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synthetic_residuals.py
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synthetic_residuals.py
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import os
import numpy as np
import seaborn as sb
import pandas as pd
import matplotlib.pyplot as plt
from graph_sign_test import az_whiteness_test
from triangular_tricom_graph import TriCommunityGraph
RESULT_FOLDER = "./results"
def run_simulation(signal_gen_fun, alpha, edge_index, repetitions):
stats = []
alarms = 0
for r in range(repetitions):
x = signal_gen_fun()
aztest = az_whiteness_test(x=x, edge_index_spatial=edge_index, edge_weight_temporal="auto", multivariate=True)
stats.append(aztest.statistic)
if aztest.pvalue < alpha:
alarms += 1
return alarms, stats
def run_multiple_simulations(G, alpha, considered_edge_index,
F_list, T_list, cs_list, ct_list, distrib_list,
repetitions, disable_warning):
results = []
assert len(F_list) == len(T_list)
import time
elapsed = 0
for distrib in distrib_list:
for F, T in zip(F_list, T_list):
for cs, ct in zip(cs_list, ct_list):
corr = max([cs, ct])
print(f"Test: F={F}, T={T}, corr={corr}.\tAlarm rate: ", end="")
stats = []
alarms = 0
for r in range(repetitions):
if distrib == "norm":
subtract_median = False
else:
subtract_median = True
if not disable_warning:
raise Warning("Subtracting median")
x = gen_correlated_signals_fun(F=F, T=T, G=G,
corr_spatial=cs, corr_temporal=ct,
distrib=distrib, subtract_median=subtract_median)
t = time.time()
aztest = az_whiteness_test(x=x, edge_index_spatial=considered_edge_index, multivariate=False)
elapsed += time.time() - t
stats.append(aztest.statistic)
if aztest.pvalue < alpha:
alarms += 1
alarm_rate = alarms / repetitions
print(f"Alarm rate = {alarm_rate}\t({alarms}/{repetitions})")
results.append((F, T, corr, alarm_rate, distrib))
if repetitions == 1:
savefig=os.path.join(RESULT_FOLDER,f"gsignal_c{corr}")
G.plot(signal=x[..., 0], savefig=savefig + f"T{T}_{distrib}.pdf")
# plt.title(f"median = {np.median(x)}")
# plt.tight_layout()
# plt.savefig(savefig + f"topology.pdf")
print(f"empirical median {np.median(x)}")
# import scipy.stats
# s = np.array(stats)
# scipy.stats.probplot(s, dist="norm", plot=plt)
# plt.title(f"F{F} T{T} corr={corr} A{alarm_rate} mu{np.mean(s):.3f}+-{1.0/np.sqrt(repetitions):.3f} std{np.std(s):.3f}")
# plt.show()
runs = len(distrib_list)*len(F_list)*len(ct_list)*repetitions
print("Elapsed times: ", elapsed, "for a total of ", runs, "runs")
print("Average run time: ", elapsed/runs)
df = pd.DataFrame(results, columns=["F", "T", "corr", "alarm_rate", "distrib"])
df = df.astype(dict(F=int, T=int, corr=float, alarm_rate=float, distrib=str))
return df, x
def plot_results(df, name, subplot_dist=True):
F_list = df["F"].unique()
distrib_list = df["distrib"].unique()
# col_list, col_name = F_list, "F"
# row_list, row_name = distrib_list, "distrib"
# if col_list.size == 1 and row_list.size > 1:
# tmp = row_list
# row_list = col_list
# col_list = tmp
if F_list.size > distrib_list.size:
col_list, col_name = F_list, "F"
row_list, row_name = distrib_list, "distrib"
else:
col_list, col_name = distrib_list, "distrib"
row_list, row_name = F_list, "F"
cols = col_list.size
ax = None
if subplot_dist:
rows = row_list.size
fig, ax = plt.subplots(figsize=(3*cols, 3*rows))
else:
rows = 1
# for d, distrib in enumerate(distrib_list):
for r, row_el in enumerate(row_list):
if not subplot_dist:
fig, ax = plt.subplots(figsize=(3*cols, 3*rows))
r = 0
# for i, F in enumerate(F_list):
for c, col_el in enumerate(col_list):
plt.subplot(rows, cols, r * cols + c + 1)
extra_args = dict(annot=True, vmin=0, vmax=1)
if r < rows-1:
extra_args["xticklabels"] = []
if c > 0:
extra_args["yticklabels"] = []
if c < cols-1:
extra_args["cbar"] = False
df_ = df.where(df[col_name] == col_el).where(df[row_name] == row_el)
df_ = df_.dropna().astype(dict(corr=float, T=int))
hm_ = sb.heatmap(df_.pivot("corr", 'T', "alarm_rate"),
**extra_args)
# plt.axis("equal")
if r < rows - 1:
plt.xlabel("")
# plt.ylabel("")
if c > 0:
plt.ylabel("")
# tit = col_el if col_name == "distrib" else row_el
if col_name == "distrib":
distrib = col_el
F = row_el
else:
distrib = row_el
F = col_el
# plt.rcParams.update({
# "text.usetex": True,
# "font.family": "Helvetica"
# })
if len(F_list) == 1 and F==1:
plt.title(f"{DISTRIBUTIONS[distrib]}")
else:
plt.title(f"{DISTRIBUTIONS[distrib]} (F={F})")
if not subplot_dist:
plt.tight_layout()
plt.savefig(os.path.join(RESULT_FOLDER, f'{name}_heatmap_alarmrate_{distrib}.pdf'))
if subplot_dist:
plt.tight_layout()
plt.savefig(os.path.join(RESULT_FOLDER, f'{name}_heatmap_alarmrate.pdf'))
plt.show()
def make_table(df):
df_ = df.pivot_table(values="alarm_rate", index=['distrib', 'corr'], columns=["F", "T"])
print(df_.to_latex())
def gen_correlated_signals_fun(F, T, G, corr_spatial, corr_temporal, distrib="norm", subtract_median=False):
x = gen_nullmedian_signal(shape=(T, G.num_nodes, F), distrib=distrib)
x = gen_correlated_signal(x=x, G=G, c_space=corr_spatial, c_time=corr_temporal)
if subtract_median:
x -= np.median(x)
return x
AVAILABLE_DISTRIBUTIONS = ["norm", "chi2(1)", "chi2(5)", "bi-norm", "chi2(1)-chi2(5)", "bi-unif14"]
def gen_nullmedian_signal(shape: tuple, distrib: str="norm"):
"""
Generates iid graph signals from different distributions
:param shape: (3-tuple) generally in the format (T, N, F)
:param distrib: (str) identifier of the type of distribution
:return:
"""
if distrib == "norm":
x = np.random.randn(*shape)
elif distrib == "chi2(1)":
import scipy.stats
x = scipy.stats.chi2(df=1).rvs(size=shape)
x -= scipy.stats.chi2(df=1).ppf(0.5)
elif distrib == "chi2(5)":
import scipy.stats
x = scipy.stats.chi2(df=5).rvs(size=shape)
x -= scipy.stats.chi2(df=5).ppf(0.5)
# elif distrib == "mix":
# import scipy.stats
# mask = np.random.rand(*shape) > .7
# x = mask * scipy.stats.chi2(df=1).rvs(size=shape)
# x += (1 - mask) * scipy.stats.chi2(df=5).rvs(size=shape)
elif distrib == "bi-norm":
import scipy.stats
mask = np.random.rand(*shape) > .5
x = mask * np.random.randn(*shape)+3.
x += (1 - mask) * np.random.randn(*shape)-3.
elif distrib == "chi2(1)-chi2(5)":
import scipy.stats
mask = np.random.rand(*shape) > .5
x = mask * scipy.stats.chi2(df=1).rvs(size=shape)
x += (1 - mask) * scipy.stats.chi2(df=5).rvs(size=shape) * (-1.)
elif distrib == "bi-unif14":
import scipy.stats
mask = np.random.rand(*shape) > .5
x = mask * np.random.rand(*shape)
x += (1 - mask) * np.random.rand(*shape) * (-4.)
else:
raise NotImplementedError(f"Distribution {distrib} is not available")
return x
def gen_correlated_signal(x, G, c_space, c_time):
from einops import rearrange
x_ = G.adj.dot(rearrange(x, "T N F -> N (T F)"))
x_new = x + c_space * rearrange(x_, "N (T F) -> T N F", F=x.shape[-1])
# x_new[2:] += c_time * (x_new[1:-1] + x_new[:-2])
edge_den = G.num_edges / G.num_nodes
x_new[1:] += c_time * edge_den * x_new[:-1]
return x_new
def to_grid(list1, list2):
return [l1 for l1 in list1 for _ in list2], \
[l2 for _ in list1 for l2 in list2]
# DISTRIBUTIONS_UNIMODAL = {"norm": "$\mathcal N(0,1)$",
# "chi2(1)": "$\chi_2(1)$",
# "chi2(5)": "$\chi_2(5)$"}
# DISTRIBUTIONS_MIXTURE = {"bi-norm": "$\mathcal N(-3,1) + \mathcal N(3,1)",
# "chi2(1)-chi2(5)": "$\chi_2(1)-\chi_2(5)$",
# "bi-unif14": "$U[-4,0)+U[0,1)"}
DISTRIBUTIONS_UNIMODAL = {"norm": "N(0,1)",
"chi2(1)": "chi2(1)",
"chi2(5)": "chi2(5)"}
DISTRIBUTIONS_MIXTURE = {"bi-norm": "N(-3,1) + N(3,1)",
"chi2(1)-chi2(5)": "chi2(1) - chi2(5)",
"bi-unif14": "U[-4,0) + U[0,1)"}
DISTRIBUTIONS = {**DISTRIBUTIONS_UNIMODAL, **DISTRIBUTIONS_MIXTURE}
def main(experiment, show_signal=False, disable_warning=False):
G = TriCommunityGraph(communities=3, connectivity="triangle")
if show_signal:
x = np.random.randn(G.num_nodes).reshape(-1, 1)
G.plot(signal=x)
plt.tight_layout()
plt.savefig(os.path.join(RESULT_FOLDER, "static-graph-signal.pdf"))
plt.show()
alpha = 0.05
rep = 1000
graphs = ["sparse"]
distrib = ["norm"]
F_list = [1, 2] #, 4, 8]
T_list = [1, 10] #, 100, 1000]
corr_spatial = [0.04, 0.16]
corr_temporal = corr_spatial
if experiment == "viz":
distrib = ["bi-unif14"]
distrib = ["chi2(1)"]
distrib = ["norm"]
F_list, T_list = to_grid([1], [500])
corr_spatial = [0.0, 0.04, 0.16, 0.64]
corr_temporal = corr_spatial
rep = 1
if experiment == "run-time":
# rep = 100
F_list, T_list = to_grid([1], [10000])
corr_spatial = [0.01]
corr_temporal = corr_spatial
if experiment[:5] == "power":
# Check detection rates for different distributions (regardless of the symmetry)
if experiment == "power-unimodal":
distrib = list(DISTRIBUTIONS_UNIMODAL.keys())
elif experiment == "power-mixture":
distrib = list(DISTRIBUTIONS_MIXTURE.keys())
F_list, T_list = to_grid([1], [1, 10, 100, 1000])
corr_spatial = [0.0, 0.01, 0.04, 0.16]
corr_temporal = corr_spatial
if experiment == "symmetry":
# Check different distributions
distrib = AVAILABLE_DISTRIBUTIONS
F_list, T_list = to_grid([1, 4, 8], [10, 100, 1000])
corr_spatial = [0.0]
corr_temporal = corr_spatial
if experiment == "sparse-full-only-time":
# Compare sparse vs full
F_list, T_list = to_grid([1, 4, 8], [1, 10, 100, 1000])
# corr_spatial = [0.0, 0.01, 0.04, 0.16]
# corr_temporal, corr_spatial = to_grid([0.0, 0.01, 0.04, 0.16], [0])
corr_temporal, corr_spatial = to_grid([0], [0.0, 0.01, 0.04, 0.16])
graphs = ["sparse", "complete"]
if experiment == "sparse-full":
# Compare sparse vs full
F_list, T_list = to_grid([1, 4, 8], [1, 10, 100, 1000])
# corr_spatial = [0.0, 0.01, 0.04, 0.16]
# corr_temporal, corr_spatial = to_grid([0.0, 0.01, 0.04, 0.16], [0])
corr_temporal = [0.0, 0.01, 0.04, 0.16]
corr_spatial = corr_temporal
graphs = ["sparse", "complete"]
if experiment == "t-vs-f_time-space":
# Compare T vs F
F_list = [ 1, 16, 64, 256, 1024, 1, 1, 1, 1]
T_list = [ 1, 1, 1, 1, 1, 16, 64, 256, 1024]
corr_temporal = [0.0, 0.01, 0.04, 0.16]
corr_spatial = corr_temporal
distrib = ["norm"]
graphs = ["sparse"]
if experiment == "t-vs-f_no-space":
# Compare T vs F
F_list = [ 1, 16, 64, 256, 1024, 1, 1, 1, 1]
T_list = [ 1, 1, 1, 1, 1, 16, 64, 256, 1024]
corr_temporal, corr_spatial = to_grid([0.0, 0.01, 0.04, 0.16], [0])
distrib = ["norm"]
graphs = ["sparse"]
if experiment == "debug-full0":
rep = 1000
F_list, T_list = to_grid([1], [1])
# corr_spatial = [0.0, 0.01, 0.04, 0.16]
# corr_temporal, corr_spatial = to_grid([0.0, 0.01, 0.04, 0.16], [0])
corr_temporal, corr_spatial = to_grid([0], [0.0, 0.01, 0.04, 0.16])
graphs = ["complete"]
common_args = dict(F_list=F_list, T_list=T_list,
distrib_list=distrib, cs_list=corr_spatial, ct_list=corr_temporal,
repetitions=rep, alpha=alpha, disable_warning=disable_warning)
from triangular_tricom_graph import Graph
edge_index_complete = [[i, j] for i in range(G.num_nodes) for j in range(G.num_nodes) if i != j]
edge_index_complete = np.array(edge_index_complete).T
G_full = Graph(edge_index=edge_index_complete, node_position=G.node_position)
for graph in graphs:
if graph == "sparse":
considered_edge_index = G.edge_index
elif graph == "complete":
considered_edge_index = G_full.edge_index
else:
raise NotImplementedError()
df, x = run_multiple_simulations(G=G, considered_edge_index=considered_edge_index, **common_args)
df.to_csv(path_or_buf=RESULT_FOLDER + "/dataframe_" + experiment + ".csv")
name = experiment if graph == "sparse" else experiment+"_"+graph
print(f"Plotting experiment {name}")
plot_results(df=df, name=name)
make_table(df=df)
if rep == 1:
G.plot()
if __name__ == "__main__":
#Figure 3
main("power-unimodal", disable_warning=True)
main("power-mixture", disable_warning=True)
#Figure 5 (Supp. Mat.)
main("viz")
#Figure 7 (Supp. Mat.)
main("sparse-full")