aggmetrics: Aggregating Classification Performance Measures for Machine Learning

We propose a unified algebraic framework for classification performance evaluation that encompasses binary, multiclass, multilabel, ordinal, hierarchical, cost-sensitive, and soft-label settings within a single formalism. The foundation is a representation of actual and predicted labels as binary indicator matrices, combined with three aggregation operators -- global, column-wise, and row-wise -- that correspond exactly to micro, macro/weighted, and exemplar averaging. Any binary performance measure expressed in terms of true/positive/negative counts extends automatically to all settings by substituting these operators, generating multiclass and multilabel versions without measure-specific derivations. The framework further accommodates soft classifier outputs via argmax or thresholding, soft ground truth via triangular norms, ordinal classification via membership functions or cumulative encodings, and cost-sensitive evaluation via a cost matrix that subsumes MAE and MSE as special cases. We establish several theoretical results: micro-averaging equals denominator-weighted macro-averaging; the product $t$-norm is the unique one preserving the confusion-matrix partition; skew-invariant measures are characterised as functions of recall and specificity; and micro-precision, micro-recall, and micro-$F_1$ are all equal to accuracy in multiclass settings. Empirical illustrations on synthetic and real data confirm the theoretical findings.

Reliable evaluation of inter-annotator agreement (IAA) is important for assessing the consistency of annotation processes. While established IAA metrics such as Cohen's kappa, Fleiss' kappa, and Krippendorff's alpha are commonly applied in single-label settings, multi-label tasks require additional decisions about how full label sets, joint selections, and joint omissions should be compared. In this work, we present Multi-Label Agreement (MLA), a flexible framework for evaluating agreement in multi-label annotation tasks. MLA preserves the full binary label vectors assigned to each item and uses average pairwise Hamming agreement, thereby accounting for both joint selections and joint omissions. Its pooled-marginal form is not a mathematically independent coefficient: it is a chance-disagreement-weighted average of label-wise Fleiss/Scott-type coefficients and is closely related to Krippendorff's alpha with normalized Hamming distance. The framework supports pooled-marginal, Gwet AC1, and fixed-baseline normalizations, yields item-level, label-level, and corpus-level results, and includes a conditional minimum-agreement diagnostic. Through a worked example and Monte Carlo simulations, we show how the resulting values depend on label prevalence, the declared label inventory, and the selected model of expected agreement. We also provide a Python implementation. MLA thus offers a transparent and interpretable framework for multi-label agreement analysis without claiming that one normalization is universally preferable.

Validating an LLM judge against human annotations usually means reporting several agreement statistics: accuracy, precision, recall, $F_1$, Cohen's $κ$, and one or more rank correlations. A survey of 24 recent LLM-as-judge papers finds metric choice entangled with the judgment scale, tie handling, invalid outputs, and abstention handling, and those choices rarely stated. For binary criteria -- the common case in rubric-based evaluation, where each criterion is graded MET or UNMET -- most of the reported numbers are redundant: Pearson's $r$, Spearman's $ρ$, Kendall's $τ_b$, the phi coefficient $φ$, and the Matthews Correlation Coefficient all reduce to a single number on non-degenerate binary data, so reporting several of them only creates an illusion of corroborating evidence. Cohen's $κ$ is the one agreement coefficient that adds information: it shares $φ$'s numerator but normalizes differently, and the gap between them measures how far the judge's positive-label rate has drifted from the human's. We then trace what changes when a judge may abstain with a CANNOT_ASSESS verdict: the three common ways of handling abstentions are not interchangeable preprocessing choices but answer different questions, and they break the binary equivalences. The same equivalences reappear, up to a negligible finite-sample correction, for multi-judge ensembles scored with Fleiss' $κ$ or Krippendorff's $α$. We close with a reporting checklist that names the judgment scale, the abstention and tie handling mode, coverage, the confusion matrix, and the aggregation level alongside any scalar agreement coefficient.