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1. Statistical Rank Selection for Incomplete Low-rank Matrices

   https://doi.org/10.1109/ICASSP.2019.8682540  

   Zhang, Rui; Shapiro, Alexander; Xie, Yao (May 2019, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))
2. Low-rank factorization for rank minimization with nonconvex regularizers

   https://doi.org/10.1007/s10589-021-00276-5  

   Sagan, April; Mitchell, John E. (June 2021, Computational Optimization and Applications)
3. Higher rank hyperbolicity

   https://doi.org/10.1007/s00222-020-00955-w  

   Kleiner, Bruce; Lang, Urs (August 2020, Inventiones mathematicae)

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4. Bayesian Rank-Clustering

   https://doi.org/10.1017/psy.2025.10014  

   Pearce, Michael; Erosheva, Elena A (June 2025, Psychometrika)

   Abstract This article proposes a new statistical model to infer interpretable population-level preferences from ordinal comparison data. Such data is ubiquitous, e.g., ranked choice votes, top-10 movie lists, and pairwise sports outcomes. 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, the ranks of some objects may not be statistically distinguishable. This could happen due to insufficient data or to the true underlying object qualities being equal. Because uncertainty communication in estimates of overall rankings is notoriously difficult, we take a different approach and allow groups of objects to have equal ranks or berank-clusteredin our model. Existing models related to rank-clustering are limited by their inability to handle a variety of ordinal data types, to quantify uncertainty, or by the need to pre-specify the number and size of potential rank-clusters. We solve these limitations through our proposed BayesianRank-Clustered Bradley–Terry–Luce (BTL)model. We accommodate rank-clustering via parameter fusion by imposing a novel spike-and-slab prior on object-specific worth parameters in the BTL family of distributions for ordinal comparisons. We demonstrate rank-clustering on simulated and real datasets in surveys, elections, and sports analytics. 

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5. Juvenile rank acquisition is associated with fitness independent of adult rank

   https://doi.org/10.1098/rspb.2019.2969  

   Strauss, Eli D.; Shizuka, Daizaburo; Holekamp, Kay E. (March 2020, Proceedings of the Royal Society B: Biological Sciences)

   Social rank is a significant determinant of fitness in a variety of species. The importance of social rank suggests that the process by which juveniles come to establish their position in the social hierarchy is a critical component of development. Here, we use the highly predictable process of rank acquisition in spotted hyenas to study the consequences of variation in rank acquisition in early life. In spotted hyenas, rank is ‘inherited’ through a learning process called ‘maternal rank inheritance.’ This pattern is very consistent: approximately 80% of juveniles acquire the exact rank expected under the rules of maternal rank inheritance. The predictable nature of rank acquisition in these societies allows the process of rank acquisition to be studied independently from the ultimate rank that each juvenile attains. In this study, we use Elo-deviance scores, a novel application of the Elo-rating method, to calculate each juvenile's deviation from the expected pattern of maternal rank inheritance during development. Despite variability in rank acquisition among juveniles, most of these juveniles come to attain the exact rank expected of them according to the rules of maternal rank inheritance. Nevertheless, we find that transient variation in rank acquisition in early life is associated with long-term fitness consequences for these individuals: juveniles ‘underperforming’ their expected ranks show reduced survival and lower lifetime reproductive success than better-performing peers, and this relationship is independent of both maternal rank and rank achieved in adulthood. We also find that multiple sources of early life adversity have cumulative, but not compounding, effects on fitness. Future work is needed to determine if variation in rank acquisition directly affects fitness, or if some other variable, such as maternal investment or juvenile condition, causes variation in both of these outcomes. 

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