Minimax lower bounds for function estimation on graphs

TL;DR

This paper establishes fundamental lower bounds on the accuracy of estimating functions on large graphs, considering smoothness and shape assumptions, to guide future method development.

Contribution

It derives minimax rates for regression and classification on graphs under smoothness and shape conditions using the graph Laplacian.

Findings

Minimax lower bounds are established for function estimation on graphs.

Results depend on the graph Laplacian and smoothness assumptions.

Provides theoretical benchmarks for future graph-based learning methods.

Abstract

We study minimax lower bounds for function estimation problems on large graph when the target function is smoothly varying over the graph. We derive minimax rates in the context of regression and classification problems on graphs that satisfy an asymptotic shape assumption and with a smoothness condition on the target function, both formulated in terms of the graph Laplacian.