Lenore Cowen

Christopher Ratigan, Kyle Heuton, Carissa Wang et al.

The ROC curve is widely used to assess binary classification performance. Yet for some applications such as alert systems for hospitalized patient monitoring, conventional ROC analysis cannot capture crucial factors that impact deployment, such as enforcing a minimum precision constraint to avoid false alarm fatigue or imposing an upper bound on the number of predicted positives to represent the capacity of hospital staff. The usual area under the curve metric also does not reflect asymmetric costs for false positives and false negatives. In this paper we address all three of these issues. First, we show how the subset of classifiers that meet given precision and capacity constraints can be represented as a feasible region in ROC space. We establish the geometry of this feasible region. We then define the partial area of lesser classifiers, a performance metric that is monotonic with cost and only accounts for the feasible portion of ROC space. Averaging this area over a desired range of cost parameters results in the partial volume over the ROC surface, or partial VOROS. In experiments predicting mortality risk using vital sign history on the MIMIC-IV dataset, we show this cost-aware metric is better than alternatives for ranking classifiers in hospital alert applications.

Christopher Ratigan, Lenore Cowen

While the area under the ROC curve is perhaps the most common measure that is used to rank the relative performance of different binary classifiers, longstanding field folklore has noted that it can be a measure that ill-captures the benefits of different classifiers when either the actual class values or misclassification costs are highly unbalanced between the two classes. We introduce a new ROC surface, and the VOROS, a volume over this ROC surface, as a natural way to capture these costs, by lifting the ROC curve to 3D. Compared to previous attempts to generalize the ROC curve, our formulation also provides a simple and intuitive way to model the scenario when only ranges, rather than exact values, are known for possible class imbalance and misclassification costs.

Lenore Cowen, Kapil Devkota, Xiaozhe Hu et al.

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a data-driven diffusion process. Unlike related diffusion methods, DSDs incorporate information across time scales, which allows for the intrinsic data structure to be inferred in a parameter-free manner. This article develops a theory for DSD based on the multitemporal emergence of mesoscopic equilibria in the underlying diffusion process. New algorithms for denoising and dimension reduction with DSD are also proposed and analyzed. These approaches are based on a weighted spectral decomposition of the underlying diffusion process, and experiments on synthetic datasets and real biological networks illustrate the efficacy of the proposed algorithms in terms of both speed and accuracy. Throughout, comparisons with related methods are made, in order to illustrate the distinct advantages of DSD for datasets exhibiting multiscale structure.