相关论文: Tree-indexed processes

To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

We consider stochastic processes with (or without) memory whose evolution is encoded by a finite or infinite rooted tree. The main goal is to compare the entropy rates of a given base process and a second one, to be considered as a…

In this article, we have proposed several approaches for post processing a large ensemble of prediction models or rules. The results from our simulations show that the post processing methods we have considered here are promising. We have…

The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex…

Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…

The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…

Staged trees are a recently-developed, powerful family of probabilistic graphical models. An equivalence class of staged trees has now been characterised, and two fundamental statistical operators have been defined to traverse the…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. Burdzy and Pal in their paper proposed a continuous version of graphical models --…

We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…

In~\cite{fgs}, the class of Poisson representable processes was introduced. Several well-known processes were shown not to belong to this class, with examples including both the Curie Weiss model and the Ising model on $ \mathbb{Z}^2 $ for…

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…

This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…

In this paper we study stochastic process indexed by $\mathbb {Z}$ constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a…

This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…

Causal inference is essential for data-driven decision-making, as it aims to uncover causal relationships from observational data. However, identifying causality remains challenging due to the potential for confounding and the distinction…