nb_samples_list):
p, q, loss_fun = param["p"], param["q"], param["loss_fun"]
a = 0
grad_index = 0
grad = [[] for _ in range(len(nb_samples_list))]
time_save = []
for nb_samples in nb_samples_list:
print("")
print(nb_samples)
t_optimized = 0
pos_with_t_optimized = [i for i, x in enumerate(T_pos[a]) if x == t_optimized]
pos_with_t_optimized_kept, nb_sample_same_T = np.unique(
np.random.choice(pos_with_t_optimized, size=nb_samples),
return_counts=True)
time_init = time.time()
for r in range(10):
print(".", end="")
L = 0
for b in range(len(pos_with_t_optimized_kept)):
index_i = [0] * len(T_pos[a])
index_k = [0] * len(T_pos[a])
for t in range(len(T_pos[a])):
if t == pos_with_t_optimized_kept[b]:
index_i[t], index_k[t] = np.s_[:], np.s_[:]
else:
index_i[t] = np.random.choice(len(p[T_pos[a][t]]),
size=nb_sample_same_T[b],
p=p[T_pos[a][t]])
index_k[t] = np.zeros(nb_sample_same_T[b], dtype=int)
for i in range(nb_sample_same_T[b]):
index_k[t][i] = np.random.choice(len(q[T_pos[a][t]]),
size=1,
p=T[T_pos[a][t]][index_i[t][i], :] /
p[T_pos[a][t]][index_i[t][i]])[0]
if pos_with_t_optimized_kept[b] == 0:
L += loss_fun[a](np.expand_dims(X1[a](*index_i).T, 2),
np.expand_dims(X2[a](*index_k).T, 1)
).sum(axis=0) * param["alpha"][a]
else:
L += loss_fun[a](np.expand_dims(X1[a](*index_i), 2),
np.expand_dims(X2[a](*index_k), 1)
).sum(axis=0) * param["alpha"][a]
L = L / nb_samples
grad[grad_index].append(L)
time_save.append((time.time() - time_init) / 10)
grad_index += 1
return grad, time_save
def make_datasets(dataset_path, cluster, dimension=10, D=(2, 5), std=0.15, rdm_seed=42, nb_dataset=2):
N = np.sum(cluster)
distance, closest = [0] * nb_dataset, [0] * nb_dataset
pq = [np.random.rand(N), np.random.rand(N)]
for nb_dataset_i in range(nb_dataset):
np.random.seed(rdm_seed + nb_dataset_i * 123)
for c in range(len(cluster)):
mean = np.random.rand(dimension)
cov = np.diag(np.random.rand(dimension) * std)
correlation = np.random.rand(dimension * dimension).reshape(dimension, dimension) * std / 2
correlation[np.arange(dimension), np.arange(dimension)] = 0
correlation = (correlation + correlation.T) / 2
correlation = np.eye(dimension) + correlation
cov = cov @ correlation @ cov
if c == 0:
gaussians = np.random.multivariate_normal(mean, cov, cluster[c])
else:
gaussians = np.concatenate((gaussians, np.random.multivariate_normal(mean, cov, cluster[c])))
neigh = sklearn.neighbors.NearestNeighbors(n_neighbors=D[1] + 2)
neigh.fit(gaussians)
distance[nb_dataset_i], closest[nb_dataset_i] = neigh.kneighbors(gaussians)
for d in range(D[0], D[1]):
print(d)
dict_dataset = {}
for nb_dataset_i in range(nb_dataset):
distance_d, closest_d = distance[nb_dataset_i][:, :d], closest[nb_dataset_i][:, :d]
size_tensor = "N," * d
size_tensor = size_tensor[:-1]
# TODO: This is VERY ugly
C = eval("np.zeros((" + size_tensor + "))")
# TODO: and also this
def f(value, matrix, *x):
# print(x)
matrix[x] += value
return matrix
for n in range(N):
for perm in list(itertools.permutations(closest_d[n, :])):
C = f(1, C, *perm)
# save_value = closest_d[n, -1]
# closest_d[n, 1:] = closest_d[n, :-1]
# closest_d[n, 0] = save_value
dict_dataset["C" + str(nb_dataset_i + 1)] = C
dict_dataset["cluster"] = cluster
dict_dataset["D"] = D
dict_dataset["std"] = std
dict_dataset["rdm_seed"] = rdm_seed
dict_dataset["p"] = pq[0] / np.sum(pq[0])
dict_dataset["q"] = pq[1] / np.sum(pq[1])
dataset_name = "hypergraphs_" + str(d) + "_" + str(N)
if args["save"]:
with open(dataset_path + dataset_name + ".pickle", "wb") as handle:
pickle.dump(dict_dataset, handle)
def store_gradient(path_pickle, out_pickle, nb_point, D, outer_iteration, nb_samples_list):
for i in outer_iteration:
print("outer iteration:", i)
np.random.rand(1234 + i * 123)
T, param, T_pos, C1, C2 = find_T(nb_iter=i,
dataset_path=path_pickle + "hypergraphs_" + str(D) + "_" + str(nb_point) +
".pickle",
nb_samples=200)
grad, time_save = diff_grad(T=T, param=param, T_pos=T_pos, X1=C1, X2=C2, nb_samples_list=nb_samples_list)
dict_grad_time = {"grad": grad, "time_save": time_save}
if args["save"]:
with open(out_pickle + "_" + str(i) + "_" + str(D) + "_" + str(nb_point) + ".pickle", "wb") as handle:
pickle.dump(dict_grad_time, handle)
# def full_grad(pickle_path):
# # T, param, T_pos, X1, X2
# p, q, loss_fun = param["p"], param["q"], param["loss_fun"]
# grad = []
# a = 0
# L = 0
# t_optimized = 1
# pos_with_t_optimized = [i for i, x in enumerate(T_pos[a]) if x == t_optimized]
# # print(pos_with_t_optimized)
# G = 0
# for b in pos_with_t_optimized:
# if b == 1:
# for i in range(len(p[T_pos[a][0]])):
# print(".", end="")
# for k in range(len(q[T_pos[a][2]])):
# for l in range(len(p[T_pos[a][0]])):
# for n in range(len(q[T_pos[a][2]])):
# G += loss_fun[a](np.expand_dims(X1[a](i, np.s_[:], k), 0),
# np.expand_dims(X2[a](l, np.s_[:], n), 1)) \
# * T[T_pos[a][0]][i, l] \
# * T[T_pos[a][2]][k, n]
# # print(G.shape)
#
# elif b == 2:
# for i in range(len(p[T_pos[a][0]])):
# print(".", end="")
# for j in range(len(q[T_pos[a][1]])):
# for l in range(len(p[T_pos[a][0]])):
# for m in range(len(q[T_pos[a][1]])):
# G += loss_fun[a](np.expand_dims(X1[a](i, j, np.s_[:]), 0),
# np.expand_dims(X2[a](l, m, np.s_[:]), 1)) \
# * T[T_pos[a][1]][i, l] \
# * T[T_pos[a][2]][j, m]
# else:
# pass
# return G
def display_grad(pickle_path, D, outer_iteration, nb_point, nb_samples_list):
nb_samples_list = np.array(nb_samples_list)
marker = ["", "", "|", "^", "s"]
color = ["", "", "r", "b", "g"]
for outer_iteration_i in outer_iteration:
plt.figure(outer_iteration_i)
for d in range(D[0], D[1]):
if outer_iteration_i == outer_iteration[0]:
print("nb element in the tensor L of size N^d" + str(d) + " : ", nb_point ** (2*(d-1)))
with open(pickle_path + "_" + str(outer_iteration_i) + "_" + str(d) + "_" + str(nb_point) +
".pickle", "rb") as handle:
dict_dataset = pickle.load(handle)
grad, time = dict_dataset["grad"], dict_dataset["time_save"]
best_grad_approx = 0
for r in range(10):
best_grad_approx += grad[-1][r]
best_grad_approx = best_grad_approx / 10
list_mean_diff, list_std_diff = np.zeros(len(grad)), np.zeros(len(grad))
keep_diff_zero = []
for i in range(len(grad)):
diff = []
for r in range(10):
diff.append(np.linalg.norm(grad[i][r] - best_grad_approx)/np.linalg.norm(best_grad_approx))
list_mean_diff[i] = np.mean(diff)
list_std_diff[i] = np.std(diff)
# print(nb_samples_list[i], " |Time: ", time[i],
# " |Diff: ", np.mean(diff), np.std(diff))
if list_mean_diff[i] != 1:
keep_diff_zero.append(i)
# print(keep_diff_zero)
keep_diff_zero = np.array(keep_diff_zero, dtype=int)
plt.plot(nb_samples_list[keep_diff_zero], list_mean_diff[keep_diff_zero],
# color=color[d],
label=str(d) + "-order tensor", marker=marker[d], markersize=6)
min_std_list = list_mean_diff - list_std_diff
# min_std_list[min_std_list < 10**-2] = list_mean_diff[min_std_list < 10**-2]
plt.fill_between(nb_samples_list[keep_diff_zero],
list_mean_diff[keep_diff_zero] + list_std_diff[keep_diff_zero],
min_std_list[keep_diff_zero],
alpha=0.2)
# plt.errorbar(nb_samples_list, list_mean_diff, yerr=list_std_diff,
# color=color[d],
# label='Standard deviation error bar')
plt.xscale("log")
plt.yscale("log")
plt.xlabel("Number of samples $M$")
plt.ylabel("$\\frac{\\ norm{\\nabla \\mathcal{E} - \\widehat{\\nabla \\mathcal{E}}}_F}{\\ norm{\\nabla \\mathcal{E}}_F}$")
plt.legend(loc=0, fontsize=10)
tikzplotlib.save("./gradient_experiment/fig/" + str(nb_point) + "/fig_" + str(outer_iteration_i) + ".tex")
if args["save"]:
plt.savefig("./gradient_experiment/fig/" + str(nb_point) + "/fig_" + str(outer_iteration_i) + ".pdf")
plt.show()
# auie
if __name__ == "__main__":
parser = argparse.ArgumentParser(description='OTT')
parser.add_argument('--seed', type=int, default=42)
parser.add_argument('--cluster', type=str, default="10,20,25")
parser.add_argument('--outer_iteration', type=str, default="5,10,20,50,100,200,500,1000")
parser.add_argument('--nb_samples', type=str, default="1,5,10,50,100,500,1000,5000,10000,50000,100000")
parser.add_argument('-p', '--plot', action="store_true")
parser.add_argument('-d', '--dataset', action="store_true")
parser.add_argument('-s', '--save', action="store_true")
parser.add_argument('--D', type=str, default="2,5")
parser.add_argument('--pickle_path', type=str,
default="./gradient_experiment/pickle/")
# nb_samples_list = [1, 5, 10, 50, 100, 500, 1000, 5000, 10000, 50000] # ,50000]#,100000] #,100000]:
args = parser.parse_args()
args = vars(args)
if "," in args["D"]:
args["D"] = [int(x) for x in args["D"].split(",")]
else:
args["D"] = (2, int(args["D"]))
np.random.seed(args["seed"])
args["outer_iteration"] = [int(x) for x in args["outer_iteration"].split(",")]
args["nb_samples"] = [int(x) for x in args["nb_samples"].split(",")]
cluster = [int(x) for x in args["cluster"].split(",")]
if args["dataset"]:
make_datasets(dataset_path="./gradient_experiment/dataset/",
cluster=cluster,
dimension=10,
D=args["D"],
std=0.15,
rdm_seed=42)
elif args["plot"]:
display_grad(args["pickle_path"],
outer_iteration=args["outer_iteration"],
D=args["D"],
nb_point=sum(cluster),
nb_samples_list=args["nb_samples"])
else:
store_gradient(path_pickle="./gradient_experiment/dataset/",
out_pickle="./gradient_experiment/pickle/",
nb_point=sum(cluster),
D=args["D"][1],
outer_iteration=args["outer_iteration"],
nb_samples_list=args["nb_samples"])