Smoothing complex-valued signals on Graphs with Monte-Carlo

TL;DR

This paper presents novel Monte-Carlo-based smoothing estimators for complex signals on graphs using Determinantal Point Processes, with implementation and performance analysis on a ranking task.

Contribution

It introduces DPP-based smoothing estimators for complex graph signals, focusing on subsets forming trees and unicycles, with a Julia implementation and empirical evaluation.

Findings

Effective smoothing of complex signals demonstrated

Performance benefits shown on ranking problem

New estimators based on DPPs introduced

Abstract

We introduce new smoothing estimators for complex signals on graphs, based on a recently studied Determinantal Point Process (DPP). These estimators are built from subsets of edges and nodes drawn according to this DPP, making up trees and unicycles, i.e., connected components containing exactly one cycle. We provide a Julia implementation of these estimators and study their performance when applied to a ranking problem.