Related papers: Statistical ranking and combinatorial Hodge theory
We study the typical behavior of a generalized version of Google's PageRank algorithm on a large family of inhomogeneous random digraphs. This family includes as special cases directed versions of classical models such as the…
Let $\grad$, $\curl$, and $\dv$ be the graph-theoretic analogues of the gradient, curl, and divergence operators from multivariate calculus. The graph Laplacian $-\dv \grad$ gives rise to the celebrated Laplacian matrix, while the matrix…
Existing learning-to-rank methods for road networks often fail to incorporate origin-destination (OD) flows and route information, limiting their ability to model long-range spatial dependencies. To address this gap, we propose HetGL2R, a…
Rankings are central to decision-making in fields ranging from education to online platforms, yet classical deterministic methods such as the Borda count method or Copeland-type pairwise methods ignore uncertainty due to sampling noise or…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
Health care delivery is a collaborative process, requiring close coordination among networks of providers with specialized expertise. Yet in the United States, care is often spread across multiple disconnected providers (e.g., primary care…
Rank-based approaches are among the most popular nonparametric methods for univariate data in tackling statistical problems such as hypothesis testing due to their robustness and effectiveness. However, they are unsatisfactory for more…
Unbalanced data arises in many learning tasks such as clustering of multi-class data, hierarchical divisive clustering and semisupervised learning. Graph-based approaches are popular tools for these problems. Graph construction is an…
This work examines the conditions for asymptotic and exponential convergence of saddle flow dynamics of convex-concave functions. First, we propose an observability-based certificate for asymptotic convergence, directly bridging the gap…
We examine three methods for ranking by pairwise comparison: Principal Eigenvector, HodgeRank and Tropical Eigenvector. It is shown that the choice of method can produce arbitrarily different rank order.To be precise, for any two of the…
The Helmholtzian matrix of a graph $G=(V(G),E(G))$ is a graph-theoretic analogue of the vector Laplacian (or Helmholtz operator) [S. Li, L. Lu, J.F. Wang, A graph discretization of vector Laplacian, 379 (2026) 446--460]. Motivated by the…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
In this paper, we establish a connection between ranking theory and general equilibrium theory. First of all, we show that the ranking vector of PageRank or Invariant method is precisely the equilibrium of a special Cobb-Douglas market.…
The bipartite graph is a ubiquitous data structure that can model the relationship between two entity types: for instance, users and items, queries and webpages. In this paper, we study the problem of ranking vertices of a bipartite graph,…
Rank aggregation is an essential approach for aggregating the preferences of multiple agents. One rule of particular interest is the Kemeny rule, which maximises the number of pairwise agreements between the final ranking and the existing…
Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive…
We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…
We consider the problem of statistical inference for ranking data, specifically rank aggregation, under the assumption that samples are incomplete in the sense of not comprising all choice alternatives. In contrast to most existing methods,…
The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can…