Change Point Detection in Pairwise Comparison Data with Covariates

Abstract: This paper introduces the novel piecewise stationary covariate-assisted ranking estimation (PS-CARE) model for analyzing time-evolving pairwise comparison data, enhancing item ranking accuracy through the integration of covariate information. By partitioning the data into distinct, stationary segments, the PS-CARE model adeptly detects temporal shifts in item rankings, known as change points, whose number and positions are initially unknown. Leveraging the minimum description length (MDL) principle, this paper establishes a statistically consistent model selection criterion to estimate these unknowns. The practical optimization of this MDL criterion is done with the pruned exact linear time (PELT) algorithm. Empirical evaluations reveal the method's promising performance in accurately locating change points across various simulated scenarios. An application to an NBA dataset yielded meaningful insights that aligned with significant historical events, highlighting the method's practical utility and the MDL criterion's effectiveness in capturing temporal ranking changes. To the best of the authors' knowledge, this research pioneers change point detection in pairwise comparison data with covariate information, representing a significant leap forward in the field of dynamic ranking analysis.