Gaussian Processes for Edge Flow Prediction with Active Learning
Sravanthi Gurugubelli, Sundeep Prabhakar Chepuri · 2023
We focus on modeling distributions of functions over simplicial complexes using Gaussian processes, specifically targeting edge flow prediction. Edge flow prediction refers to predicting the flows on a subset of unobserved edges given the edge flows on the other edges. We model edge flows in simplicial complexes as a function whose prior distribution is modeled by a Gaussian process. We then design the kernel covariance function of the Gaussian process such that it is aware of the higher-order structure present in the simplicial complexes. Since the proposed model is based on Gaussian processes, it intrinsically models the uncertainty in predictions. The uncertainty scores output by the model for every point (i.e., edge feature) in the input space allow us to perform active learning, where we iteratively select edges on which to measure flow for improved model performance with limited training samples. The efficiency of the proposed model is validated by performing edge flow prediction experiments on real-world networks. The proposed model is observed to outperform the state-of-the-art edge flow prediction algorithm. The performance of the proposed model is observed to improve further with active learning.