Related papers: Ranking-based rich-get-richer processes

Ranking models are typically designed to provide rankings that optimize some measure of immediate utility to the users. As a result, they have been unable to anticipate an increasing number of undesirable long-term consequences of their…

Although the foundations of ranking are well established, the ranking literature has primarily been focused on simple, unimodal models, e.g. the Mallows and Plackett-Luce models, that define distributions centered around a single total…

We establish a connection between policy evaluation in Markov decision processes and PageRank in network analysis. For a fixed policy, we show that the value function of a discounted Markov decision process can be obtained, up to an…

We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…

We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the…

Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…

We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…

Motivated by a risk process with positive and negative premium rates, we consider a real-valued Markov additive process with finitely many background states. This additive process linearly increases or decreases while the background state…

In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a…

We investigate whether preferences for objects received via a matching mechanism are influenced by how highly agents rank them in their reported rank order list. We hypothesize that all else equal, agents receive greater utility for the…

The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…

We develop two models for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both are based on the mixture transition distribution, which constructs a transition probability tensor with additive mixing of…

This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber…

We consider models for molecular sequence evolution in which the transition rates at each site depend on the local sequence context, giving rise to a time-inhomogeneous Markov process in which sites evolve under a complex dependency…

A well-studied randomized election algorithm proceeds as follows: In each round the remaining candidates each toss a coin and leave the competition if they obtain heads. Of interest is the number of rounds required and the number of…

Virtually anything can be and is ranked; people, institutions, countries, words, genes. Rankings reduce complex systems to ordered lists, reflecting the ability of their elements to perform relevant functions, and are being used from…

The article presents a general discrete time dividend valuation model when the dividend growth rate is a general continuous variable. The main assumption is that the dividend growth rate follows a discrete time semi-Markov chain with…

This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…

We introduce a new framework for web page ranking -- reinforcement ranking -- that improves the stability and accuracy of Page Rank while eliminating the need for computing the stationary distribution of random walks. Instead of relying on…

We explore two notions of stationary processes. The first is called a random-step Markov process in which the stationary process of states, $(X_i)_{i \in \mathbb{Z}}$ has a stationary coupling with an independent process on the positive…