def estimate_network(A, nbre_noeuds, L, Delta, T, type_diffusion):
num_cascades = numpy.zeros((1,nbre_noeuds))
Psi2 = numpy.zeros((nbre_noeuds, nbre_noeuds))
Psi1 = numpy.zeros((nbre_noeuds, nbre_noeuds))
T3 = list()
i = 0
nbre_infections = 0
max_infections = 0
while i < nbre_noeuds:
nbre_infections += len(L[i])
if len(L[i]) > max_infections:
max_infections = len(L[i])
i += 1
T3 = []
i = 0
while i < max_infections:
T3.append(numpy.zeros((nbre_noeuds,nbre_noeuds)))
i += 1
L_sorted = []
L_int = copy.copy(L)
L_non_touche = []
i = 0
j = 0
while i < nbre_noeuds:
while j < len(L[i]):
L_int[i][j] = (i,j,L[i][j])
j += 1
L_sorted += L_int[i]
if len(L[i]) == 0:
L_non_touche.append(i)
i += 1
j = 0
L_sorted.sort(key = lambda tup : tup[2])
c = 0
X = []
i_int = 0
j_int = 0
tho_int = 0.
while c < nbre_infections:
for (i_int,j_int,tho_int) in X:
if tho_int + Delta[i_int][j_int] < L_sorted[c][2] :
X.remove((i_int,j_int,tho_int))
else:
if type_diffusion == 'exp':
Psi2[L_sorted[c][0]][i_int] += L_sorted[c][2] - tho_int
T3[L_sorted[c][1]][L_sorted[c][0]][i_int] = 1
elif type_diffusion == 'pl' and L_sorted[c][2] - tho_int > 1 :
Psi2[L_sorted[c][0]][i_int] += math.log(L_sorted[c][2] - tho_int)
T3[L_sorted[c][1]][L_sorted[c][0]][i_int] = 1. / (L_sorted[c][2] - tho_int)
elif type_diffusion == 'rayleigh':
Psi2[L_sorted[c][0]][i_int] += 0.5*((L_sorted[c][2] - tho_int)**2)
T3[L_sorted[c][1]][L_sorted[c][0]][i_int] = 1. * (L_sorted[c][2] - tho_int)
if L_sorted[c][2] > 0:
X.append(L_sorted[c])
for i in L_non_touche:
if type_diffusion == 'exp':
Psi1[L_sorted[c][0]][i] += T - L_sorted[c][2]
elif type_diffusion == 'pl':
Psi1[L_sorted[c][0]][i] += math.log(T - L_sorted[c][2])
elif type_diffusion == 'rayleigh':
Psi1[L_sorted[c][0]][i] += (T - L_sorted[c][2])**2
c += 1
"""As explained in the presentation, we do an optimization algorithm by itering the calculus.
Because we only want to compute Psi1 and Psi2 one time we have developed formation_densite which
uses the global variables Psi1 and Psi2 and a matrix B.
It returns the value and the gradient of the log-likelihood"""
def formation_densite(Beta=numpy.ones((nbre_noeuds,nbre_noeuds))):
Psi2_grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi1_grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi3_grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi1_intermediaire = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi2_intermediaire = numpy.zeros((nbre_noeuds,nbre_noeuds))
grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi1_grad = copy.copy(Psi1)
Psi1_intermediaire = copy.copy(numpy.dot(-Psi1,Beta.transpose()))
Psi2_grad = copy.copy(Psi2.transpose())
Psi2_intermediaire = copy.copy(numpy.dot(-Psi2,Beta))
produit_densite = list()
produit_densite_log = list()
produit_gradient = numpy.zeros((nbre_noeuds,nbre_noeuds))
c = 0
while c < max_infections:
produit_densite.append(copy.copy(numpy.dot(T3[c],Beta)))
produit_gradient = produit_gradient + matrix_inverse_elements(produit_densite[c],T3[c])
produit_densite_log.append(copy.copy(log_elements(produit_densite[c])))
c += 1
grad = copy.copy((Psi1_grad + Psi2_grad) - (produit_gradient))
for i in range(len(grad)):
for j in range(len(grad[i])):
if Beta[i,j] == 0:
grad[i,j] = 0
return ((- somme_diag_elements(Psi1_intermediaire) - somme_diag_elements(Psi2_intermediaire) - somme_diag_elements(sum(produit_densite_log)))/max_infections, grad/max_infections)
"""We then take a initial matrix and we operate a gradient-descent on it to find the estimated matrix"""
Beta = numpy.ones((nbre_noeuds,nbre_noeuds))
(value,gradient) = formation_densite(Beta)
gradient_initial = norm_matrix(gradient,1)
gradient_intermediaire = 0.00000001
k = 0
while norm_matrix(gradient,1) > 0.1 and norm_matrix(gradient,1) < 4 * gradient_initial and abs((norm_matrix(gradient,1) - gradient_intermediaire)/gradient_intermediaire) > 0.000005:
Beta = soft_thres(Beta-0.0005*gradient,0.000001)
for i in range(0,len(Beta)):
for j in range(0,len(Beta[i])):
if Beta[i,j] < 0:
Beta[i,j] = 0
if k >= 1:
gradient_intermediaire = norm_matrix(gradient,1)
(value,gradient) = formation_densite(Beta)
k += 1
print('optimization completed')
"""In order to compare the result with the estimated matrix, we use the following indicators"""
accuracy = 1.0
acc_num = 0.
acc_den = 0.
MAE = 0.
MAS = 0.
for i in range (0,len(A)):
for j in range(0,len(A)):
if A[i,j] > 0 and Beta[i,j] > 0:
acc_den
elif A[i,j] > 0 or Beta[i,j] > 0:
acc_num += 1.
acc_den += 1.
if A[i,j] > 0:
MAE += abs(A[i,j] - Beta[i,j]) / A[i,j]
if Beta[i,j] > 0:
MAS += abs(A[i,j] - Beta[i,j]) / Beta[i,j]
if acc_den > 0:
accuracy -= acc_num / acc_den
return (Beta,(accuracy,MAE,MAS))
def estimate_network_NetRate(A, C, nbre_noeuds, T, type_diffusion, nbre_infections,mu,return_value=False):
Psi2 = numpy.zeros((nbre_noeuds, nbre_noeuds))
Psi1 = numpy.zeros((nbre_noeuds, nbre_noeuds))
T3 = list()
nbre_touche_potentiel = numpy.zeros((nbre_noeuds,nbre_noeuds))
c = 0
indice_dernier_noeud_touche = 0
while c < nbre_infections:
i = nbre_noeuds - 1
mat_int = C[c].argsort()
T3.append(numpy.zeros((nbre_noeuds,nbre_noeuds)))
while (i >= 0 and (C[c][mat_int[i]] > -1)) :
j = 0
while j < i:
nbre_touche_potentiel[mat_int[j],mat_int[i]] += 1
if (C[c][mat_int[j]] != -1):
if(type_diffusion == 'exp'):
Psi2[mat_int[i]][mat_int[j]] += C[c][mat_int[i]] - C[c][mat_int[j]]
T3[c][mat_int[i]][mat_int[j]] = 1
elif (type_diffusion == 'pl') and (C[c][mat_int[i]]-C[c][mat_int[j]] > 1):
Psi2[mat_int[i]][mat_int[j]] += math.log(C[c][mat_int[i]]-C[c][mat_int[j]])
T3[c][mat_int[i]][mat_int[j]] = 1 / (C[c][mat_int[i]]-C[c][mat_int[j]])
elif (type_diffusion == 'rayleigh'):
Psi2[mat_int[i]][mat_int[j]] += 0.5*((C[c][mat_int[i]] - C[c][mat_int[j]])*(C[c][mat_int[i]] - C[c][mat_int[j]]))
T3[c][mat_int[i]][mat_int[j]] = C[c][mat_int[i]]-C[c][mat_int[j]]
j += 1
i -= 1
indice_dernier_noeud_touche = i + 1
#Dans le calcul de Psi1, exceptionnellement on compte dans le sens inverse
while i >= 0: #On obtient des j qui ont une valeur nulle
j = nbre_noeuds - 1
while j >= indice_dernier_noeud_touche :
if type_diffusion == 'exp':
Psi1[mat_int[j]][mat_int[i]] += T - C[c][mat_int[j]]
elif type_diffusion == 'pl' and T > 1:
Psi1[mat_int[j]][mat_int[i]] += math.log(T-C[c][mat_int[j]])
elif type_diffusion == 'rayleigh':
Psi1[mat_int[j]][mat_int[i]] += 0.5*(T-C[c][mat_int[j]])*(T-C[c][mat_int[j]]);
j -= 1
i -= 1
c += 1
def formation_densite(Beta=numpy.ones((nbre_noeuds,nbre_noeuds))):
Psi2_grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi1_grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi3_grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi1_intermediaire = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi2_intermediaire = numpy.zeros((nbre_noeuds,nbre_noeuds))
grad = numpy.zeros((nbre_noeuds,nbre_noeuds))
Psi1_grad = copy.copy(Psi1)
Psi1_intermediaire = copy.copy(numpy.dot(-Psi1,Beta.transpose()))
Psi2_grad = copy.copy(Psi2.transpose())
Psi2_intermediaire = copy.copy(numpy.dot(-Psi2,Beta))
produit_densite = list()
produit_densite_log = list()
produit_gradient = numpy.zeros((nbre_noeuds,nbre_noeuds))
c = 0
while c < nbre_infections:
produit_densite.append(copy.copy(numpy.dot(T3[c],Beta)))
produit_gradient = produit_gradient + matrix_inverse_elements(produit_densite[c],T3[c])
produit_densite_log.append(copy.copy(log_elements(produit_densite[c])))
c += 1
grad = copy.copy((Psi1_grad + Psi2_grad) - (produit_gradient))
for i in range(len(grad)):
for j in range(len(grad[i])):
if Beta[i,j] == 0:
grad[i,j] = 0
def hessienne():
while c < nbre_infections:
i = 0
j = 0
k = 0
while i < nbre_noeuds:
j = 0
while j < nbre_noeuds:
k = 0
while k < nbre_noeuds:
if produit_densite[c][j,j] != 0:
hessienne[i*nbre_noeuds+j][k*nbre_noeuds+j] += T3[c][i,j]*T3[c][k,j]/(produit_densite[c][j,j]**2)
k += 1
j += 1
i += 1
c+=1
return ((- somme_diag_elements(Psi1_intermediaire) - somme_diag_elements(Psi2_intermediaire) - somme_diag_elements(sum(produit_densite)))/nbre_infections, grad/nbre_infections)
"""We then take a initial matrix and we operate a gradient-descent on it to find the estimated matrix"""
Alpha2 = 0.5 *numpy.ones((nbre_noeuds,nbre_noeuds))
i = 0
j = 0
while i < nbre_noeuds:
while j < nbre_noeuds:
if nbre_touche_potentiel[i,j] == 0:
Alpha2[i,j] = 0
j+=1
i += 1
j = 0
k = 0
(value,gradient) = formation_densite(Alpha2)
value_int = 0
gradient_intermediaire = 0.00001
while k < 10000 and norm_matrix(gradient,1) > 0.1:
Alpha2 = copy.copy(soft_thres(Alpha2 - 0.0005 * gradient,mu))
i = 0
while i < len(Alpha2):
while j < len(Alpha2[i]):
if Alpha2[i,j] < 0:
Alpha2[i,j] = 0
j += 1
i += 1
j = 0
(value,gradient) = formation_densite(Alpha2)
if k % 1000 == 0:
print('GRADIENT -> {}'.format(norm_matrix(gradient,1)))
print('DIFF --> {}'.format(abs((norm_matrix(gradient,1) - gradient_intermediaire)/gradient_intermediaire)))
print(value)
if k % 500000 == 0:
print(k/500000)
if k % 1000 == 0 and k > 0:
print(k)
k += 1
if return_value:
return Alpha2,value
else:
return Alpha2