Related papers: Dirichlet Depths for Point Process

The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point…

Dependent Dirichlet processes (DDP) have been widely applied to model data from distributions over collections of measures which are correlated in some way. On the other hand, in recent years, increasing research efforts in machine learning…

Statistical depth, a useful tool to measure the center-outward rank of multivariate and functional data, is still under-explored in temporal point processes. Recent studies on point process depth proposed a weighted product of two terms -…

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant…

We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to…

While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning…

Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…

Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…

Temporal point processes (TPPs) model the timing of discrete events along a timeline and are widely used in fields such as neuroscience and fi- nance. Statistical depth functions are powerful tools for analyzing centrality and ranking in…

In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data…

Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional…

Point process models are of great importance in real world applications. In certain critical applications, estimation of point process models involves large amounts of sensitive personal data from users. Privacy concerns naturally arise…

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…

The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It is motivated with the study of groups of clustered data. Each group is modelled through a level two Dirichlet…

Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…

In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to…

We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using…

Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…

The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference…