Label Distribution Learning using the Squared Neural Family on the Probability Simplex

Label distribution learning (LDL) provides a framework wherein a distribution over categories rather than a single category is predicted, with the aim of addressing ambiguity in labeled data. Existing research on LDL mainly focuses on the task of point estimation, i.e., pinpointing an optimal distribution in the probability simplex conditioned on the input sample. In this paper, we estimate a probability distribution of all possible label distributions over the simplex, by unleashing the expressive power of the recently introduced Squared Neural Family (SNEFY). With the modeled distribution, label distribution prediction can be achieved by performing the expectation operation to estimate the mean of the distribution of label distributions. Moreover, more information about the label distribution can be inferred, such as the prediction reliability and uncertainties. We conduct extensive experiments on the label distribution prediction task, showing that our distribution modeling based method can achieve very competitive label distribution prediction performance compared with the state-of-the-art baselines. Additional experiments on active learning and ensemble learning demonstrate that our probabilistic approach can effectively boost the performance in these settings, by accurately estimating the prediction reliability and uncertainties.