R的多元霍克斯分布

Question

I have a list of N categories that a user can click on. Lets say there are K such users totally. I have the past 3 months data which tells which user has clicked on which category on which date for how many times. For ex - {20th June 2016 : [10,15,12,15]} this dict is for a particular user and says on 20th June he clicked on categories 10,12 once and 15 twice.

Given this data, I want to use a Multivariate Hawks distribution to model this, so that I can predict which categories a user will click on based on the past categories(same and different categories) that have been clicked.

I have already looked at a number of examples. http://jheusser.github.io/2013/09/08/hawkes.html uses a univariate Hawks distribution using ptproc package. ptproc however, doesn't exist now.

I want to feed some random initialization of the mean, alpha and beta parameters and want the model to perform Maximum Likelihood estimation using EM algorithm to find the best values of parameters and return it.

Using the hawkes package,

library(hawkes)
lambda0 <- c(0.2,0.2)
alpha   <- matrix(c(0.5,0,0,0.5),byrow=TRUE,nrow=2)
beta    <- c(0.7,0.7)
history <- simulateHawkes(lambda0,alpha,beta,3600)
l       <- likelihoodHawkes(lambda0,alpha,beta,history)

This computes the likelihood for some random initialization of parameters. How do I find the best parameters by using EM algorithm and maximizing the likelihood here for Multivariate Hawkes distribution ?

Thanks!

Answer 1

params_hawkes <- optim(c(rep(1,2), rep(0.2,4),rep(2,2)), nloglik_bi_hawkes, history = history)

The optim function can be used for finding the best parameters.

nloglik_bi_hawkes <- function(params, history){
mu <- c(params[1],params[2])
alpha <- matrix(c(params[3],params[4],params[5],params[6]),byrow=TRUE,nrow=2)
beta <- c(params[7], params[8])
return(likelihoodHawkes(mu, alpha, beta, history))
}

Here, the alpha, beta and mu are initialized to random values then updated by minimizing the negative log likelihood.

The final list of parameters is stored in param_hawkes