Publications

Topics:
  1. M. Pegoraro, S. Vedula, A. A. Rosenberg, I. Tallini, E. Rodolà, A. M. Bronstein, Vector quantile regression on manifolds, Proc. AIStats, 2024 details

    Vector quantile regression on manifolds

    M. Pegoraro, S. Vedula, A. A. Rosenberg, I. Tallini, E. Rodolà, A. M. Bronstein
    Proc. AIStats, 2024

    Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined on an Euclidean domain. Although the notion of quantiles was recently extended to multi-variate distributions, QR for multi-variate distributions on manifolds remains underexplored, even though many important applications inherently involve data distributed on, e.g., spheres (climate and geological phenomena), and tori (dihedral angles in proteins). By leveraging optimal transport theory and c-concave functions, we meaningfully define conditional vector quantile functions of high-dimensional variables on manifolds (M-CVQFs). Our approach allows for quantile estimation, regression, and computation of conditional confidence sets and likelihoods. We demonstrate the approach’s efficacy and provide insights regarding the meaning of non-Euclidean quantiles through synthetic and real data experiments.

    Y. Chen, H. Ye, S. Vedula, A. M. Bronstein, R. Dreslinski, T. Mudge, N. Talati, Demystifying graph sparsification algorithms in graph properties preservation, Proc.Int'l Conf. on Very Large Databases (VLDB), 2024 details

    Demystifying graph sparsification algorithms in graph properties preservation

    Y. Chen, H. Ye, S. Vedula, A. M. Bronstein, R. Dreslinski, T. Mudge, N. Talati
    Proc.Int'l Conf. on Very Large Databases (VLDB), 2024

    Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the downstream task while minimizing the graph’s size. Graph algorithms often suffer from long execution time due to the irregularity and the large real-world graph size. Graph sparsification can be applied to greatly reduce the run time of graph algorithms by substituting the full graph with a much smaller sparsified graph, without significantly degrading the output quality. However, the interaction between numerous sparsifiers and graph properties is not widely explored, and the potential of graph sparsification is not fully understood.
    In this work, we cover 16 widely-used graph metrics, 12 representative graph sparsification algorithms, and 14 real-world input graphs spanning various categories, exhibiting diverse characteristics, sizes, and densities. We developed a framework to extensively assess the performance of these sparsification algorithms against graph metrics, and provide insights to the results. Our study shows that there is no one sparsifier that performs the best in preserving all graph properties, e.g. sparsifiers that preserve distance-related graph properties (eccentricity) struggle to perform well on Graph Neural Networks (GNN). This paper presents a comprehensive experimental study evaluating the performance of sparsification algorithms in preserving essential graph metrics. The insights inform future research in incorporating matching graph sparsification to graph algorithms to maximize benefits while minimizing quality degradation. Furthermore, we provide a framework to facilitate the future evaluation of evolving sparsification algorithms, graph metrics, and ever-growing graph data.