# Learning to Defer ### Oracle Collaborative Accuracy If a human oracle can process at most $\alpha \times 100\%$ of total examples, they are said to have $\alpha$ _review capacity_. For a dataset $D=\left\{\left(x_{i}, y_{i}\right)\right\}_{i=1}^{n}$, for a predictive model $f\left(x_{i}\right)$ generating a review score (uncertainity) $u\left(x_{i}\right)$, the Oracle-Model Collaborative Accuracy for example $x_{i}$ is $ \text { OC-Acc }\left(x_{i} \mid \alpha\right)= \begin{cases}1 & \text { if } u\left(x_{i}\right)>q_{1-\alpha} \\ \mathbb{I}\left(f\left(x_{i}\right)=y_{i}\right) & \text { otherwise }\end{cases} $ where $q_{1-\alpha}$ is the $(1-\alpha)^{\text {th }}$ quantile of the model's review scores $\left\{u\left(x_{i}\right)\right\}_{i=1}^{n}$ over the entire dataset. Over the whole dataset, OC-ACC = $\frac{1}{n} \sum_{i=1}^{n} \text { OC-Acc }\left(x_{i} \mid \alpha\right)$. OC-Acc thus describes the performance of a collaborative system which defers to a human oracle when the review score $u(x_i)$ is high, and relies on the model prediction otherwise, capturing the real-world usage and performance of the underlying model in a way that traditional metrics fail to. Issues: - Relies on a set threshold on the prediction score. This limits the metric’s ability in describing model performance when compared to thresholdagnostic metrics like AUC. - can be sensitive to the class imbalance in datasets, appearing overly optimistic for model predictions that are biased toward negative class, similar to traditional accuracy metrics. See: [[Classification Metrics and Evaluation]] --- ## References 1. Measuring and Improving Model-Moderator Collaboration using Uncertainty Estimation, Kivlichan et al, 2022