What is noise-tolerant learning? I was reading this Development and validation of phenotype classifiers across multiple sites in the observational health data sciences and informatics network and came across the below paragraph. Can you please help me understand what does the highlighted term noise-tolerant learning or noisy-labeled training data` mean with a simple example and how is it useful when we don't have labels in our dataset etc? I am learning ML and your inputs would be helpful.

To address the scarcity of labeled training data, Chen et al used
active learning to intelligently select training samples for labeling,
demonstrating that classifier performance could be preserved with
fewer samples.16 Another trend is the use of “silver standard training
sets,” a semisupervised approach where training samples are labeled
using an imperfect heuristic rather than by manual review.17–22 The
intuition is that noise-tolerant classifiers trained on imperfectly
labeled data will abstract higher order properties of the phenotype
beyond the original labeling heuristic (so-called “noise-tolerant
learning”23).

 A: The paper is clear enough, noise-tolerant learning, in this case, is about label noise. In this case the labels are medical diagnosis, in part decided automatically by some algorithm. Such decisions can be noisy so the labels will be noisy.
So this is about learning algorithms which is robust against possible label noise. To give some context, the first part of the abstract of that paper is

Objective
Accurate electronic phenotyping is essential to support collaborative
observational research. Supervised machine learning methods can be
used to train phenotype classifiers in a high-throughput manner using
imperfectly labeled data. We developed 10 phenotype classifiers using
this approach and evaluated performance across multiple sites within
the Observational Health Data Sciences and Informatics (OHDSI)
network.

And the paper 23 from the references is General Bounds on the Number of Examples
Needed for Learning Probabilistic Concepts, which indeed contains theorems about classification noise (the term used in that paper.)
