Multivariate Hawkes Processes for Large-Scale Inference
نویسندگان
چکیده
In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems, both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Scalable LowRank Hawkes Process (SLRHP) framework introduces a lowrank approximation of the kernel matrix that allows to perform the nonparametric learning of the d triggering kernels in at most O(ndr) operations, where r is the rank of the approximation (r d, n). This comes as a major improvement to the existing state-of-the-art inference algorithms that require O(nd) operations. Furthermore, the low-rank approximation allows SLRHP to learn representative patterns of interaction between event types, which is usually valuable for the analysis of complex processes in real-world networks.
منابع مشابه
Bayesian Inference for Latent Hawkes Processes
Hawkes processes are multivariate point processes that model excitatory interactions among vertices in a network. Each vertex emits a sequence of discrete events: points in time with associated content, or marks. Unlike Poisson processes, Hawkes processes allow events on one vertex to influence the subsequent rate of events on downstream vertices. With this property, they are ideally suited to ...
متن کاملFrom point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining
This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A...
متن کاملSome limit theorems for Hawkes processes and application to financial statistics
In the context of statistics for random processes, we prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] when T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the observations are imposed by a discrete scheme wit...
متن کاملScaling limits for Hawkes processes and application to financial statistics
We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] in the limit T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the observations are imposed by a discrete scheme with mesh ∆ over [0, T ] up to some further ti...
متن کاملUniversal Models of Multivariate Temporal Point Processes (With Supplementary Appendix Containing Proofs)
With the rapidly increasing availability of event stream data there is growing interest in multivariate temporal point process models to capture both qualitative and quantitative features of this type of data. Recent research on multivariate point processes have focused in inference and estimation problems for restricted classes of models such as continuous time Bayesian networks, Markov jump p...
متن کامل