Marked Point Process Model Research Articles

Optimal decision rules for marked point process models

We study a Markov decision problem in which the state space is the set of finite marked point patterns in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the transitions are governed by a birth-death-growth process. We show that thinning points with large marks maximises the discounted total expected reward when births follow a Poisson process and marks grow logistically. Explicit values for the thinning threshold and the discounted total expected reward over finite and infinite horizons are also provided. When the points are required to respect a hard core distance, upper and lower bounds on the discounted total expected reward are derived.

Unveiling the web of interactions: Analyzing dynamic customer engagements across multiple websites

Online customers exhibit unique dynamic patterns during their journey. In the early phases, customers gather different information from multiple websites. Collectively, the information serves as references, helping customers to make informed decisions. Further, inferior options are eliminated until the journey converges on a single website for conversion. In this study, we examine the dynamic interactions among online customers and websites. To capture the dynamics, we propose a metric, momentum of information-building and incorporate the measure into a dynamically and mutually exciting marked point process model. We apply the proposed model to clickstream data for hotel bookings and find strong evidence of dynamic behavior. Also, we show that ignoring the dynamics may lead to bias in estimating the carryover and spillover effects and diminish the prediction accuracy of website visits and conversions. Furthermore, we offer recommendations for effective advertising strategies focusing on key aspects such as advertising density, timing, and targeting.

Unveiling Multi-Agent Strategies: A Data-Driven Approach for Extracting and Evaluating Team Tactics from Football Event and Freeze-Frame Data

Studying collective behavior in opposing multi-agent teams is crucial across game theory, robotics, and sports analytics. In sports, especially football, team tactics involve intricate strategic spatial and action behaviors displayed as event sequences during possession. Understanding and analyzing these tactics is essential for successful training, strategic planning, and on-field success. While traditional approaches, such as notational and statistical analyses, offer valuable insights into team tactics, they often lack a comprehensive consideration of contextual information, thereby limiting the holistic evaluation of teams’ performances. To bridge this gap and capture the nuanced intricacies of team tactics, we employed advanced methodologies. The sequential pattern mining algorithm PrefixSpan was utilized to extract tactical patterns from possession sequences, enabling a deeper understanding of how teams strategize and adapt during play. Additionally, the neural marked spatio temporal point process (NMSTPP) model was leveraged to model and predict team behaviors, facilitating a fair comparison among teams. The evaluation of team possessions was further enhanced through the innovative holistic possession utilization score metrics, providing a more nuanced assessment of performance. In our experimental exploration, we identified and classified five distinct team tactics, validated the efficacy of the NMSTPP model when integrating StatsBomb 360 data, and conducted a comprehensive analysis of English Premier League teams during the 2022/2023 season. The results were visualized using radar plots and scatter plots with mean shift clustering. Lastly, the potential applications to RoboCup were discussed.

MoMENt: Marked Point Processes with Memory-Enhanced Neural Networks for User Activity Modeling

Marked temporal point process models (MTPPs) aim to model event sequences and event markers (associated features) in continuous time. These models have been applied to various application domains where capturing event dynamics in continuous time is beneficial, such as education systems, social networks, and recommender systems. However, current MTPPs suffer from two major limitations, i.e., inefficient representation of event dynamic’s influence on marker distribution and losing fine-grained representation of historical marker distributions in the modeling. Motivated by these limitations, we propose a novel model called M arked P o int Processes with M emory- E nhanced N eural Ne t works (MoMENt) that can capture the bidirectional interrelations between markers and event dynamics while providing fine-grained marker representations. Specifically, MoMENt is constructed of two concurrent networks: Recurrent Activity Updater (RAU) to capture model event dynamics and Memory-Enhanced Marker Updater (MEMU) to represent markers. Both RAU and MEMU components are designed to update each other at every step to model the bidirectional influence of markers and event dynamics. To obtain a fine-grained representation of maker distributions, MEMU is devised with external memories that model detailed marker-level features with latent component vectors. Our extensive experiments on six real-world user interaction datasets demonstrate that MoMENt can accurately represent users’ activity dynamics, boosting time, type, and marker predictions, as well as recommendation performance up to 76.5%, 65.6%, 77.2%, and 57.7%, respectively, compared to baseline approaches. Furthermore, our case studies show the effectiveness of MoMENt in providing meaningful and fine-grained interpretations of user-system relations over time, e.g., how user choices influence their future preferences in the recommendation domain.

Spatio-Temporal Marked Point Process Model to Understand Forest Fires in the Mediterranean Basin

AbstractUnderstanding and predicting forest fires have proved a highly difficult endeavour, which requires extending and adapting complex models used in different fields. Here, we apply a marked point process approach, commonly used in ecology, which uses multiple Gaussian random fields to represent dynamics of Mediterranean forest fires in a spatio-temporal distribution model. Inference is carried out using Integrated Nested Laplace Approximation (INLA) with , an accessible and computationally efficient approach for Bayesian hierarchical modelling, which is not yet widely used in species distribution models. Using the marked point process approach, intensity of forest fires and dispersion were predicted using socioeconomic factors and environmental and fire-related variables. This demonstrates the advantage of complex model components in accounting for spatio-temporal dynamics that are not explained by environmental variables. Introduction of spatio-temporal marked point process can provide a more realistic perspective of a system, which is of particular importance for a practical and impact-focused worldwide problem such as forest fires.Supplementary materials accompanying this paper appear online.

Joint modelling of landslide counts and sizes using spatial marked point processes with sub-asymptotic mark distributions

Abstract To accurately quantify landslide hazard in a region of Turkey, we develop new marked point-process models within a Bayesian hierarchical framework for the joint prediction of landslide counts and sizes. We leverage mark distributions justified by extreme-value theory, and specifically propose ‘sub-asymptotic’ distributions to flexibly model landslide sizes from low to high quantiles. The use of intrinsic conditional autoregressive priors, and a customised adaptive Markov chain Monte Carlo algorithm, allow for fast fully Bayesian inference. We show that sub-asymptotic mark distributions provide improved predictions of large landslide sizes, and use our model for risk assessment and hazard mapping.

Presence-Only for Marked Point Process Under Preferential Sampling

Preferential sampling models have garnered significant attention in recent years. Although the original model was developed for geostatistics, it founds applications in other types of data, such as point processes in the form of presence-only data. While this has been recognized in the Statistics literature, there is value in incorporating ideas from both presence-only and preferential sampling literature. In this paper, we propose a novel model that extends existing ideas to handle a continuous variable collected through opportunistic sampling. To demonstrate the potential of our approach, we apply it to sardine biomass data collected during commercial fishing trips. While the data is intuitively understood, it poses challenges due to two types of preferential sampling: fishing events (presence data) are non-random samples of the region, and fishermen tend to set their nets in areas with a high quality and value of catch (i.e., bigger schools of the target species). We discuss theoretical and practical aspects of the problem, and propose a well-defined probabilistic approach. Our approach employs a data augmentation scheme that predicts the number of unobserved fishing locations and corresponding biomass (in kg). This allows for evaluation of the Poisson Process likelihood without the need for numerical approximations. The results of our case study may serve as an incentive to use data collected during commercial fishing trips for decision-making aimed at benefiting both ecological and economic aspects. The proposed methodology has potential applications in a variety of fields, including ecology and epidemiology, where marked point process model are commonly used.

Sequential Adversarial Anomaly Detection for One-Class Event Data

We consider the sequential anomaly detection problem in the one-class setting when only the anomalous sequences are available and propose an adversarial sequential detector by solving a minimax problem to find an optimal detector against the worst-case sequences from a generator. The generator captures the dependence in sequential events using the marked point process model. The detector sequentially evaluates the likelihood of a test sequence and compares it with a time-varying threshold, also learned from data through the minimax problem. We demonstrate our proposed method’s good performance using numerical experiments on simulations and proprietary large-scale credit card fraud data sets. The proposed method can generally apply to detecting anomalous sequences. History: W. Nick Street served as the senior editor for this article. Funding: This work is partially supported by the National Science Foundation [Grants CAREER CCF-1650913, DMS-1938106, and DMS-1830210] and grant support from Macy’s Technology. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://doi.org/10.24433/CO.2329910.v1 and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2023.0026 ).

Fitting three-dimensional Laguerre tessellations by hierarchical marked point process models

We present a general statistical methodology for analysing a Laguerre tessellation data set viewed as a realization of a marked point process model. In the first step, for the points, we use a nested sequence of multiscale processes which constitute a flexible parametric class of pairwise interaction point process models. In the second step, for the marks/radii conditioned on the points, we consider various exponential family models where the canonical sufficient statistic is based on tessellation characteristics. For each step, parameter estimation based on maximum pseudolikelihood methods is tractable. For model selection, we consider maximized log pseudolikelihood functions for models of the radii conditioned on the points. Model checking is performed using global envelopes and corresponding tests in both steps and moreover by comparing observed and simulated tessellation characteristics in the second step. We apply our methodology for a 3D Laguerre tessellation data set representing the microstructure of a polycrystalline metallic material, where simulations under a fitted model may substitute expensive laboratory experiments.

A joint spatial marked point process model for dengue and severe dengue in Medellin, Colombia

The spatial distribution of surveillance-reported dengue cases and severity are usually analyzed separately, assuming independence between the spatial distribution of non-severe and severe cases. Given the availability of data for the individual geo-location of surveillance-notified dengue cases, we conducted a spatial analysis to model non-severe and severe dengue simultaneously, using a hierarchical Bayesian model. We fit a joint model to the spatial pattern formed by dengue cases as well as to the severity status of the cases. Results showed that age and socioeconomic status were associated with dengue presence, and there was evidence of clustering for overall cases but not for severity. Our findings inform decision making to address the preparedness or implementation of dengue control strategies at the local level.

Modeling Epistemic Uncertainty in Offshore Wind Farm Production Capacity to Reduce Risk.

Financial stakeholders in offshore wind farm projects require predictions of energy production capacity to better manage the risk associated with investment decisions prior to construction. Predictions for early operating life are particularly important due to the dual effects of cash flow discounting and the anticipated performance growth due to experiential learning. We develop a general marked point process model for the times to failure and restoration events of farm subassemblies to capture key uncertainties affecting performance. Sources of epistemic uncertainty are identified in design and manufacturing effectiveness. The model then captures the temporal effects of epistemic and aleatory uncertainties across subassemblies to predict the farm availability-informed relative capacity (maximum generating capacity given the technical state of the equipment). This performance measure enables technical performance uncertainties to be linked to the cost of energy generation. The general modeling approach is contextualized and illustrated for a prospective offshore wind farm. The production capacity uncertainties can be decomposed to assess the contribution of epistemic uncertainty allowing the value of gathering information to reduce risk to beexamined.

A self‐exciting marked point process model for drought analysis

AbstractA self‐exciting marked point process approach is proposed to model clustered low‐flow events. It combines a self‐exciting ground process designed to capture the temporal clustering behavior of extreme values and an extended Generalized Pareto mark distribution for the exceedances over a subasymptotic threshold. The model takes into account the dependence between the magnitude and occurrence time of exceedances and allows for closed‐form inference on tail probabilities and large quantiles. It is used to analyze daily water levels from the Rivière des Mille Îles (Québec, Canada) and to characterize drought patterns in the Montréal area. The model is useful to generate short‐term probability forecasts and to estimate the return period of major droughts. This information on the drought events is critical to water resource professionals in planning, designing, building, and managing more efficient water resource systems to hedge against the water shortage in case of extreme droughts.

Marked point process analysis of epidermal nerve fibres.

Epidermal nerve fibre (ENF) density and summed length of ENFs per epidermal surface area are reduced, and ENFs may appear more clustered within the epidermis in subjects suffering from diabetic neuropathy compared to healthy subjects. Therefore, it is important to understand the spatial behaviour of ENFs in healthy and neuropathy subjects. By using confocal microscopy data , we study the spatial structure of epidermal nerves by regarding the nerve tree locations as realizations of marked point processes . The termination points of the fibres of a nerve tree are used to define a reactive territory which is taken as a mark for the nerve tree location. We study the differences in the spatial pattern of ENFs between healthy subjects and subjects suffering from mild diabetic neuropathy by using Ripley's function and the mark correlation function. In addition, we propose a marked sequential point process model for the nerve tree locations. Data are replicated point patterns, where we have several patterns from each subject and from eachgroup.

Assessing Goodness-of-Fit in Marked Point Process Models of Neural Population Coding via Time and Rate Rescaling.

Marked point process models have recently been used to capture the coding properties of neural populations from multiunit electrophysiological recordings without spike sorting. These clusterless models have been shown in some instances to better describe the firing properties of neural populations than collections of receptive field models for sorted neurons and to lead to better decoding results. To assess their quality, we previously proposed a goodness-of-fit technique for marked point process models based on time rescaling, which for a correct model produces a set of uniform samples over a random region of space. However, assessing uniformity over such a region can be challenging, especially in high dimensions. Here, we propose a set of new transformations in both time and the space of spike waveform features, which generate events that are uniformly distributed in the new mark and time spaces. These transformations are scalable to multidimensional mark spaces and provide uniformly distributed samples in hypercubes, which are well suited for uniformity tests. We discuss the properties of these transformations and demonstrate aspects of model fit captured by each transformation. We also compare multiple uniformity tests to determine their power to identify lack-of-fit in the rescaled data. We demonstrate an application of these transformations and uniformity tests in a simulation study. Proofs for each transformation are provided in the appendix.

AUTOMATIC TUMULI DETECTION IN LIDAR BASED DIGITAL ELEVATION MAPS

Abstract. In this study, we aim to identify Iron Age tumuli with a probabilistic method, in digital terrain models extracted from airborne LiDAR measurements. Our task was particularly challenging due to the strong and uneven elevation of the ground where tumuli are located. In addition, the area is densely covered by vegetation, mainly by forests, which makes it difficult to create a surface model. The difficulty was exacerbated by the fact that the height and width of tumuli is very diverse but incomparably smaller than the extension of the area. In contrast to the various visualization techniques (openness, local relief model) used since decades for identifying tumuli, our method recognises these features automatically. Our approach is based on a Marked Point Process Model (MPP), which due to its inverse methodology, allows us to detect tumuli with high precision, especially in comparison with bottom-up methods. We quantitatively evaluated the method on six test data sets and we demonstrated its advantages compared to a traditional Hough transform-based method.

Tuberculosis bacteria analysis in acid fast stained images of sputum smear

Tuberculosis (TB) basically originates due to bacteria, influences the developing nations and disrupts their economy severely. TB like diseases are with a high mortality rate worldwide, but early detection highly increases the chances of survival. This paper presents a novel method for TB bacteria segmentation and classification using microscopic images (MI). Manual identification of the bacterial cell is a very difficult process. The automation in TB bacteria detection is the objective of this article using MI processing. The proposed segmentation method first performs the image enhancement followed by bacteria region masking. Further, the marking of bacteria points is performed by the marked point process model. Finally, the complete bacteria are identified by the superellipse and supervised variational contour models. The features are extracted using bag of visual words and handcrafted work for the image classification. Simulation results confirm the superiority of the proposed method as compared with the state-of-the-art methods.

Connected-Tube MPP Model for Unsupervised 3D Fiber Detection

In this paper, we extend our previous 2D connected-tube marked point process (MPP) model to a 3D connected-tube MPP model for fiber detection. In the 3D case, a tube is represented by a cylinder model with two spherical areas at its ends. The spherical area is used to define connection priors that encourage connection of tubes that belong to the same fiber. Since each long fiber can be fitted by a series of connected short tubes, the proposed model is capable of detecting curved long tubes. We present experimental results on fiber-reinforced composite material images to show the performance of our method.

Is-ClusterMPP: clustering algorithm through point processes and influence space towards high-dimensional data

Clustering via marked point processes and influence space, Is-ClusterMPP, is a new unsupervised clustering algorithm through adaptive MCMC sampling of a marked point processes of interacting balls. The designed Gibbs energy cost function makes use of k-influence space information. It detects clusters of different shapes, sizes and unbalanced local densities. It aims at dealing also with high-dimensional datasets. By using the k-influence space, Is-ClusterMPP solves the problem of local heterogeneity in densities and prevents the impact of the global density in the detection of unbalanced classes. This concept reduces also the input values amount. The curse of dimensionality is handled by using a local subspace clustering principal embedded in a weighted similarity metric. Balls covering data points are constituting a configuration sampled from a marked point process (MPP). Due to the choice of the energy function, they tends to cover neighboring data, which share the same cluster. The statistical model of random balls is sampled through a Monte Carlo Markovian dynamical approach. The energy is balancing different goals. (1) The data driven objective function is provided according to k-influence space. Data in a high-dense region are favored to be covered by a ball. (2) An interaction part in the energy prevents the balls full overlap phenomenon and favors connected groups of balls. The algorithm through Markov dynamics, does converge towards configurations sampled from the MPP model. This algorithm has been applied in real benchmarks through gene expression data set of various sizes. Different experiments have been done to compare Is-ClusterMPP against the most well-known clustering algorithms and its efficiency is claimed.

Continuous Prediction of Cognitive State Using A Marked-Point Process Modeling Framework.

Behavioral outcomes in many cognitive tasks are often recorded in a trial structure at discrete times. To adapt to this structure, neural encoder and decoder models have been built to take into account the trial organization to characterize the connection between brain dynamics and behavior, e.g. through latent dynamical models. The challenge of these models is that they are limited to discrete trial times while neural data is continuous. Here, we propose a marked-point process framework to characterize multivariate behavioral outcomes recorded during a trial-structured cognitive task, to build an estimation of cognitive state at a fine time resolution. We propose a state-space marked-point process modeling framework to characterize the relationship between observed behavior and underlying dynamical cognitive processes. We define the framework for a class of behavioral readouts by a response time and a discrete mark signifying an observed binary decision, and develop the state estimation and system identification steps. We define the filter and smoother for the marked-point process observation and develop an EM algorithm to estimate the model's free parameters. We demonstrate this modeling approach in a behavioral readout captured while participants perform an emotional conflict resolution task (ECR) and show that we can estimate underlying cognitive processes at a fine temporal resolution beyond the trial by trial approach.

NARROW GAP DETECTION IN MICROSCOPE IMAGES USING MARKED POINT PROCESS MODELING.

Differentiating objects separated by narrow gaps is a challenging and important task in analyzing microscopic images. These small separations provide useful information for applications that require detailed boundary information and/or an accurate particle count. We present a new approach to the modeling of these gaps based on a marked point process(MPP) framework. We propose to model narrow gaps as geometric structures called channels, and define Gibbs energies for these models. The Reversible-jump Markov chain Monte Carlo(RJMCMC) algorithm embedded with simulated annealing is used as an optimization method, and the switching kernel in an RJMCMC is newly designed to speed up the algorithm. In this paper, we also propose a method to exploit a detected channel configuration to reduce bridging channel defects in conventional segmentation algorithms. Experimental results demonstrate that the proposed channel modeling methods are successful in detecting gaps between closely adjacent objects. The results also show that the proposed interaction parameter control method improves boundary precision in the segmentation of microscopic images.