Related papers: The Bradley--Terry condition is $L_1$--testable
We study the problem of vertex-weighted online bipartite matching with stochastic rewards where matches may fail with some known probability and the decision maker has to adapt to the sequential realization of these outcomes. Recent works…
On being told that a piece of work he thought was his discovery had duplicated an earlier mathematician's work, Larry Shepp once replied "Yes, but when {\em I} discovered it, it {\em stayed} discovered". In this spirit we give discussion…
We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…
Iterative load balancing algorithms for indivisible tokens have been studied intensively in the past. Complementing previous worst-case analyses, we study an average-case scenario where the load inputs are drawn from a fixed probability…
Traditional statistical inference on ordinal comparison data results in an overall ranking of objects, e.g., from best to worst, with each object having a unique rank. However, ranks of some objects may not be statistically distinguishable.…
We study the algorithmic complexity of the problem of deciding whether a Linear Time Invariant dynamical system with rational coefficients has bounded trajectories. Despite its ubiquitous and elementary nature in Systems and Control, it…
Aldous-Broder algorithm is a famous algorithm used to sample a uniform spanning tree of any finite connected graph $G$, but it is more general: given an irreducible and reversible Markov chain $M$ on $G$ started at $r$, the tree rooted at…
Bradley-Terry-Luce (BTL) model estimation is a well-established strategy to rank a collection of items given a dataset of pairwise comparisons. Although the theoretical performance of BTL estimation methods, such as spectral and maximum…
Gerber and Li in \cite{GeLi} formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent…
Consider a parametric statistical model $P(\mathrm{d}x|\theta)$ and an improper prior distribution $\nu(\mathrm{d}\theta)$ that together yield a (proper) formal posterior distribution $Q(\mathrm{d}\theta|x)$. The prior is called strongly…
In self-consuming generative models that train on their own outputs, alignment with user preferences becomes a recursive rather than one-time process. We provide the first formal foundation for analyzing the long-term effects of such…
We revisit the problem of inferring the overall ranking among entities in the framework of Bradley-Terry-Luce (BTL) model, based on available empirical data on pairwise preferences. By a simple transformation, we can cast the problem as…
Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…
This paper deals with model checking problems with respect to LTL properties under fairness assumptions. We first present an efficient algorithm to deal with a fragment of fairness assumptions and then extend the algorithm to handle…
We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
Individual fairness, the notion that "similar individuals should be treated similarly," provides a strong and flexible fairness guarantee for algorithmic decision makers. However, a barrier to implementing individual fairness in practice is…
Over the last few years, there has been a growing interest in the prediction and modelling of competitive sports outcomes, with particular emphasis placed on this area by the Bayesian statistics and machine learning communities. In this…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
This technical report studies the problem of ranking from pairwise comparisons in the classical Bradley-Terry-Luce (BTL) model, with a focus on score estimation. For general graphs, we show that, with sufficiently many samples, maximum…