Classification with Trust: A Supervised Approach based on Sequential Ellipsoidal Partitioning

TL;DR

This paper introduces SEP-C, a convex optimization-based classifier that partitions data into ellipsoids to assess trust in predictions, exposing dataset irregularities without hyperparameters or kernels.

Contribution

The paper proposes a novel supervised classifier that uses sequential ellipsoidal partitioning and Bayes' formula to compute trust scores, independent of data distribution or class imbalance.

Findings

Effective on XOR and circle datasets

Exposes dataset irregularities such as overlap

Does not require hyperparameters or kernels

Abstract

Standard metrics of performance of classifiers, such as accuracy and sensitivity, do not reveal the trust or confidence in the predicted labels of data. While other metrics such as the computed probability of a label or the signed distance from a hyperplane can act as a trust measure, these are subjected to heuristic thresholds. This paper presents a convex optimization-based supervised classifier that sequentially partitions a dataset into several ellipsoids, where each ellipsoid contains nearly all points of the same label. By stating classification rules based on this partitioning, Bayes' formula is then applied to calculate a trust score to a label assigned to a test datapoint determined from these rules. The proposed Sequential Ellipsoidal Partitioning Classifier (SEP-C) exposes dataset irregularities, such as degree of overlap, without requiring a separate exploratory data analysis. The rules of classification, which are free of hyperparameters, are also not affected by class-imbalance, the underlying data distribution, or number of features. SEP-C does not require the use of non-linear kernels when the dataset is not linearly separable. The performance, and comparison with other methods, of SEP-C is demonstrated on the XOR-problem, circle dataset, and other open-source datasets.