Point Process Framework Research Articles

An Embedded Marked Point Process Framework for Three-Level Object Population Analysis.

In this paper, we introduce a probabilistic approach for extracting the complex hierarchical object structures from the digital images used by various vision applications. The proposed framework extends conventional marked point process (MPP) models by: 1) admitting object-subobject ensembles in parent-child relationships; and 2) allowing corresponding objects to form coherent object groups, by a Bayesian segmentation of the population. Different from earlier, highly domain specific attempts on MPP generalization, the proposed model is defined at an abstract level, providing clear interfaces for applications in various domains. We also introduce a global optimization process for the multi-layer framework for finding optimal entity configurations, considering the observed data, prior knowledge, and interactions between the neighboring and the hierarchically related objects. The proposed method is demonstrated in three different application areas: built in area analysis in remotely sensed images, traffic monitoring on airborne, and mobile laser scanning (Lidar) data and optical circuit inspection. A new benchmark database is published for the three test cases, and the model's performance is quantitatively evaluated.

Neural spike train similarity algorithm detects differences in temporal patterning of bat echolocation call sequences

Bats emit echolocation sounds in complex temporal sequences that change to accommodate dynamic surroundings. Efforts to quantify how these patterns change have included analysis of inter-pulse intervals, sonar sound groups, and changes in individual signal parameters. No standardized method has been adopted for quantifying whether sequences of echolocation calls are similar or different beyond these individual dimensions. Here, a new method is presented for assessing the similarity in temporal structure between trains of bat echolocation sounds. The spike-train similarity space (SSIMS) algorithm, originally designed for neural data analysis, was applied to determine which features of the environment influence temporal patterning of echolocation sounds emitted by flying big brown bats (Eptesicus fuscus). Using a relational point-process framework, SSIMS was able to discriminate between pulse sequences recorded in different flight environments, as well as to separate flights depending on the bat’s expectation of its surroundings based on previous experience.

0461 BEYOND THE INDEX: QUANTITATIVE PHENOTYPING OF APNEA

Clinically, sleep apnea is characterized using metrics such as the Apnea-Hypopnea Index (AHI), a single rate averaged over the total sleep time. While clinically informative, it does not reflect either context or temporal distribution of the events. Thus, it is possible for patients with identical AHIs to present vastly different apnea phenotypes. Additionally, while descriptors relating factors such as sleep stage and position to apnea events can provide useful clinical information, current methods do not quantify the degree to which these factors contribute to the events. It is therefore crucial to develop phenotyping methods that can disambiguate differences in apnea event context, as well as in the relative contributions of different behavioral and physiological factors. We develop a point process approach for quantifying the contributions of different polysomnographic (PSG) observations to the instantaneous respiratory event probability. A point process is any system that can be represented as a series of stochastic momentary events, which is governed by time-varying instantaneous rate or probability. We use a generalized linear model (GLM) framework to estimate the degree to which sleep stage, body position, and previous event timing predicts the instantaneous probability of an event occurring. We applied our point process framework to technician-scored PSGs from a cohort of subjects with severe disease (AHI>30). Models including only position and sleep stage were poor predictors of sleep apnea (Kolmogorov-Smirnov test on time rescaled events). However, by adding the timing of past apnea events to the model, we observed a marked improvement to the model goodness-of-fit. Moreover, the degree to which past events influenced future apnea probability showed heterogeneity and clustering across subjects. These results indicate that past apnea history may be a major influencing factor on apnea probability. This suggests that a single apnea event, while mediated by other factors such as position and stage, may set off a cascade of subsequent respiratory events. Therefore, the structure of the history dependence may be a novel feature for apnea phenotyping and target for evaluating the effects of clinical intervention. NINDS R01 NS-096177 (M.J.P.).

Forest point processes for the automatic extraction of networks in raster data

In this paper, we propose a new stochastic approach for the automatic detection of network structures in raster data. We represent a network as a set of trees with acyclic planar graphs. We embed this model in the probabilistic framework of spatial point processes and determine the most probable configuration of trees by stochastic sampling. That is, different configurations are constructed randomly by modifying the graph parameters and by adding or removing nodes and edges to/ from the current trees. Each configuration is evaluated based on the probabilities for these changes and an energy function describing the conformity with a predefined model. By using the Reversible jump Markov chain Monte Carlo sampler, an approximation of the global optimum of the energy function is iteratively reached. Although our main target application is the extraction of rivers and tidal channels in digital terrain models, experiments with other types of networks in images show the transferability to further applications. Qualitative and quantitative evaluations demonstrate the competitiveness of our approach with respect to existing algorithms.

Volatility estimation under one-sided errors with applications to limit order books

For a semi-martingale $X_{t}$, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation $\langle X,X\rangle_{t}$ is constructed based on observations in the vicinity of $X_{t}$. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive $n^{-1/3}$ as optimal convergence rate in a high-frequency framework with $n$ observations (in mean). We discuss a potential application for the estimation of the integrated squared volatility of an efficient price process $X_{t}$ from intra-day order book quotes.

Multiple objects detection in biological images using a marked point process framework.

The marked point process framework has been successfully developed in the field of image analysis to detect a configuration of predefined objects. The goal of this paper is to show how it can be particularly applied to biological imagery. We present a simple model that shows how some of the challenges specific to biological data are well addressed by the methodology. We further describe an extension to this first model to address other challenges due, for example, to the shape variability in biological material. We finally show results that illustrate the MPP framework using the "simcep" algorithm for simulating populations of cells.

NETWORK DETECTION IN RASTER DATA USING MARKED POINT PROCESSES

Abstract. We propose a new approach for the automatic detection of network structures in raster data. The model for the network structure is represented by a graph whose nodes and edges correspond to junction-points and to connecting line segments, respectively; nodes and edges are further described by certain parameters. We embed this model in the probabilistic framework of marked point processes and determine the most probable configuration of objects by stochastic sampling. That is, different graph configurations are constructed randomly by modifying the graph entity parameters, by adding and removing nodes and edges to/ from the current graph configuration. Each configuration is then evaluated based on the probabilities of the changes and an energy function describing the conformity with a predefined model. By using the Reversible Jump Markov Chain Monte Carlo sampler, a global optimum of the energy function is determined. We apply our method to the detection of river and tidal channel networks in digital terrain models. In comparison to our previous work, we introduce constraints concerning the flow direction of water into the energy function. Our goal is to analyse the influence of different parameter settings on the results of network detection in both, synthetic and real data. Our results show the general potential of our method for the detection of river networks in different types of terrain.

NETWORK DETECTION IN RASTER DATA USING MARKED POINT PROCESSES

We propose a new approach for the automatic detection of network structures in raster data. The model for the network structure is represented by a graph whose nodes and edges correspond to junction-points and to connecting line segments, respectively; nodes and edges are further described by certain parameters. We embed this model in the probabilistic framework of marked point processes and determine the most probable configuration of objects by stochastic sampling. That is, different graph configurations are constructed randomly by modifying the graph entity parameters, by adding and removing nodes and edges to/ from the current graph configuration. Each configuration is then evaluated based on the probabilities of the changes and an energy function describing the conformity with a predefined model. By using the Reversible Jump Markov Chain Monte Carlo sampler, a global optimum of the energy function is determined. We apply our method to the detection of river and tidal channel networks in digital terrain models. In comparison to our previous work, we introduce constraints concerning the flow direction of water into the energy function. Our goal is to analyse the influence of different parameter settings on the results of network detection in both, synthetic and real data. Our results show the general potential of our method for the detection of river networks in different types of terrain.

Using verified species distribution models to inform the conservation of a rare marine species

AbstractAimGiven the paucity of data on the distribution of habitats and species for most marine species, particularly those that are rare and in need of protection, there is a need to model species distributions. Using the fan mussel, Atrina fragilis (Pennant 1777), as our case species, the aim of the study was to predict new areas of occurrence for A. fragilis, estimate the extent of potentially suitable areas, determine the proportion of these areas that are included in the recently designated nature conservation MPAs off the west of Scotland and identify possible environmental drivers in the distribution of A. fragilis.LocationWest coast of Scotland, UK.MethodsUsing a point process framework, we modelled presence‐only data, including historic records. A quadrat survey employing digital still photography was conducted in areas of high and low suitability to verify the model, and subsequently, a targeted survey was undertaken in areas predicted as highly suitable by the models using towed video cameras.ResultsFive environmental variables were of prime importance in explaining the distribution of A. fragilis. The results from the verification survey support model performance. Atrina fragilis was found in 80% of the targeted transects undertaken. Approximately 14% of the total area predicted as suitable for A. fragilis occurred within recently designated marine protected areas (MPAs) indicating considerable potential for recolonization given suitable protection.Main conclusionsThe verified model suggests that limited presence‐only and historical records of rare species can perform well within a SDM framework allowing the identification of further suitable areas. The prominence of bathymetric ruggedness in the models is unexpected, given the understood ecological niche for A. fragilis and pinnids in general, but is consistent with the fact that seabed topography can offer protection from fishing pressure. These results will inform restoration objectives of the MPA network.

Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions - a crime case study

ABSTRACTMany physical and sociological processes are represented as discrete events in time and space. These spatio-temporal point processes are often sparse, meaning that they cannot be aggregated and treated with conventional regression models. Models based on the point process framework may be employed instead for prediction purposes. Evaluating the predictive performance of these models poses a unique challenge, as the same sparseness prevents the use of popular measures such as the root mean squared error. Statistical likelihood is a valid alternative, but this does not measure absolute performance and is therefore difficult for practitioners and researchers to interpret. Motivated by this limitation, we develop a practical toolkit of evaluation metrics for spatio-temporal point process predictions. The metrics are based around the concept of hotspots, which represent areas of high point density. In addition to measuring predictive accuracy, our evaluation toolkit considers broader aspects of predictive performance, including a characterisation of the spatial and temporal distributions of predicted hotspots and a comparison of the complementarity of different prediction methods. We demonstrate the application of our evaluation metrics using a case study of crime prediction, comparing four varied prediction methods using crime data from two different locations and multiple crime types. The results highlight a previously unseen interplay between predictive accuracy and spatio-temporal dispersion of predicted hotspots. The new evaluation framework may be applied to compare multiple prediction methods in a variety of scenarios, yielding valuable new insight into the predictive performance of point process-based prediction.

A Point Process Framework for Predicting Popularity of Content in Online Social Networks

In this paper, we extend previous models to predict the popularity of user-generated content for online social networks (OSNs). We focus on Twitter as the most popular and widely used micro-blogging online social network, and specifically measure the popularity of a brand’s tweet by analyzing the time-series path of its subsequent activities (i.e. retweets, replies and marks as favorite) using multivariate marked Hawkes process models. Self and mutually exciting point process models as a multivariate class are adopted to simulate popularity growth patterns of brand post contents on Twitter. While previous self-exciting point process models aggregate the three types of events into one stream of information and therefore ignore exciting effects among different types of events, this study focuses on incorporating the event type into the predictive models for content popularity, explicitly looking at the effects of various types of users’ activities on Twitter. We aim to develop a mutually exciting point process model in order to incorporate such effects among different types of events. Our results suggest that the mutual-exciting point process model outperforms the self-exciting point process model to predict the popularity of online content, as it is able to capture mutual excitement effects and cross interactions between a sequence of events from one type to another. These results are useful in developing and executing a plan for online activities by the brand owners.

Uncovering statistical features of bradycardia severity in premature infants using a point process model.

Premature infants are susceptible to a variety of life-threatening events. Underdeveloped cardiovascular control due to an immature autonomic nervous system can lead to recurrent bradycardias that reduce blood flow and oxygen to critical organs, and result in long-term developmental disabilities or sudden death. In this study, we investigate the use of a novel point process framework to model heart rate dynamics in premature infants, including the full range of bradycardia severity. We find that the lognormal distribution accurately models the R-R interval time series, due to the long-tail nature of the distribution. We also find that the degree of bradycardia severity is correlated with distinct clustering features of the point-process indices in regions encompassing and adjacent to bradycardias. This underlying property in heart rate dynamics may provide valuable statistical information for quantifying the vulnerability of premature infants to develop bradycardia.

Assessing real-time RR-QT frequency-domain measures of coupling and causality through inhomogeneous point-process bivariate models.

Ventricular repolarization instability is known to be related to arrhythmogenesis and increased risk of sudden cardiac death. These repolarization dynamics are linked to the distance between T-wave and Q-wave occurrences (QT) on the ECG, and they are coupled with R-wave to R-wave interval variability (RRV). Several efforts have been dedicated to the analysis of QT-RR interactions in order to provide both a quantification of the coupling and estimates of intrinsic repolarization dynamics. However, a methodology able to quantify dynamic changes in repolarization variability unrelated to RRV dynamics is still needed. In this study, we propose a bivariate model embedded within a multiple inhomogeneous point-process framework to obtain time-varying tracking of (causal) interactions between QT variability (QTV), a marker of repolarization variability, and RRV. Data from 15 healthy subjects undergoing a tilt table test were analyzed. Our results demonstrate that the model effectively captures the time-varying mutual QTV-RRV interactions. The analysis of time-varying coherence confirms that head-up tilt is associated with a decrease in linear QTV-RRV coupling, while time-varying directed coherence shows that intrinsic QTV becomes more prominent during head-up tilt.

Fluctuation scaling in neural spike trains

The fluctuation scaling (FS) law has been observed in a wide variety of phenomena. It states that the variance of a quantity has a power function relation with the mean. Since Taylor found it in ecological systems [1], the FS law has been demonstrated in many natural and social systems, showing a universality of the law [2]. In this study, The FS law for neural spike trains is formulated using the framework of renewal point processes. In order to quantify the variability of neural firing, two quantities: inter-spike interval (ISI) and spike count, are often measured from spike trains. We first consider the ISI statistics. Let t1,t2,…,tn be a sequence of spike times, and xi=ti-ti-1(i=2,…,n) be ISIs. Letμ=E(X) and σ2=Var(X) denote the mean and variance of ISI, respectively. We consider spike trains such that under a stationary condition σ2 has a power function relation with μ as σ2=ϕμα. (1) The scaling exponent α characterizes the 'intrinsic' dispersion of neuronal firing. For a Poisson (random) process, α=2. On the other hand, α>2(α<2) implies the tendency for the timing of spikes to be over (under) dispersed for large means, and under (over) dispersed for small means. Consider next the counting statistics. Let N(t,t+Δ] be the number of spikes occurred in the counting window (t,t+Δ]. We prove that if the spike train is a renewal process and the interval statistics has the scaling property (1), then the variance of N(t,t+Δ] per unit time is asymptotically scaled by the mean of N(t,t+Δ] per unit time (i.e., the rate) as Var(N(t,t+Δ])Δ=ϕE(N(t,t+Δ])Δβ (2) with β=3-α for Δ>>1. In the presentation, I show the following two results: The fluctuation scaling law emerges in the first-passage time to a threshold of certain diffusion processes (i.e., integrate-and-fire models). The likelihood function of spike trains is constructed, based on which I propose a method for extracting the scaling exponent from nonstationary spike trains. This method is applied to biological spike train data to characterize the variability of neuronal firing. Possible implications of these results are discussed in terms of characterizing intrinsic dynamics of neuronal discharge.

Sequential spatial analysis of large datasets with applications to modern earthwork compaction roller measurement values

In the context of road construction, modern earthwork compaction rollers equipped with sensors collect a virtually continuous flow of soil property measurements. This sequential, spatial data can be utilized to improve the quality control of the compaction process through the introduction of intelligent compaction. These roller measurement values are observed indirectly through non-linear measurement operators, non-stationary, inherently multivariate with complex correlation structures, and collected in huge quantities. The problem of modeling and estimation in a spatially correlated setting with large amounts of data is well known and many approaches can be found in the literature. Very few studies have been completed investigating sequential, spatially correlated data outside of a point process framework. We propose a sequential, spatial mixed-effects model and develop a sequential, spatial backfitting algorithm to estimate fixed effects and several independent, spatially correlated processes. This new algorithm is demonstrated in a simulation study and applied to earthwork compaction data.

A Shape‐Aware Model for Discrete Texture Synthesis

AbstractWe present a novel shape‐aware method for synthesizing 2D and 3D discrete element textures consisting of collections of distinct vector graphics objects. Extending the long‐proven point process framework, we propose a shape process, a novel stochastic model based on spatial measurements that fully take into account the geometry of the elements. We demonstrate that our approach is well‐suited for discrete texture synthesis by example. Our model enables for both robust statistical parameter estimation and reliable output generation by Monte Carlo sampling. Our numerous experiments show that contrary to current state‐of‐the‐art techniques, our algorithm manages to capture anisotropic element distributions and systematically prevents undesirable collisions between objects.

A point process framework for modeling electrical stimulation of the auditory nerve

Model-based studies of responses of auditory nerve fibers to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe spiking activity while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of individual auditory nerve fibers that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semianalytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data of response to high and low pulse rate stimulation. We find that the model, although constructed to fit data from single and paired pulse experiments, can accurately predict responses to unmodulated and modulated pulse train stimuli. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.

Detection of soldering defects in Printed Circuit Boards with Hierarchical Marked Point Processes

In this paper we introduce a probabilistic approach for optical quality checking of solder pastes (SP) in Printed Circuit Boards (PCB). Dealing with unregistered image inputs, our task is to address at the same time SP identification, and detection of special soldering errors, called scooping. For this reason we introduce a novel Hierarchical Marked Point Process (HMPP) framework, which is able to handle the paste and scooping extraction problems simultaneously, so that the SPs and included scoops have a parent–child relationship. A global optimization process attempts to find the optimal configuration of entities, considering the observed data, prior knowledge, and interactions between the neighboring circuit elements. The proposed method is evaluated on a real PCB image set containing more than 3000 SPs and 600 scooping artifacts. A morphology-based baseline method is also introduced for the problem and used as reference for qualitative and quantitative comparison against the proposed model.

Spatial distribution of Hevea brasiliensis trunk phloem necrosis within a plot: aggregation but no evidence of constraint on cumulated growth

SummaryTrunk phloem necrosis (TPN) is a major constraint in rubber (Hevea brasiliensis) plantations. Current knowledge supports a scenario of a multi‐factor physiological ‘disease’ caused by an accumulation of endogenous and exogenous stresses. Without evidence of a pathogen, the apparent spread of the syndrome from tree to tree along the planting line, strongly suggested the implication of a major local soil constraint. The objectives of the study were to address, within a plot, three points of the above scenario: the short‐distance aggregation of affected trees; their correspondence with local micro‐areas facing the highest environmental constraints; and the relative weakness of TPN trees that had accumulated several stresses since planting. The study was conducted in a young rubber tree stand (clone RRIM 600) of Northeast Thailand, where the number of TPN affected individuals was 8% after 3 years of tapping. Trunk girth and trunk basal area were used as indicators of local environmental constraints. Spatial patterns were analysed using the framework of marked point processes and K functions. The results confirmed the short‐distance aggregation of TPN affected trees. But, TPN trees were not located within micro‐areas where trees had a lower trunk basal area than average. Hence, the clusters of TPN do not occur in the most constraining environmental micro‐areas of the plot in terms of growth since planting. Moreover, from comparison of girth, current girth increment and height of bark consumption, we infer that TPN trees were not smaller and less vigorous than other trees before the syndrome outbreak. Finally, our conclusions mean the previous scenario driven by major soil constraints becomes a ‘more complex scenario’ in which specific soil conditions (not the most constraining in term of cumulated growth), possibly in interaction with inter‐individual competition, induce a late and subtle stress favouring a necrotic reaction against tapping stress.

A Granger causality measure for point process models of ensemble neural spiking activity.

The ability to identify directional interactions that occur among multiple neurons in the brain is crucial to an understanding of how groups of neurons cooperate in order to generate specific brain functions. However, an optimal method of assessing these interactions has not been established. Granger causality has proven to be an effective method for the analysis of the directional interactions between multiple sets of continuous-valued data, but cannot be applied to neural spike train recordings due to their discrete nature. This paper proposes a point process framework that enables Granger causality to be applied to point process data such as neural spike trains. The proposed framework uses the point process likelihood function to relate a neuron's spiking probability to possible covariates, such as its own spiking history and the concurrent activity of simultaneously recorded neurons. Granger causality is assessed based on the relative reduction of the point process likelihood of one neuron obtained excluding one of its covariates compared to the likelihood obtained using all of its covariates. The method was tested on simulated data, and then applied to neural activity recorded from the primary motor cortex (MI) of a Felis catus subject. The interactions present in the simulated data were predicted with a high degree of accuracy, and when applied to the real neural data, the proposed method identified causal relationships between many of the recorded neurons. This paper proposes a novel method that successfully applies Granger causality to point process data, and has the potential to provide unique physiological insights when applied to neural spike trains.