Matthias Templ

Matthias Templ

Compositional data must be analysed through log-ratios: scale invariance, the defining axiom of the field, leaves no alternative. The centred log-ratio divides by the geometric mean of every part, so a single contaminated component shifts every centred-log-ratio coordinate at once, displacing the log-ratio vector by a fixed amount that no choice of coordinates can reduce. We develop a theory of cellwise contamination on the simplex around this observation. A scale-invariant contamination model built from multiplicative perturbation combines with a propagation theorem showing that corruption of a single raw part induces a rank-one shift of the log-ratio vector, with direction determined by the contrast matrix. The resulting perturbation pattern is not equivalent to any independent cellwise contamination model in log-ratio coordinates -- so standard Euclidean cellwise methods applied to log-ratios are ill-posed under the simplex contamination mechanism. For estimators whose Euclidean cellwise breakdown is witnessed by a column-concentrated configuration -- a class including MCD, $S$-, $τ$-, and coordinate-wise $M$-estimators of location and scatter -- the cellwise breakdown value on the simplex is reduced by the factor $(D-1)/D$ relative to its Euclidean counterpart, a reduction that is tight and arises purely from the normalisation mismatch between $nD$ raw cells and $n(D-1)$ ilr cells. The cellwise influence function for the variation matrix carries a diagnostic fingerprint: contamination of a single part inflates exactly one row and column, identifying the responsible component. These results form the theoretical foundation for cellwise-robust methods on the simplex; a companion paper develops a cellwise-robust PCA estimator that exploits the propagation geometry and demonstrates it on simulated and geochemical data.

Matthias Templ, Oscar Thees, Roman Müller

Statistical data anonymization increasingly relies on fully synthetic microdata, for which classical identity disclosure measures are less informative than an adversary's ability to infer sensitive attributes from released data. We introduce RAPID (Risk of Attribute Prediction--Induced Disclosure), a disclosure risk measure that directly quantifies inferential vulnerability under a realistic attack model. An adversary trains a predictive model solely on the released synthetic data and applies it to real individuals' quasi-identifiers. For continuous sensitive attributes, RAPID reports the proportion of records whose predicted values fall within a specified relative error tolerance. For categorical attributes, we propose a baseline-normalized confidence score that measures how much more confident the attacker is about the true class than would be expected from class prevalence alone, and we summarize risk as the fraction of records exceeding a policy-defined threshold. This construction yields an interpretable, bounded risk metric that is robust to class imbalance, independent of any specific synthesizer, and applicable with arbitrary learning algorithms. We illustrate threshold calibration, uncertainty quantification, and comparative evaluation of synthetic data generators using simulations and real data. Our results show that RAPID provides a practical, attacker-realistic upper bound on attribute-inference disclosure risk that complements existing utility diagnostics and disclosure control frameworks.

Matthias Templ

Methods of deep learning have become increasingly popular in recent years, but they have not arrived in compositional data analysis. Imputation methods for compositional data are typically applied on additive, centered or isometric log-ratio representations of the data. Generally, methods for compositional data analysis can only be applied to observed positive entries in a data matrix. Therefore one tries to impute missing values or measurements that were below a detection limit. In this paper, a new method for imputing rounded zeros based on artificial neural networks is shown and compared with conventional methods. We are also interested in the question whether for ANNs, a representation of the data in log-ratios for imputation purposes, is relevant. It can be shown, that ANNs are competitive or even performing better when imputing rounded zeros of data sets with moderate size. They deliver better results when data sets are big. Also, we can see that log-ratio transformations within the artificial neural network imputation procedure nevertheless help to improve the results. This proves that the theory of compositional data analysis and the fulfillment of all properties of compositional data analysis is still very important in the age of deep learning.