Varyty

Varyty is a hypothetical metric used in data analysis to quantify the variability of a dataset across features and samples. Conceptually, it combines dispersion measures (such as feature-wise variance), distributional diversity (entropy across feature values), and inter-sample dispersion to yield a single score or a vector of scores describing different aspects of variability.

Origin and etymology: The term blends "vary" with the suffix -ty to denote a state or quality. It emerged in informal online discussions and teaching materials in the early 2020s as a compact way to refer to data variability beyond simple variance.

Definition and computation: In simple forms, varyty may be defined globally as the average of normalized variances across features. In richer forms, it is a weighted sum of: (a) mean feature variance, (b) feature-wise entropy, and (c) average pairwise distance between samples in the feature space. Variants include global varyty (across all features) and local varyty (per-feature or per-sample).

Applications: varyty is used for model robustness assessment, data collection planning, feature selection, anomaly detection, and evaluation of synthetic data quality.

Limitations: varyty is sensitive to feature scaling and outliers, depends on chosen normalization, and definitions vary, making cross-study comparisons difficult.

See also: variance, diversity, entropy, data quality metrics, dataset shift.