Related papers: Spatio-temporal determinantal point processes
Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…
Numerous powerful point process models have been developed to understand temporal patterns in sequential data from fields such as health-care, electronic commerce, social networks, and natural disaster forecasting. In this paper, we develop…
We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
Determinantal point processes (DPPs) have recently proved to be a useful class of models in several areas of statistics, including spatial statistics, statistical learning and telecommunications networks. They are models for repulsive (or…
We review how to simulate continuous determinantal point processes (DPPs) and improve the current simulation algorithms in several important special cases as well as detail how certain types of conditional simulation can be carried out.…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
A temporal point process is a stochastic process that predicts which type of events is likely to happen and when the event will occur given a history of a sequence of events. There are various examples of occurrence dynamics in the daily…
We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive…
This paper proposes a log-linear model for the latent intensity functions of a replicated spatio-temporal point process. By simultaneously fitting correlated spatial and temporal Karhunen-Lo\`eve expansions, the model produces spatial and…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…
Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities…
This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the processes are…