Related papers: Note on Computing Ratings from Eigenvectors

A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…

Matrix functions play an important role in applied mathematics. In network analysis, in particular, the exponential of the adjacency matrix associated with a network provides valuable information about connectivity, as well as about the…

The performance of algorithms, methods, and models tends to depend heavily on the distribution of cases on which they are applied, this distribution being specific to the applicative domain. After performing an evaluation in several…

In this paper we introduce an iterative voting algorithm and then use it to obtain a rating method which is very robust against collusion attacks as well as random and biased raters. Unlike the previous iterative methods, our method is not…

Attribution techniques explain the outcome of an AI model by assigning a numerical score to its inputs. So far, these techniques have mainly focused on attributing importance to static input features at a single point in time, and thus fail…

In this paper, we first study the projections onto the set of unit dual quaternions, and the set of dual quaternion vectors with unit norms. Then we propose a power method for computing the dominant eigenvalue of a dual quaternion Hermitian…

The nature of dynamics of opinion formation modeled as a decision-by-majority process in complex networks is investigated using eigenmode analysis. Hamiltonian of the system is defined, and estimated by eigenvectors of the adjacency matrix…

Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots…

Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…

In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local…

This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computing eigenvalues located inside a given disk, and the proposed…

We study the inverse power index problem for weighted voting games: the problem of finding a weighted voting game in which the power of the players is as close as possible to a certain target distribution. Our goal is to find algorithms…

We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics, and the ones obtained by combining them, are often called performability measures. We show that this computational…

Stochastic games are a classical model in game theory in which two opponents interact and the environment changes in response to the players' behavior. The central solution concepts for these games are the discounted values and the value,…

We present an exploration of a reputation system based on explicit ratings weighted by the values of corresponding financial transactions from the perspective of its ability to grant "security" to market participants by protecting them from…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

Self-play, where the algorithm learns by playing against itself without requiring any direct supervision, has become the new weapon in modern Reinforcement Learning (RL) for achieving superhuman performance in practice. However, the…

We estimate the condition number of a matrix by applying the Power Method, that is essentially a sequence of matrix-by-vector multiplications, similarly to the Lanczos method.

Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational and econometric challenges to further improve both model solution and…

We consider the problem of selecting a portfolio of entries of fixed cardinality for contests with top-heavy payoff structures, i.e. most of the winnings go to the top-ranked entries. This framework is general and can be used to model a…