Ensembles of machine learning models yield improved system performance as well as robust and interpretable uncertainty estimates; however, their inference costs can be prohibitively high. Ensemble Distribution Distillation (EnD$^2$) is an approach that allows a single model to efficiently capture both the predictive performance and uncertainty estimates of an ensemble. For classification, this is achieved by training a Dirichlet distribution over the ensemble members' output distributions via the maximum likelihood criterion. Although theoretically principled, this work shows that the criterion exhibits poor convergence when applied to large-scale tasks where the number of classes is very high. Specifically, we show that for the Dirichlet log-likelihood criterion classes with low probability induce larger gradients than high-probability classes. Hence during training the model focuses on the distribution of the ensemble tail-class probabilities rather than the probability of the correct and closely related classes. We propose a new training objective which minimizes the reverse KL-divergence to a \emph{Proxy-Dirichlet} target derived from the ensemble. This loss resolves the gradient issues of EnD$^2$, as we demonstrate both theoretically and empirically on the ImageNet, LibriSpeech, and WMT17 En-De datasets containing 1000, 5000, and 40,000 classes, respectively.

Predictive modeling has the potential to enhance human decision-making. However, many predictive models fail in practice due to problematic problem formulation in cases where the prediction target is an abstract concept or construct and practitioners need to define an appropriate target variable as a proxy to operationalize the construct of interest. The choice of an appropriate proxy target variable is rarely self-evident in practice, requiring both domain knowledge and iterative data modeling. This process is inherently collaborative, involving both domain experts and data scientists. In this work, we explore how human-machine teaming can support this process by accelerating iterations while preserving human judgment. We study the impact of two human-machine teaming strategies on proxy construction: 1) relevance-first: humans leading the process by selecting relevant proxies, and 2) performance-first: machines leading the process by recommending proxies based on predictive performance. Based on a controlled user study of a proxy construction task (N = 20), we show that the performance-first strategy facilitated faster iterations and decision-making, but also biased users towards well-performing proxies that are misaligned with the application goal. Our study highlights the opportunities and risks of human-machine teaming in operationalizing machine learning target variables, yielding insights for future research to explore the opportunities and mitigate the risks.

Ensembles of machine learning models yield improved system performance as well as robust and interpretable uncertainty estimates; however, their inference costs can be prohibitively high. Ensemble Distribution Distillation (EnD 2) is an approach that allows a single model to efficiently capture both the predictive performance and uncertainty estimates of an ensemble. For classification, this is achieved by training a Dirichlet distribution over the ensemble members' output distributions via the maximum likelihood criterion. Although theoretically principled, this work shows that the criterion exhibits poor convergence when applied to large-scale tasks where the number of classes is very high. Specifically, we show that for the Dirichlet log-likelihood criterion classes with low probability induce larger gradients than high-probability classes.