To this end, we first establish a new class of GNNs that can solve a strictly wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms.
We consider the problem of online forecasting of sequences of lengthn with total-variation at mostCn using observations contaminated by independentσsubgaussian noise. We design anO(nlogn)-time algorithm that achieves a cu-mulativesquare error of O(n1/3C2/3n σ4/3+C2n)with high probability.