Similarity measures of conditional intensity functions to test separability in multidimensional point processes

2012 ◽  
Vol 27 (5) ◽  
pp. 1193-1205 ◽  
Author(s):  
Carlos Díaz-Avalos ◽  
P. Juan ◽  
J. Mateu
Keyword(s):  
Point Processes ◽  
Similarity Measures ◽  
Conditional Intensity ◽  
Intensity Functions

scholarly journals Thinning spatial point processes into Poisson processes

2010 ◽  
Vol 42 (02) ◽  
pp. 347-358 ◽  
Author(s):  
Jesper Møller ◽  
Frederic Paik Schoenberg
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Point Processes ◽  
Death Process ◽  
Cox Process ◽  
Birth And Death Process ◽  
Conditional Intensity ◽  
Spatial Point Processes ◽  
Spatial Point

In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.

scholarly journals Patent Citation Dynamics Modeling via Multi-Attention Recurrent Networks

2019 ◽  
Author(s):  
Taoran Ji ◽  
Zhiqian Chen ◽  
Nathan Self ◽  
Kaiqun Fu ◽  
Chang-Tien Lu ◽  
...  
Keyword(s):  
Point Processes ◽  
Patent Citation ◽  
Multiple Time ◽  
Conditional Intensity ◽  
Dynamics Modeling ◽  
Proposed Model ◽  
Modeling And Forecasting ◽  
A Chain ◽  
Forward Citation ◽  
Forward Citations

Modeling and forecasting forward citations to a patent is a central task for the discovery of emerging technologies and for measuring the pulse of inventive progress. Conventional methods for forecasting these forward citations cast the problem as analysis of temporal point processes which rely on the conditional intensity of previously received citations. Recent approaches model the conditional intensity as a chain of recurrent neural networks to capture memory dependency in hopes of reducing the restrictions of the parametric form of the intensity function. For the problem of patent citations, we observe that forecasting a patent's chain of citations benefits from not only the patent's history itself but also from the historical citations of assignees and inventors associated with that patent. In this paper, we propose a sequence-to-sequence model which employs an attention-of-attention mechanism to capture the dependencies of these multiple time sequences. Furthermore, the proposed model is able to forecast both the timestamp and the category of a patent's next citation. Extensive experiments on a large patent citation dataset collected from USPTO demonstrate that the proposed model outperforms state-of-the-art models at forward citation forecasting.

On the variance to mean ratio for random variables from Markov chains and point processes

1998 ◽  
Vol 35 (2) ◽  
pp. 303-312 ◽  
Author(s):  
Timothy C. Brown ◽  
Kais Hamza ◽  
Aihua Xia
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Point Process ◽  
Continuous Time ◽  
Infinitesimal Generator ◽  
Point Processes ◽  
Random Variables ◽  
Simple Point ◽  
Conditional Intensity

Criteria are determined for the variance to mean ratio to be greater than one (over-dispersed) or less than one (under-dispersed). This is done for random variables which are functions of a Markov chain in continuous time, and for the counts in a simple point process on the line. The criteria for the Markov chain are in terms of the infinitesimal generator and those for the point process in terms of the conditional intensity. Examples include a conjecture of Faddy (1994). The case of time-reversible point processes is particularly interesting, and here underdispersion is not possible. In particular, point processes which arise from Markov chains which are time-reversible, have finitely many states and are irreducible are always overdispersed.

A Reproducing Kernel Hilbert Space Framework for Spike Train Signal Processing

2009 ◽  
Vol 21 (2) ◽  
pp. 424-449 ◽  
Author(s):  
António R. C. Paiva ◽  
Il Park ◽  
José C. Príncipe
Keyword(s):  
Signal Processing ◽  
Spike Train ◽  
Point Processes ◽  
Clustering Algorithm ◽  
Reproducing Kernel ◽  
Spike Trains ◽  
Inner Product ◽  
Inner Products ◽  
Definition Of ◽  
Intensity Functions

This letter presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a family of these inner products, the cross-intensity (CI) kernels, is analyzed in detail. This inner product family encapsulates the statistical description from the conditional intensity functions of spike trains. The problem of their estimation is also addressed. The simplest of the spike train kernels in this family provide an interesting perspective to others' work, as will be demonstrated in terms of spike train distance measures. Finally, as an application example, the RKHS framework is used to derive a clustering algorithm for spike trains from simple principles.

scholarly journals Thinning spatial point processes into Poisson processes

2010 ◽  
Vol 42 (2) ◽  
pp. 347-358 ◽  
Author(s):  
Jesper Møller ◽  
Frederic Paik Schoenberg
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Point Processes ◽  
Death Process ◽  
Cox Process ◽  
Birth And Death Process ◽  
Conditional Intensity ◽  
Spatial Point Processes ◽  
Spatial Point

In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.

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