🤖 AI Summary
Existing nonparametric prior models lack a unified framework, leaving their clustering structures and information-sharing mechanisms poorly understood.
Method: We propose the Multivariate Species Sampling (MVSS) model—the first systematic, general framework unifying mainstream finite- and infinite-dimensional dependent discrete processes. Grounded in partial exchangeability theory, MVSS characterizes multivariate dependence via random partition probability functions. We further introduce the regular MVSS subclass, whose inter-process dependence is continuously controlled by a correlation coefficient (ranging from 0 for independence to 1 for full exchangeability).
Contribution/Results: MVSS provides an interpretable, tunable modeling foundation for partially exchangeable data, revealing underlying distributional mechanisms. It substantially extends the theoretical boundaries and design flexibility of Bayesian nonparametric modeling, enabling principled construction and analysis of dependent discrete processes.
📝 Abstract
Species sampling processes have long served as the framework for studying random discrete distributions. However, their statistical applicability is limited when partial exchangeability is assumed as probabilistic invariance for the observables. Despite numerous discrete models for partially exchangeable observations, a unifying framework is currently missing, leaving many questions about the induced learning mechanisms unanswered in this setting. To fill this gap, we consider the natural extension of species sampling models to a multivariate framework, obtaining a general class of models characterized by their partially exchangeable partition probability function. A notable subclass, named regular multivariate species sampling models, exists among these models. In the subclass, dependence across processes is accurately captured by the correlation among them: a correlation of one equals full exchangeability and a null correlation corresponds to independence. Regular multivariate species sampling models encompass discrete processes for partial exchangeable data used in Bayesian models, thereby highlighting their core distributional properties and providing a means for developing new models.