Towards the Identifiability in Noisy Label Learning: A Multinomial Mixture Modelling Approach

Learning from noisy labels (LNL) is crucial in deep learning, in which one of the approaches is to identify clean-label samples from poorly-annotated datasets. Such an identification is challenging because the conventional LNL problem, which assumes only one noisy label per instance, is non-identifiable, i.e., clean labels cannot be estimated theoretically without additional heuristics. This paper presents a novel data-driven approach that addresses this issue without requiring any heuristics about clean samples. We discover that the LNL problem becomes identifiable if there are at least $2C - 1$ i.i.d. noisy labels per instance, where $C$ is the number of classes. Our finding relies on the assumption of i.i.d. noisy labels and multinomial mixture modelling, making it easier to interpret than previous studies that require full-rank noisy-label transition matrices. To fulfil this condition without additional manual annotations, we propose a method that automatically generates additional i.i.d. noisy labels through nearest neighbours. These noisy labels are then used in the Expectation-Maximisation algorithm to infer clean labels. Our method demonstrably estimates clean labels accurately across various label noise benchmarks, including synthetic, web-controlled, and real-world datasets. Furthermore, the model trained with our method performs competitively with many state-of-the-art methods.