相关论文: Regenerative Composition Structures

We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…

This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges…

Ewens-Pitman's partition structure arises as a system of sampling consistent probability distributions on set partitions induced by the Pitman-Yor process. It is widely used in statistical applications, particularly in species sampling…

We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n>=1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov…

A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of…

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be…

We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting…

A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

In this article we consider the cycle structure of compositions of pairs of involutions in the symmetric group S_n chosen uniformly at random. These can be modeled as modified 2-regular graphs, giving rise to exponential generating…

Compositional data consist of known compositions vectors whose components are positive and defined in the interval (0,1) representing proportions or fractions of a "whole". The sum of these components must be equal to one. Compositional…

Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates,…

Compositional data, which are vectors of proportions constrained to the probability simplex, arise frequently in modern scientific applications, including microbiome relative abundances across body sites and cell-type mixture weights…

We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…

In this paper we study random partitions of 1,...n, where every cluster of size j can be in any of w\_j possible internal states. The Gibbs (n,k,w) distribution is obtained by sampling uniformly among such partitions with k clusters. We…

The random reversal graph offers new perspectives, allowing to study the connectivity of genomes as well as their most likely distance as a function of the reversal rate. Our main result shows that the structure of the random reversal graph…

The compound Poisson process and the Dirichlet process are the pillar structures of Renewal theory and Bayesian nonparametric theory, respectively. Both processes have many useful extensions to fulfill the practitioners needs to model the…

We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…