Accelerating maximum likelihood estimation for Hawkes point processes

Hawkes processes are point processes that can be used to build probabilistic models to describe and predict occurrence patterns of random events. They are widely used in high-frequency trading, seismic analysis and neuroscience. A critical numerical calculation in Hawkes process models is parameter estimation, which is used to fit a Hawkes process model to a data set. The parameter estimation problem can be solved by searching for a parameter set that maximises the log-likelihood. A core operation of this search process, the log-likelihood evaluation, is computationally demanding if the number of data points is large. To accelerate the computation, we present a log-likelihood evaluation strategy which is suitable for hardware acceleration. We then design and optimise a pipelined engine based on our proposed strategy. In the experiments, an FPGA-based implementation of the proposed engine is shown to be up to 72 times faster than a single-core CPU, and 10 times faster than an 8-core CPU.