Determinantal point process models and statistical inference : Extended version

Abstract

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric models, where the likelihood and moment expressions can be easily evaluated and realizations can be quickly simulated. We discuss how statistical inference is conducted using the likelihood or moment properties of DPP models, and we provide freely available software for simulation and statistical inference.

References in corpus (2)

• Determinantal point processes for machine learning
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces

Cited by in corpus (66)

• Diversity in Machine Learning
• Quantifying repulsiveness of determinantal point processes
• Point Processes with Gaussian Boson Sampling
• On the topology of random complexes built over stationary point processes
• Efficient simulation of the Ginibre point process
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• Convex and non-convex regularization methods for spatial point processes intensity estimation
• Bayesian Inference for Latent Biologic Structure with Determinantal Point Processes (DPP)
• Polynomial Ensembles and Recurrence Coefficients
• A spatio-temporal multi-scale model for Geyer saturation point process: application to forest fire occurrences
• CLIP-It! Language-Guided Video Summarization
• Exact Sampling of Determinantal Point Processes without Eigendecomposition
• Approximate Inference in Continuous Determinantal Point Processes
• Simulating Coulomb gases and log-gases with hybrid Monte Carlo algorithms
• Large gap asymptotics for the generating function of the sine point process
• Kronecker Determinantal Point Processes
• Fluctuations of observables for free fermions in a harmonic trap at finite temperature
• A determinantal point process for column subset selection
• On two ways to use determinantal point processes for Monte Carlo integration
• Spatial networks with wireless applications
• Orthogonal series estimation of the pair correlation function of a spatial point process
• Parsimonious Hierarchical Modeling Using Repulsive Distributions
• Gaussian Determinantal Processes: a new model for directionality in data
• Inference for determinantal point processes without spectral knowledge
• Rates of estimation for determinantal point processes
• Comparative evaluation of point process forecasts
• Maximum likelihood estimation of determinantal point processes
• A bound of the $\beta$-mixing coefficient for point processes in terms of their intensity functions
• Territorial behaviour of buzzards versus random matrix spacing distributions
• Incomplete determinantal processes: from random matrix to Poisson statistics
• Diffraction Theory of Point Processes: Systems with Clumping and Repulsion
• Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations
• Perfect Simulation of Determinantal Point Processes
• Deep Determinantal Point Processes
• A Polynomial Time MCMC Method for Sampling from Continuous DPPs
• Interactions Between Different Birds of Prey as a Random Point Process
• Bessel kernel determinants and integrable equations
• On spatial and spatio-temporal multi-structure point process models
• Determinantal Sampling Designs
• Stein's method and Papangelou intensity for Poisson or Cox process approximation
• A tutorial on estimator averaging in spatial point process models
• Effective Visualization and Analysis of Recommender Systems
• Approximation of Functions: Optimal Sampling and Complexity
• Energy-Based Processes for Exchangeable Data
• Normal approximation for associated point processes via Stein's method with applications to determinantal point processes
• Optimal Design Emulators: A Point Process Approach
• Signal reconstruction using determinantal sampling
• Circulant $L$-ensembles in the thermodynamic limit
• On determinantal point processes with nonsymmetric kernels
• Coverage probability in wireless networks with determinantal scheduling
• Determinantal thinning of point processes with network learning applications
• Spatial modeling and analysis of cellular networks using the Ginibre point process: A tutorial
• Hyperuniform and rigid stable matchings
• Graphical structure of conditional independencies in determinantal point processes
• DPPy: Sampling DPPs with Python
• Testing Determinantal Point Processes
• Approximation intensity for pairwise interaction Gibbs point processes using determinantal point processes
• Median-based estimation of the intensity of a spatial point process
• Moment convergence of the generalized maximum composite likelihood estimators for determinantal point processes
• Nonparametric estimation of continuous DPPs with kernel methods
• On sampling determinantal and Pfaffian point processes on a quantum computer
• Multi-type branching processes with immigration generated by point processes
• Regularization techniques for inhomogeneous (spatial) point processes intensity and conditional intensity estimation
• Intracell Interference Characterization and Cluster Inference for D2D Communication
• Choosing the Best of Both Worlds: Diverse and Novel Recommendations through Multi-Objective Reinforcement Learning
• Learning from DPPs via Sampling: Beyond HKPV and symmetry