Identifiability of Label Noise Transition Matrix

The noise transition matrix plays a central role in the problem of learning from noisy labels. Among many other reasons, a significant number of existing solutions rely on access to it. Estimating the transition matrix without using ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recent works proposing solutions for learning from instance-dependent noisy labels, we lack a unified understanding of when such a problem remains identifiable, and therefore learnable. This paper seeks to provide answers to a sequence of related questions: What are the primary factors that contribute to the identifiability of a noise transition matrix? Can we explain the observed empirical successes? When a problem is not identifiable, what can we do to make it so? We will relate our theoretical findings to the literature and hope to provide guidelines for developing effective solutions for battling instance-dependent label noise.