# Pairwise Comparisons with Flexible Time-Dynamics

## TL;DR

This paper introduces a flexible probabilistic model for pairwise comparisons over time, using Gaussian processes to capture dynamic skill variations, with efficient inference and superior predictive performance demonstrated on sports data.

## Contribution

It presents a novel continuous-time Gaussian process-based model for pairwise comparisons that effectively captures time-varying dynamics and scales efficiently to large datasets.

## Key findings

- Outperforms existing models in predictive accuracy
- Scales to millions of observations efficiently
- Provides insightful visualizations of data dynamics

## Abstract

Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We achieve this by replacing the static parameters of a class of popular pairwise-comparison models by continuous-time Gaussian processes; the covariance function of these processes enables expressive dynamics. We develop an efficient inference algorithm that computes an approximate Bayesian posterior distribution. Despite the flexbility of our model, our inference algorithm requires only a few linear-time iterations over the data and can take advantage of modern multiprocessor computer architectures. We apply our model to several historical databases of sports outcomes and find that our approach outperforms competing approaches in terms of predictive performance, scales to millions of observations, and generates compelling visualizations that help in understanding and interpreting the data.