The Resistance to Label Noise in K-NN and DNN Depends on its Concentration

TL;DR

This paper explores how label noise affects K-NN and DNN classifiers, revealing that noise concentration significantly impacts their robustness, and provides an analytic approximation for K-NN error under noisy labels.

Contribution

The paper derives an analytic expression approximating K-NN error with label noise and shows its relevance as a first-order approximation for DNN error, explaining DNN robustness.

Findings

DNN predictions depend on local neighborhood labels.

An analytic expression for K-NN error under label noise is proposed.

Higher noise concentration leads to greater performance degradation.

Abstract

We investigate the classification performance of K-nearest neighbors (K-NN) and deep neural networks (DNNs) in the presence of label noise. We first show empirically that a DNN's prediction for a given test example depends on the labels of the training examples in its local neighborhood. This motivates us to derive a realizable analytic expression that approximates the multi-class K-NN classification error in the presence of label noise, which is of independent importance. We then suggest that the expression for K-NN may serve as a first-order approximation for the DNN error. Finally, we demonstrate empirically the proximity of the developed expression to the observed performance of K-NN and DNN classifiers. Our result may explain the already observed surprising resistance of DNN to some types of label noise. It also characterizes an important factor of it showing that the more concentrated the noise the greater is the degradation in performance.