Linear-Time Inference for Pairwise Comparisons with Gaussian-Process Dynamics

We present a probabilistic model of pairwise-comparison outcomes that can encode variations over time. To this end, we replace the real-valued parameters of a class of generalized linear comparison models by function-valued stochastic processes. In particular, we use Gaussian processes; their kernel function can express time dynamics in a flexible way. We give an algorithm that performs approximate Bayesian inference in linear time. We test our model on several sports datasets, and we find that our approach performs favorably in terms of predictive performance. Additionally, our method can be used to visualize the data effectively.