Module `HawkesPyLib.core.logll`

Functions

def uvhp_expo_logL(param_vec: numpy.ndarray, sample_vec: numpy.ndarray, tn: float) ‑> float

Log-likelihood function for a Hawkes Process with single exponential kernel

param_vec : np.ndarray: array of parameter: [mu, eta, theta]
sample_vec : np.ndarray: array of timestamps. Must be sorted in ascending order. All timestamps must be positive.
tn : float: End time of the Hawkes process. Must be larger or equal than the last timestamp i.e. tn >= sample_vec[-1]

def uvhp_expo_logL_grad(param_vec: numpy.ndarray, sample_vec: numpy.ndarray, tn: float) ‑> numpy.ndarray

Gradient of the log-likelihood function for a Hawkes Process with single exponential kernel

param_vec : np.ndarray: array of parameter: [mu, eta, theta]
sample_vec : np.ndarray: array of timestamps. Must be sorted in ascending order. All timestamps must be positive.
tn : float: End time of the Hawkes process. Must be larger or equal than the last timestamp i.e. tn >= sample_vec[-1]

np.ndarray: The negative value of each gradient: [mu gradient, eta gradient, theta gradient]

def uvhp_sum_expo_logL(param_vec: numpy.ndarray, sample_vec: numpy.ndarray, tn: float) ‑> float

Log-likelihood function for a Hawkes Process with P-sum exponential kernel

param_vec : np.ndarray: array of parameter: [mu, eta, theta1, theta2, …, thetaP]
sample_vec : np.ndarray: array of timestamps. Must be sorted in ascending order. All timestamps must be positive.
tn : float: End time of the Hawkes process. Must be larger or equal than the last timestamp i.e. tn >= sample_vec[-1]

def uvhp_sum_expo_logL_grad(param_vec: numpy.ndarray, sample_vec: numpy.ndarray, tn: float) ‑> numpy.ndarray

Gradient of the log-likelihood function for a Hawkes Process with P-sum exponential kernel

param_vec : np.ndarray: array of parameter: [mu, eta, theta1, theta2, …, thetaP]
sample_vec : np.ndarray: array of timestamps. Must be sorted in ascending order. All timestamps must be positive.
tn : float: End time of the Hawkes process. Must be larger or equal than the last timestamp i.e. tn >= sample_vec[-1]

np.ndarray: The negative value of each gradient: [mu gradient, eta gradient, theta1 gradient, …, thetaP gradient]

def uvhp_approx_powl_cut_logL(param_vec: numpy.ndarray, sample_vec: numpy.ndarray, tn: float, m: float, M: int) ‑> float

Log-likelihood function for a Hawkes Process with approximate power-law kernel with cutoff component

param_vec : np.ndarray: array of parameter: [mu, eta, theta1, theta2, …, thetaP]
sample_vec : np.ndarray: array of timestamps. Must be sorted in ascending order. All timestamps must be positive.
tn : float: End time of the Hawkes process. Must be larger or equal than the last timestamp i.e. tn >= sample_vec[-1]
m : float: Fixed kernel variable
M : int: Fixed kernel variable

def uvhp_approx_powl_logL(param_vec: numpy.ndarray, sample_vec: numpy.ndarray, tn: float, m: float, M: int) ‑> float

Log-likelihood function for a Hawkes Process with approximate power-law kernel without cutoff component

param_vec : np.ndarray: array of parameter: [mu, eta, theta1, theta2, …, thetaP]
sample_vec : np.ndarray: array of timestamps. Must be sorted in ascending order. All timestamps must be positive.
tn : float: End time of the Hawkes process. Must be larger or equal than the last timestamp i.e. tn >= sample_vec[-1]
m : float: Fixed kernel variable
M : int: Fixed kernel variable