Point process intensities and statistical estimation thereof

August 1, 2016 — July 7, 2021

branching
point processes
spatial
statmech

Suspiciously similar content

On understanding and estimating the intensity function of inhomogeneous Poisson point processes.

Figure 1

1 References

Aalen, Odd O. 1978. “Nonparametric Inference for a Family of Counting Processes.” The Annals of Statistics.
Aalen, Odd O. 1989. “A Linear Regression Model for the Analysis of Life Times.” Statistics in Medicine.
Andersen, Borgan, Gill, et al. 1997. Statistical models based on counting processes. Springer series in statistics.
Arora, Ge, Ma, et al. 2015. “Simple, Efficient, and Neural Algorithms for Sparse Coding.” In Proceedings of The 28th Conference on Learning Theory.
Bacry, Bompaire, Gaïffas, et al. 2020. “Sparse and Low-Rank Multivariate Hawkes Processes.” Journal of Machine Learning Research.
Bacry, and Muzy. 2016. “First- and Second-Order Statistics Characterization of Hawkes Processes and Non-Parametric Estimation.” IEEE Transactions on Information Theory.
Baddeley, and Turner. 2000. “Practical Maximum Pseudolikelihood for Spatial Point Patterns.” Australian & New Zealand Journal of Statistics.
Bashtannyk, and Hyndman. 2001. “Bandwidth Selection for Kernel Conditional Density Estimation.” Computational Statistics & Data Analysis.
Bauwens, and Hautsch. 2006. “Stochastic Conditional Intensity Processes.” Journal of Financial Econometrics.
Berman, and Diggle. 1989. “Estimating Weighted Integrals of the Second-Order Intensity of a Spatial Point Process.” Journal of the Royal Statistical Society. Series B (Methodological).
Berman, and Turner. 1992. “Approximating Point Process Likelihoods with GLIM.” Journal of the Royal Statistical Society. Series C (Applied Statistics).
Besag. 1977. “Efficiency of Pseudolikelihood Estimation for Simple Gaussian Fields.” Biometrika.
Bowsher. 2007. “Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models.” Journal of Econometrics.
Brémaud. 1972. “A Martingale Approach to Point Processes.”
Brémaud, Massoulié, and Ridolfi. 2005. “Power Spectra of Random Spike Fields and Related Processes.” Advances in Applied Probability.
Brown, Cai, and Zhou. 2010. “Nonparametric Regression in Exponential Families.” The Annals of Statistics.
Chaudhuri. 1991. “Nonparametric Estimates of Regression Quantiles and Their Local Bahadur Representation.” The Annals of Statistics.
Chilinski, and Silva. 2020. “Neural Likelihoods via Cumulative Distribution Functions.” arXiv:1811.00974 [Cs, Stat].
Claeskens, Krivobokova, and Opsomer. 2009. “Asymptotic Properties of Penalized Spline Estimators.” Biometrika.
Cox, D. R. 1965. “On the Estimation of the Intensity Function of a Stationary Point Process.” Journal of the Royal Statistical Society: Series B (Methodological).
Cox, Dennis D., and O’Sullivan. 1990. “Asymptotic Analysis of Penalized Likelihood and Related Estimators.” The Annals of Statistics.
Crisan, and Míguez. 2014. “Particle-Kernel Estimation of the Filter Density in State-Space Models.” Bernoulli.
Cronie, Ottmar, Moradi, and Biscio. 2021. “Statistical Learning and Cross-Validation for Point Processes.” arXiv:2103.01356 [Math, Stat].
Cronie, O., and van Lieshout. 2016. “Bandwidth Selection for Kernel Estimators of the Spatial Intensity Function.” arXiv:1611.10221 [Stat].
Cucala. 2008. “Intensity Estimation for Spatial Point Processes Observed with Noise.” Scandinavian Journal of Statistics.
Cunningham, Shenoy, and Sahani. 2008. “Fast Gaussian Process Methods for Point Process Intensity Estimation.” In Proceedings of the 25th International Conference on Machine Learning. ICML ’08.
Diggle, Peter J. 1979. “On Parameter Estimation and Goodness-of-Fit Testing for Spatial Point Patterns.” Biometrics.
Diggle, Peter. 1985. “A Kernel Method for Smoothing Point Process Data.” Journal of the Royal Statistical Society. Series C (Applied Statistics).
Drovandi, Pettitt, and McCutchan. 2016. “Exact and Approximate Bayesian Inference for Low Integer-Valued Time Series Models with Intractable Likelihoods.” Bayesian Analysis.
Eden, Frank, Barbieri, et al. 2004. “Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering.” Neural Computation.
Eichler, Dahlhaus, and Dueck. 2016. “Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions.” Journal of Time Series Analysis.
Ellis. 1991. “Density Estimation for Point Processes.” Stochastic Processes and Their Applications.
Fan, and Li. 2001. “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties.” Journal of the American Statistical Association.
Fatalov. 2012. “Integral Functionals for the Exponential of the Wiener Process and the Brownian Bridge: Exact Asymptotics and Legendre Functions.” Mathematical Notes.
Flaxman, Teh, and Sejdinovic. 2016. “Poisson Intensity Estimation with Reproducing Kernels.” arXiv:1610.08623 [Stat].
Gaïffas, and Guilloux. 2012. “High-Dimensional Additive Hazards Models and the Lasso.” Electronic Journal of Statistics.
Gelfand, and Banerjee. 2010. “Multivariate Spatial Process Models.” In Handbook of Spatial Statistics.
Green. 1987. “Penalized Likelihood for General Semi-Parametric Regression Models.” International Statistical Review / Revue Internationale de Statistique.
Guan. 2008. “A Goodness-of-Fit Test for Inhomogeneous Spatial Poisson Processes.” Biometrika.
Gui, and Li. 2005. “Penalized Cox Regression Analysis in the High-Dimensional and Low-Sample Size Settings, with Applications to Microarray Gene Expression Data.” Bioinformatics.
Hansen. 2010. “Penalized Maximum Likelihood Estimation for Generalized Linear Point Processes.” arXiv:1003.0848 [Math, Stat].
Hansen, Reynaud-Bouret, and Rivoirard. 2015. “Lasso and Probabilistic Inequalities for Multivariate Point Processes.” Bernoulli.
Hawe, Kleinsteuber, and Diepold. 2013. “Analysis Operator Learning and Its Application to Image Reconstruction.” IEEE Transactions on Image Processing.
Helmers, and Mangku. 1999. “Statistical Estimation of Poisson Intensity Functions.” ANN. INST. STAT. MATH.
Hurvich, Simonoff, and Tsai. 1998. “Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion.” Journal of the Royal Statistical Society. Series B (Statistical Methodology).
Jensen, and Künsch. 1994. “On Asymptotic Normality of Pseudo Likelihood Estimates for Pairwise Interaction Processes.” Annals of the Institute of Statistical Mathematics.
Jensen, and Møller. 1991. “Pseudolikelihood for Exponential Family Models of Spatial Point Processes.” The Annals of Applied Probability.
Juban, Fugon, and Kariniotakis. 2007. “Probabilistic Short-Term Wind Power Forecasting Based on Kernel Density Estimators.” In.
Koenker, and Mizera. 2006. “Density Estimation by Total Variation Regularization.” Advances in Statistical Modeling and Inference.
Konishi, and Kitagawa. 1996. “Generalised Information Criteria in Model Selection.” Biometrika.
Kroll. 2016. “Concentration Inequalities for Poisson Point Processes with Application to Adaptive Intensity Estimation.” arXiv:1612.07901 [Math, Stat].
Krumin, and Shoham. 2009. “Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions.” Neural Computation.
Lee, Lim, and Ong. 2016. “Hawkes Processes with Stochastic Excitations.” In ICML.
Lindsey. 1995. “Fitting Parametric Counting Processes by Using Log-Linear Models.” Journal of the Royal Statistical Society. Series C (Applied Statistics).
Marcus, Marblestone, and Dean. 2014. “The atoms of neural computation.” Science.
Marteau-Ferey, Bach, and Rudi. 2020. “Non-Parametric Models for Non-Negative Functions.” In Proceedings of the 34th International Conference on Neural Information Processing Systems. NIPS ’20.
Marzen, and Crutchfield. 2020. “Inference, Prediction, and Entropy-Rate Estimation of Continuous-Time, Discrete-Event Processes.” arXiv:2005.03750 [Cond-Mat, Physics:nlin, Stat].
Micchelli, and Olsen. 2000. “Penalized Maximum-Likelihood Estimation, the Baum–Welch Algorithm, Diagonal Balancing of Symmetric Matrices and Applications to Training Acoustic Data.” Journal of Computational and Applied Mathematics.
Mishra, Rizoiu, and Xie. 2016. “Feature Driven and Point Process Approaches for Popularity Prediction.” In Proceedings of the 25th ACM International Conference on Information and Knowledge Management. CIKM ’16.
Møller, and Waagepetersen. 2017. “Some Recent Developments in Statistics for Spatial Point Patterns.” Annual Review of Statistics and Its Application.
Ng, and Zammit-Mangion. 2020. “Non-Homogeneous Poisson Process Intensity Modeling and Estimation Using Measure Transport.” arXiv:2007.00248 [Stat].
Olshausen, and Field. 1996. “Natural image statistics and efficient coding.” Network (Bristol, England).
Omi, Ueda, and Aihara. 2020. “Fully Neural Network Based Model for General Temporal Point Processes.” arXiv:1905.09690 [Cs, Stat].
Panaretos, and Zemel. 2016. “Separation of Amplitude and Phase Variation in Point Processes.” The Annals of Statistics.
Pnevmatikakis. 2017. “Compressed Sensing and Optimal Denoising of Monotone Signals.” In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).
Puri, and Tuan. 1986. “Maximum Likelihood Estimation for Stationary Point Processes.” Proceedings of the National Academy of Sciences of the United States of America.
Rásonyi, and Tikosi. 2022. “On the Stability of the Stochastic Gradient Langevin Algorithm with Dependent Data Stream.” Statistics & Probability Letters.
Ravanbakhsh, Schneider, and Poczos. 2016. “Deep Learning with Sets and Point Clouds.” In arXiv:1611.04500 [Cs, Stat].
Reynaud-Bouret. 2003. “Adaptive Estimation of the Intensity of Inhomogeneous Poisson Processes via Concentration Inequalities.” Probability Theory and Related Fields.
Reynaud-Bouret, Rivoirard, Grammont, et al. 2014. “Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis.” The Journal of Mathematical Neuroscience.
Reynaud-Bouret, and Roy. 2007. “Some Non Asymptotic Tail Estimates for Hawkes Processes.” Bulletin of the Belgian Mathematical Society - Simon Stevin.
Reynaud-Bouret, and Schbath. 2010. “Adaptive Estimation for Hawkes Processes; Application to Genome Analysis.” The Annals of Statistics.
Riabiz, Ardeshiri, and Godsill. 2016. “A Central Limit Theorem with Application to Inference in α-Stable Regression Models.” In.
Rizoiu, Xie, Sanner, et al. 2017. “Expecting to Be HIP: Hawkes Intensity Processes for Social Media Popularity.” In World Wide Web 2017, International Conference on. WWW ’17.
Schelldorfer, Meier, and Bühlmann. 2014. “GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using ℓ1-Penalization.” Journal of Computational and Graphical Statistics.
Schoenberg. 2005. “Consistent Parametric Estimation of the Intensity of a Spatial–Temporal Point Process.” Journal of Statistical Planning and Inference.
Silverman. 1982. “On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method.” The Annals of Statistics.
———. 1984. “Spline Smoothing: The Equivalent Variable Kernel Method.” The Annals of Statistics.
Smith, and Brown. 2003. “Estimating a State-Space Model from Point Process Observations.” Neural Computation.
Soen, Mathews, Grixti-Cheng, et al. 2021. “UNIPoint: Universally Approximating Point Processes Intensities.” arXiv:2007.14082 [Cs, Stat].
Städler, and Mukherjee. 2013. “Penalized Estimation in High-Dimensional Hidden Markov Models with State-Specific Graphical Models.” The Annals of Applied Statistics.
Stefanski, and Carroll. 1990. “Deconvolving Kernel Density Estimators.” Statistics.
Thrampoulidis, Abbasi, and Hassibi. 2015. “LASSO with Non-Linear Measurements Is Equivalent to One With Linear Measurements.” In Advances in Neural Information Processing Systems 28.
Tsuchida, Ong, and Sejdinovic. 2023. “Squared Neural Families: A New Class of Tractable Density Models.”
Turlach. 1993. “Bandwidth Selection in Kernel Density Estimation: A Review.”
van de Geer, Bühlmann, Ritov, et al. 2014. “On Asymptotically Optimal Confidence Regions and Tests for High-Dimensional Models.” The Annals of Statistics.
van Lieshout. 2011. “On Estimation of the Intensity Function of a Point Process.” Methodology and Computing in Applied Probability.
Willett, and Nowak. 2007. “Multiscale Poisson Intensity and Density Estimation.” IEEE Transactions on Information Theory.
Witten, Tibshirani, and Hastie. 2009. “A Penalized Matrix Decomposition, with Applications to Sparse Principal Components and Canonical Correlation Analysis.” Biostatistics.
Wörmann, Hawe, and Kleinsteuber. 2013. “Analysis Based Blind Compressive Sensing.” IEEE Signal Processing Letters.
Wu, Müller, and Zhang. 2013. “Functional Data Analysis for Point Processes with Rare Events.” Statistica Sinica.
Zhang, Rui, Walder, and Rizoiu. 2020. “Variational Inference for Sparse Gaussian Process Modulated Hawkes Process.” In Proceedings of the AAAI Conference on Artificial Intelligence.
Zhang, Cun-Hui, and Zhang. 2014. “Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).