TopKSignal: A Convex Optimization Tool for Signal Reconstruction from Multiple Ranked Lists

• Activity Number: 448 - The Contribution of Convex Optimization to New Statistical Concepts
• Type: Topic Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistical Computing
• Author(s): Bastian Pfeifer* and Luca Vitale and Michael G. Schimek
• Companies: IMI Statistical Bioinformatics, Medical University of Graz, Austria and Medical University of Graz, Austria; University of Salerno, Salerno, Italy and IMI Statistical Bioinformatics, Medical University of Graz, Austria
• Keywords: Ranking Data; Convex Optimization; Constraint; Poisson Bootstrap; Top-k Items

Abstract

The ranking of items is widely used to rate their relative quality or relevance across multiple assessments (by humans or machines). Beyond classical rank aggregation, it is of interest to estimate the, usually unobservable, latent signals that inform a consensus ranking. Under the only assumption of independent assessments, we introduce indirect inference via convex optimization in combination with Poisson Bootstrap. This approach allows us to overcome major numerical limitations of a recent distribution function approach (Svendova and Schimek, 2017, CSDA, 115, 122-135). The relationships between the rankers and the observed item orderings are represented by means of a set of constraints. The estimation strategy is to reduce the noise between the these rankings until optimal latent signals can be obtained. Algorithms for full and reduced linear and quadratic convex optimizations were implemented in R in the package TopKSignal. The final estimates are obtained from Poisson Bootstrap. Advantages are high-quality parameter estimates as well as error bounds, and a substantially reduced computational burden compared to standard Bootstrap.