Graph Laplacian Learning with Exponential Family Noise
Changhao Shi Gal Mishne
A common challenge in applying graph machine learning methods is that the
underlying graph of a system is often unknown. Although different graph
inference methods have been proposed for continuous graph signals, inferring
the graph structure underlying other types of data, such as discrete counts, is
under-explored. In this paper, we generalize a graph signal processing (GSP)
framework for learning a graph from smooth graph signals to the exponential
family noise distribution to model various data types. We propose an
alternating algorithm that estimates the graph Laplacian as well as the
unobserved smooth representation from the noisy signals. We demonstrate in
synthetic and real-world data that our new algorithm outperforms competing
Laplacian estimation methods under noise model mismatch.