Human-in-the-loop: Towards Label Embeddings for Measuring Classification Difficulty

Uncertainty in machine learning models is a timely and vast field of research. In supervised learning, uncertainty can already occur in the first stage of the training process, the annotation phase. This scenario is particularly evident when some instances cannot be definitively classified. In other words, there is inevitable ambiguity in the annotation step and hence, not necessarily a "ground truth" associated with each instance. The main idea of this work is to drop the assumption of a ground truth label and instead embed the annotations into a multidimensional space. This embedding is derived from the empirical distribution of annotations in a Bayesian setup, modeled via a Dirichlet-Multinomial framework. We estimate the model parameters and posteriors using a stochastic Expectation Maximization algorithm with Markov Chain Monte Carlo steps. The methods developed in this paper readily extend to various situations where multiple annotators independently label instances. To showcase the generality of the proposed approach, we apply our approach to three benchmark datasets for image classification and Natural Language Inference. Besides the embeddings, we can investigate the resulting correlation matrices, which reflect the semantic similarities of the original classes very well for all three exemplary datasets.