Binary classification is one of the oldest, most prevalent, and studied problems in machine learning. However, the metrics used to evaluate model performance have received comparatively little attention. The area under the receiver operating characteristic curve (AUROC) has long been a standard choice for model comparison. Despite its advantages, AUROC is not always ideal, particularly for problems that are invariant to local exchange of classes (LxC), a new form of metric invariance introduced in this work. To address this limitation, we propose LxCIM (LxC-invariant metric), which is not only rank-based and invariant under local exchange of classes, but also intuitive, logically consistent, and always computable, while enabling more detailed analysis through the cumulative accuracy-decision rate curve. Moreover, LxCIM exhibits clear theoretical connections to AUROC, accuracy, and the area under the accuracy-decision rate curve (AUDRC). These relationships allow for multiple complementary interpretations: as a symmetric form of AUROC, a rank-based analogue of accuracy, or a more representative and more interpretable variant of AUDRC. Finally, we demonstrate the direct applicability of LxCIM to the bivariate causal discovery problem (which exhibits invariance to local exchange of classes) and show how it addresses the acknowledged limitations of existing metrics used in this field. All code and implementation details are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.

In recent years fairness in machine learning (ML) has emerged as a highly active area of research and development. Most define fairness in simple terms, where fairness means reducing gaps in performance or outcomes between demographic groups while preserving as much of the accuracy of the original system as possible. This oversimplification of equality through fairness measures is troubling. Many current fairness measures suffer from both fairness and performance degradation, or "levelling down," where fairness is achieved by making every group worse off, or by bringing better performing groups down to the level of the worst off. When fairness can only be achieved by making everyone worse off in material or relational terms through injuries of stigma, loss of solidarity, unequal concern, and missed opportunities for substantive equality, something would appear to have gone wrong in translating the vague concept of 'fairness' into practice. This paper examines the causes and prevalence of levelling down across fairML, and explore possible justifications and criticisms based on philosophical and legal theories of equality and distributive justice, as well as equality law jurisprudence. We find that fairML does not currently engage in the type of measurement, reporting, or analysis necessary to justify levelling down in practice. We propose a first step towards substantive equality in fairML: "levelling up" systems by design through enforcement of minimum acceptable harm thresholds, or "minimum rate constraints," as fairness constraints. We likewise propose an alternative harms-based framework to counter the oversimplified egalitarian framing currently dominant in the field and push future discussion more towards substantive equality opportunities and away from strict egalitarianism by default. N.B. Shortened abstract, see paper for full abstract.

We address the problem of inferring the causal direction between two variables by comparing the least-squares errors of the predictions in both possible directions. Under the assumption of an independence between the function relating cause and effect, the conditional noise distribution, and the distribution of the cause, we show that the errors are smaller in causal direction if both variables are equally scaled and the causal relation is close to deterministic. Based on this, we provide an easily applicable algorithm that only requires a regression in both possible causal directions and a comparison of the errors. The performance of the algorithm is compared with various related causal inference methods in different artificial and real-world data sets.