Related papers: Every cutoff profile is possible

We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work…

In this article, we consider products of ergodic Markov chains and discuss their cutoffs in the total variation. Through a new inequality relating the total variation and the Hellinger distance, we may identify the total variation cutoffs…

Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…

We propose a simple extension of top-down decision tree learning heuristics such as ID3, C4.5, and CART. Our algorithm achieves provable guarantees for all target functions $f: \{-1,1\}^n \to \{-1,1\}$ with respect to the uniform…

The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…

The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…

Earlier work by Diaconis and Saloff-Coste gives a spectral criterion for a maximum separation cutoff to occur for birth and death chains. Ding, Lubetzky and Peres gave a related criterion for a maximum total variation cutoff to occur in the…

We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…

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.

We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.

We show that every graph admits a canonical tree-like decomposition into its $k$-edge-connected pieces for all $k\in\mathbb{N}\cup\{\infty\}$ simultaneously.

The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. In 1996, Diaconis surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite…

We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…

Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under…

We study the Markov chain $x_{n+1}=ax_n+b_n$ on a finite field $\mathbb{F}_p$, where $a \in \mathbb{F}_p$ is fixed and $b_n$ are independent and identically distributed random variables in $\mathbb{F}_p$. Conditionally on the Riemann…

Graphs with bounded treewidth and bounded maximum degree are known to have tree-partitions of bounded width. What can be said if the bounded treewidth assumption is strengthened to bounded pathwidth? We prove that every graph with bounded…

We study the problem of learning tree-structured Markov random fields (MRF) on discrete random variables with common support when the observations are corrupted by a $k$-ary symmetric noise channel with unknown probability of error. For…

We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal algorithm, whose prototype is the state reduction algorithm…