def gradient(theta, data, modelType):
if modelType == '6':
mu = np.array(theta[:2]).reshape(2, 1)
alpha = np.array(theta[2:6]).reshape(2, 2)
if modelType == '4':
mu = np.array([theta[0], theta[0]]).reshape(2, 1)
alpha = np.array([theta[2], theta[3], theta[3],
theta[2]]).reshape(2, 2)
if modelType == '2cross':
mu = np.array([theta[0], theta[0]]).reshape(2, 1)
alpha = np.array([0.0, theta[3], theta[3], 0.0]).reshape(2, 2)
beta = np.ones((2, 1))
pos = data[data[:, 1] == 1.0, 0].reshape(-1, 1)
neg = data[data[:, 1] == -1.0, 0].reshape(-1, 1)
pos = pos.astype(float, copy=False)
neg = neg.astype(float, copy=False)
N = pos.shape[0]
M = neg.shape[0]
T = data[-1, 0]
R11 = getR.getR11(N, beta[0, 0], pos)
R12 = getR.getR12(N, M, beta[0, 0], pos, neg)
R21 = getR.getR21(N, M, beta[1, 0], pos, neg)
R22 = getR.getR22(M, beta[1, 0], neg)
gmu1 = -T + np.sum(
1 / (mu[0, 0] + alpha[0, 0] * R11[1:] + alpha[0, 1] * R12[1:]))
gmu2 = -T + np.sum(
1 / (mu[1, 0] + alpha[1, 0] * R21[1:] + alpha[1, 1] * R22[1:]))
galpha11 = -np.sum(1-np.exp(-beta[0,0]*(T-pos)))/beta[0,0] + \
np.sum(R11[1:]/(mu[0,0]+alpha[0,0]*R11[1:]+alpha[0,1]*R12[1:]))
galpha12 = -np.sum(1-np.exp(-beta[0,0]*(T-neg)))/beta[0,0] + \
np.sum(R12[1:]/(mu[0,0]+alpha[0,0]*R11[1:]+alpha[0,1]*R12[1:]))
galpha21 = -np.sum(1-np.exp(-beta[1,0]*(T-pos)))/beta[1,0] + \
np.sum(R21[1:]/(mu[1,0]+alpha[1,0]*R21[1:]+alpha[1,1]*R22[1:]))
galpha22 = -np.sum(1-np.exp(-beta[1,0]*(T-neg)))/beta[1,0] + \
np.sum(R22[1:]/(mu[1,0]+alpha[1,0]*R21[1:]+alpha[1,1]*R22[1:]))
return -np.array([gmu1, gmu2, galpha11, galpha12, galpha21, galpha22])
def gradient(theta,data,modelType):
if modelType == '6':
mu = np.array(theta[:2]).reshape(2,1)
alpha = np.array(theta[2:6]).reshape(2,2)
if modelType == '4':
mu = np.array([theta[0],theta[0]]).reshape(2,1)
alpha = np.array([theta[2],theta[3],theta[3],theta[2]]).reshape(2,2)
if modelType == '2cross':
mu = np.array([theta[0],theta[0]]).reshape(2,1)
alpha = np.array([0.0,theta[3],theta[3],0.0]).reshape(2,2)
beta = np.ones((2,1))
pos = data[data[:,1] == 1.0,0].reshape(-1,1)
neg = data[data[:,1] == -1.0,0].reshape(-1,1)
pos = pos.astype(float,copy=False)
neg = neg.astype(float,copy=False)
N = pos.shape[0]
M = neg.shape[0]
T = data[-1,0]
R11 = getR.getR11(N,beta[0,0],pos)
R12 = getR.getR12(N,M,beta[0,0],pos,neg)
R21 = getR.getR21(N,M,beta[1,0],pos,neg)
R22 = getR.getR22(M,beta[1,0],neg)
gmu1 = -T + np.sum(1/(mu[0,0]+alpha[0,0]*R11[1:]+alpha[0,1]*R12[1:]))
gmu2 = -T + np.sum(1/(mu[1,0]+alpha[1,0]*R21[1:]+alpha[1,1]*R22[1:]))
galpha11 = -np.sum(1-np.exp(-beta[0,0]*(T-pos)))/beta[0,0] + \
np.sum(R11[1:]/(mu[0,0]+alpha[0,0]*R11[1:]+alpha[0,1]*R12[1:]))
galpha12 = -np.sum(1-np.exp(-beta[0,0]*(T-neg)))/beta[0,0] + \
np.sum(R12[1:]/(mu[0,0]+alpha[0,0]*R11[1:]+alpha[0,1]*R12[1:]))
galpha21 = -np.sum(1-np.exp(-beta[1,0]*(T-pos)))/beta[1,0] + \
np.sum(R21[1:]/(mu[1,0]+alpha[1,0]*R21[1:]+alpha[1,1]*R22[1:]))
galpha22 = -np.sum(1-np.exp(-beta[1,0]*(T-neg)))/beta[1,0] + \
np.sum(R22[1:]/(mu[1,0]+alpha[1,0]*R21[1:]+alpha[1,1]*R22[1:]))
return -np.array([gmu1,gmu2,galpha11,galpha12,galpha21,galpha22])
def likelihood(theta, data, modelType):
'''
Calculate the likelihood of hawkes model given theta and data
data is the np decomposed representation of data
'''
if modelType == '6':
mu = np.array(theta[:2]).reshape(2, 1)
alpha = np.array(theta[2:6]).reshape(2, 2)
if modelType == '4':
mu = np.array([theta[0], theta[0]]).reshape(2, 1)
alpha = np.array([theta[2], theta[3], theta[3],
theta[2]]).reshape(2, 2)
if modelType == '2cross':
mu = np.array([theta[0], theta[0]]).reshape(2, 1)
alpha = np.array([0.0, theta[3], theta[3], 0.0]).reshape(2, 2)
#Fix beta to be [1,1,1,1]
beta = np.ones((2, 1))
pos = data[data[:, 1] == 1.0, 0].reshape(-1, 1)
neg = data[data[:, 1] == -1.0, 0].reshape(-1, 1)
pos = pos.astype(float, copy=False)
neg = neg.astype(float, copy=False)
N = pos.shape[0]
M = neg.shape[0]
T = data[-1, 0]
R11 = getR.getR11(N, beta[0, 0], pos)
R12 = getR.getR12(N, M, beta[0, 0], pos, neg)
R21 = getR.getR21(N, M, beta[1, 0], pos, neg)
R22 = getR.getR22(M, beta[1, 0], neg)
L1 = -mu[0,0]*T -(alpha[0,0]/beta[0,0])*np.sum(1-np.exp(-beta[0,0]*(T-pos))) -\
(alpha[0,1]/beta[0,0])*np.sum(1-np.exp(-beta[0,0]*(T-neg))) +\
np.sum(np.log(mu[0,0]+alpha[0,0]*R11[1:]+alpha[0,1]*R12[1:]))
L2 = -mu[1,0]*T -(alpha[1,0]/beta[1,0])*np.sum(1-np.exp(-beta[1,0]*(T-pos))) -\
(alpha[1,1]/beta[1,0])*np.sum(1-np.exp(-beta[1,0]*(T-neg))) +\
np.sum(np.log(mu[1,0]+alpha[1,0]*R21[1:]+alpha[1,1]*R22[1:]))
return -L1 - L2
def likelihood(theta,data,modelType):
'''
Calculate the likelihood of hawkes model given theta and data
data is the np decomposed representation of data
'''
if modelType == '6':
mu = np.array(theta[:2]).reshape(2,1)
alpha = np.array(theta[2:6]).reshape(2,2)
if modelType == '4':
mu = np.array([theta[0],theta[0]]).reshape(2,1)
alpha = np.array([theta[2],theta[3],theta[3],theta[2]]).reshape(2,2)
if modelType == '2cross':
mu = np.array([theta[0],theta[0]]).reshape(2,1)
alpha = np.array([0.0,theta[3],theta[3],0.0]).reshape(2,2)
#Fix beta to be [1,1,1,1]
beta = np.ones((2,1))
pos = data[data[:,1] == 1.0,0].reshape(-1,1)
neg = data[data[:,1] == -1.0,0].reshape(-1,1)
pos = pos.astype(float,copy=False)
neg = neg.astype(float,copy=False)
N = pos.shape[0]
M = neg.shape[0]
T = data[-1,0]
R11 = getR.getR11(N,beta[0,0],pos)
R12 = getR.getR12(N,M,beta[0,0],pos,neg)
R21 = getR.getR21(N,M,beta[1,0],pos,neg)
R22 = getR.getR22(M,beta[1,0],neg)
L1 = -mu[0,0]*T -(alpha[0,0]/beta[0,0])*np.sum(1-np.exp(-beta[0,0]*(T-pos))) -\
(alpha[0,1]/beta[0,0])*np.sum(1-np.exp(-beta[0,0]*(T-neg))) +\
np.sum(np.log(mu[0,0]+alpha[0,0]*R11[1:]+alpha[0,1]*R12[1:]))
L2 = -mu[1,0]*T -(alpha[1,0]/beta[1,0])*np.sum(1-np.exp(-beta[1,0]*(T-pos))) -\
(alpha[1,1]/beta[1,0])*np.sum(1-np.exp(-beta[1,0]*(T-neg))) +\
np.sum(np.log(mu[1,0]+alpha[1,0]*R21[1:]+alpha[1,1]*R22[1:]))
return -L1-L2
def compensator(theta,data):
'''
Calculate the compensator for a given bivariate hawkes process sequence
'''
mu = np.array(theta[:2]).reshape(2,1)
alpha = np.array(theta[2:6]).reshape(2,2)
beta = np.ones((2,1))
data[:,0] = np.cumsum(data[:,0])
pos = data[data[:,1] == 1.0,0].reshape(-1,1)
neg = data[data[:,1] == -1.0,0].reshape(-1,1)
pos = pos.astype(float,copy=False)
neg = neg.astype(float,copy=False)
N = pos.shape[0]
M = neg.shape[0]
T = data[-1,0]
A11 = getR.getR11(N,beta[0,0],pos)
A12 = getR.getR12(N,M,beta[0,0],pos,neg)
A21 = getR.getR21(N,M,beta[1,0],pos,neg)
A22 = getR.getR22(M,beta[1,0],neg)
Lambda1 = np.zeros((N-1,1))
Lambda2 = np.zeros((M-1,1))
for i in range(1, N):
#Lambda_i is the compensator between t(i-1) and i
#therefore i ranges from 1 to N
#i-1 ranges from 0 to N-1
#when store Lambda_i into Lambda array, the first element goes to
#index 0, so on and so forth
storeIndex = i-1
dur = pos[i,0] - pos[i-1,0]
beta1 = beta[0,0]
mu1 = mu[0,0]
alpha11 = alpha[0,0]
alpha12 = alpha[0,1]
value = mu1 * dur
part1 = alpha11/beta1 * ((1+A11[i-1,0])*(1-np.exp(-beta1*dur)))
temp = neg[(neg>=pos[i-1,0]) & (neg<pos[i,0])]
if temp.shape[0] > 0:
temp = np.sum(1-np.exp(-beta1 * (pos[i,0] - temp)))
else:
temp = 0.0
part2 = alpha12/beta1 * ((1-np.exp(-beta1 * dur)) * A12[i-1,0] + temp)
value = value + part1 + part2
Lambda1[storeIndex] = value
for i in range(1, M):
storeIndex = i-1
dur = neg[i,0] - neg[i-1,0]
beta2 = beta[1,0]
mu2 = mu[1,0]
alpha21 = alpha[1,0]
alpha22 = alpha[1,1]
value = mu2 * dur
part1 = alpha22/beta2 * ((1+A22[i-1,0])*(1-np.exp(-beta2*dur)))
temp = pos[(pos>=neg[i-1,0]) & (pos<neg[i,0])]
if temp.shape[0] > 0:
temp = np.sum(1-np.exp(-beta2 * (neg[i,0] - temp)))
else:
temp = 0.0
part2 = alpha21/beta2 * ((1-np.exp(-beta2 * dur)) * A21[i-1,0] + temp)
value = value + part1 + part2
Lambda2[storeIndex] = value
return Lambda1,Lambda2