Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach

• URL: http://arxiv.org/abs/2306.06756v2
• Date: Thu, 27 Jun 2024 06:18:52 GMT
• Title: Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach
• Authors: Si Cheng, Jon Wakefield, Ali Shojaie,
• Abstract summary: Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous process conditioned on the realization of a random intensity function. Existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions.
• Score: 3.085995273374333
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial heterogeneity and dependence. However, existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions. We propose a penalized regression method for estimating covariate effects in doubly-stochastic point processes that is computationally efficient and does not require a parametric form or stationarity of the underlying intensity. Our approach is based on an approximate (discrete and deterministic) formulation of the true (continuous and stochastic) intensity function. We show that consistency and asymptotic normality of the covariate effect estimates can be achieved despite the model misspecification, and develop a covariance estimator that leads to a valid, albeit conservative, statistical inference procedure. A simulation study shows the validity of our approach under less restrictive assumptions on the data generating mechanism, and an application to Seattle crime data demonstrates better prediction accuracy compared with existing alternatives.

Related papers

• Trust-Region Sequential Quadratic Programming for Stochastic Optimization with Random Models [57.52124921268249]
  We propose a Trust Sequential Quadratic Programming method to find both first and second-order stationary points. To converge to first-order stationary points, our method computes a gradient step in each iteration defined by minimizing a approximation of the objective subject. To converge to second-order stationary points, our method additionally computes an eigen step to explore the negative curvature the reduced Hessian matrix.
  arXiv  Detail & Related papers  (2024-09-24T04:39:47Z)
• Probabilistic Conformal Prediction with Approximate Conditional Validity [81.30551968980143]
  We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution. Our method consistently outperforms existing approaches in terms of conditional coverage.
  arXiv  Detail & Related papers  (2024-07-01T20:44:48Z)
• Model Free Prediction with Uncertainty Assessment [7.524024486998338]
  We propose a novel framework that transforms the deep estimation paradigm into a platform conducive to conditional mean estimation. We develop an end-to-end convergence rate for the conditional diffusion model and establish the normality of the generated samples. Through numerical experiments, we empirically validate the efficacy of our proposed methodology.
  arXiv  Detail & Related papers  (2024-05-21T11:19:50Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Spectral Representation Learning for Conditional Moment Models [33.34244475589745]
  We propose a procedure that automatically learns representations with controlled measures of ill-posedness. Our method approximates a linear representation defined by the spectral decomposition of a conditional expectation operator. We show this representation can be efficiently estimated from data, and establish L2 consistency for the resulting estimator.
  arXiv  Detail & Related papers  (2022-10-29T07:48:29Z)
• Statistical Efficiency of Score Matching: The View from Isoperimetry [96.65637602827942]
  We show a tight connection between statistical efficiency of score matching and the isoperimetric properties of the distribution being estimated. We formalize these results both in the sample regime and in the finite regime.
  arXiv  Detail & Related papers  (2022-10-03T06:09:01Z)
• Spatially-Varying Bayesian Predictive Synthesis for Flexible and Interpretable Spatial Prediction [6.07227513262407]
  We propose a novel methodology that captures spatially-varying model uncertainty, which we call spatial Bayesian predictive synthesis. We show that our proposed spatial Bayesian predictive synthesis outperforms standard spatial models and advanced machine learning methods.
  arXiv  Detail & Related papers  (2022-03-10T07:16:29Z)
• Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints [0.0]
  We present a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a boundary value problem from a prior probability model. A statistical surrogate model of the implicit mapping, which represents the constraints, is introduced. In a second part, an application is presented to illustrate the proposed theory and is also, as such, a contribution to the three-dimensional homogenization of heterogeneous linear elastic media.
  arXiv  Detail & Related papers  (2022-02-10T16:00:10Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• Statistical optimality and stability of tangent transform algorithms in logit models [6.9827388859232045]
  We provide conditions on the data generating process to derive non-asymptotic upper bounds to the risk incurred by the logistical optima. In particular, we establish local variation of the algorithm without any assumptions on the data-generating process. We explore a special case involving a semi-orthogonal design under which a global convergence is obtained.
  arXiv  Detail & Related papers  (2020-10-25T05:15:13Z)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.