Related papers: Context Tree Prior Distributions based on Node Wei…

We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version…

The Bayesian Context Trees (BCT) framework is a recently introduced, general collection of statistical and algorithmic tools for modelling, analysis and inference with discrete-valued time series. The foundation of this development is built…

We study transformers' in-context learning of variable-length Markov chains (VOMCs), focusing on the finite-sample accuracy as the number of in-context examples increases. Compared to fixed-order Markov chains (FOMCs), learning VOMCs is…

We propose a variable splitting binary tree (VSBT) model based on Bayesian context tree (BCT) models for time series segmentation. Unlike previous applications of BCT models, the tree structure in our model represents interval partitioning…

The context tree source is a source model in which the occurrence probability of symbols is determined from a finite past sequence, and is a broader class of sources that includes i.i.d. and Markov sources. The proposed source model in this…

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…

Models for categorical sequences typically assume exchangeable or first-order dependent sequence elements. These are common assumptions, for example, in models of computer malware traces and protein sequences. Although such simplifying…

A new Bayesian modelling framework is introduced for piece-wise homogeneous variable-memory Markov chains, along with a collection of effective algorithmic tools for change-point detection and segmentation of discrete time series. Building…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

This paper describes the Context Tree Switching technique, a modification of Context Tree Weighting for the prediction of binary, stationary, n-Markov sources. By modifying Context Tree Weighting's recursive weighting scheme, it is possible…

Reconstructing the evolutionary history relating a collection of molecular sequences is the main subject of modern Bayesian phylogenetic inference. However, the commonly used Markov chain Monte Carlo methods can be inefficient due to the…

Analyzing data collected from multiple sources to estimate common and heterogeneous structures through a hierarchical model is a central task in Bayesian inference, and to this end, Bayesian factor models are one of the most widely used…

We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…

Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the…

Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric…

We present a novel prior for tree topology within Bayesian Additive Regression Trees (BART) models. This approach quantifies the hypothetical loss in information and the loss due to complexity associated with choosing the wrong tree…

Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…

The present paper investigates non-asymptotic properties of two popular procedures of context tree (or Variable Length Markov Chains) estimation: Rissanen's algorithm Context and the Penalized Maximum Likelihood criterion. First showing how…

Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants…