Related papers: Beta-Product Poisson-Dirichlet Processes
Some challenging problems in tracking multiple objects include the time-dependent cardinality, unordered measurements and object parameter labeling. In this paper, we employ Bayesian Bayesian nonparametric methods to address these…
Motivation: With the development of droplet based systems, massive single cell transcriptome data has become available, which enables analysis of cellular and molecular processes at single cell resolution and is instrumental to…
The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as…
In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal…
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…
We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…
We study a hierarchy of directed percolation (DP) processes for particle species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When the DP critical points at all levels coincide, multicritical behavior emerges, with…
Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models…
Clustering algorithms have wide applications and play an important role in data analysis fields including time series data analysis. However, in time series analysis, most of the algorithms used signal shape features or the initial value of…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Estimating causal effects from randomized experiments is only possible if participants are willing to disclose their potentially sensitive responses. Differential privacy, a widely used framework for ensuring an algorithms privacy…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Multivariate data sources with components of different information value seem to appear frequently in practice. Models in which the components change their homogeneity at different times are of significant importance. The fact whether any…
Analyzing crime events is crucial to understand crime dynamics and it is largely helpful for constructing prevention policies. Point processes specified on linear networks can provide a more accurate description of crime incidents by…
A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as…
We consider the problem of analyzing multivariate time series collected on multiple subjects, with the goal of identifying groups of subjects exhibiting similar trends in their recorded measurements over time as well as time-varying groups…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
In this paper, we showed that the no-arbitrage condition holds if the market follows the mixture of the geometric Brownian motion (GBM). The mixture of GBM can incorporate heavy-tail behavior of the market. It automatically leads us to…
We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…